Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 73.8% → 81.9%

Time: 26.5s

Alternatives: 24

Speedup: 0.5×

• 57.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
  (* j (- (* c a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
  (* j (- (* c a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
          (* j (- (* a c) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (* z (- (* x y) (* b c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 92.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 0.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 0.0%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 14.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 14.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 14.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 18.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 18.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 18.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in z around inf 63.7%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 2: 57.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(t \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.9 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-304}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-119}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (- (* i (* t b)) (* y (- (* i j) (* x z)))))
        (t_3 (* c (- (* a j) (* z b)))))
   (if (<= c -1.9e+49)
     t_3
     (if (<= c -1.9e-94)
       t_2
       (if (<= c -1.2e-218)
         t_1
         (if (<= c -9e-304)
           t_2
           (if (<= c 7e-119)
             (- (* a (- (* c j) (* x t))) (* y (* i j)))
             (if (<= c 9e+33)
               t_2
               (if (<= c 1.4e+94) t_1 (if (<= c 1.1e+105) t_2 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.9e+49) {
		tmp = t_3;
	} else if (c <= -1.9e-94) {
		tmp = t_2;
	} else if (c <= -1.2e-218) {
		tmp = t_1;
	} else if (c <= -9e-304) {
		tmp = t_2;
	} else if (c <= 7e-119) {
		tmp = (a * ((c * j) - (x * t))) - (y * (i * j));
	} else if (c <= 9e+33) {
		tmp = t_2;
	} else if (c <= 1.4e+94) {
		tmp = t_1;
	} else if (c <= 1.1e+105) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)))
    t_3 = c * ((a * j) - (z * b))
    if (c <= (-1.9d+49)) then
        tmp = t_3
    else if (c <= (-1.9d-94)) then
        tmp = t_2
    else if (c <= (-1.2d-218)) then
        tmp = t_1
    else if (c <= (-9d-304)) then
        tmp = t_2
    else if (c <= 7d-119) then
        tmp = (a * ((c * j) - (x * t))) - (y * (i * j))
    else if (c <= 9d+33) then
        tmp = t_2
    else if (c <= 1.4d+94) then
        tmp = t_1
    else if (c <= 1.1d+105) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.9e+49) {
		tmp = t_3;
	} else if (c <= -1.9e-94) {
		tmp = t_2;
	} else if (c <= -1.2e-218) {
		tmp = t_1;
	} else if (c <= -9e-304) {
		tmp = t_2;
	} else if (c <= 7e-119) {
		tmp = (a * ((c * j) - (x * t))) - (y * (i * j));
	} else if (c <= 9e+33) {
		tmp = t_2;
	} else if (c <= 1.4e+94) {
		tmp = t_1;
	} else if (c <= 1.1e+105) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)))
	t_3 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -1.9e+49:
		tmp = t_3
	elif c <= -1.9e-94:
		tmp = t_2
	elif c <= -1.2e-218:
		tmp = t_1
	elif c <= -9e-304:
		tmp = t_2
	elif c <= 7e-119:
		tmp = (a * ((c * j) - (x * t))) - (y * (i * j))
	elif c <= 9e+33:
		tmp = t_2
	elif c <= 1.4e+94:
		tmp = t_1
	elif c <= 1.1e+105:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(i * Float64(t * b)) - Float64(y * Float64(Float64(i * j) - Float64(x * z))))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.9e+49)
		tmp = t_3;
	elseif (c <= -1.9e-94)
		tmp = t_2;
	elseif (c <= -1.2e-218)
		tmp = t_1;
	elseif (c <= -9e-304)
		tmp = t_2;
	elseif (c <= 7e-119)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) - Float64(y * Float64(i * j)));
	elseif (c <= 9e+33)
		tmp = t_2;
	elseif (c <= 1.4e+94)
		tmp = t_1;
	elseif (c <= 1.1e+105)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)));
	t_3 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.9e+49)
		tmp = t_3;
	elseif (c <= -1.9e-94)
		tmp = t_2;
	elseif (c <= -1.2e-218)
		tmp = t_1;
	elseif (c <= -9e-304)
		tmp = t_2;
	elseif (c <= 7e-119)
		tmp = (a * ((c * j) - (x * t))) - (y * (i * j));
	elseif (c <= 9e+33)
		tmp = t_2;
	elseif (c <= 1.4e+94)
		tmp = t_1;
	elseif (c <= 1.1e+105)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.9e+49], t$95$3, If[LessEqual[c, -1.9e-94], t$95$2, If[LessEqual[c, -1.2e-218], t$95$1, If[LessEqual[c, -9e-304], t$95$2, If[LessEqual[c, 7e-119], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9e+33], t$95$2, If[LessEqual[c, 1.4e+94], t$95$1, If[LessEqual[c, 1.1e+105], t$95$2, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.8999999999999999e49 or 1.10000000000000003e105 < c

   1. Initial program 68.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 68.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 68.4%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 70.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 70.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 70.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 72.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 72.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 72.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 78.3%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -1.8999999999999999e49 < c < -1.9e-94 or -1.2e-218 < c < -8.9999999999999995e-304 or 7e-119 < c < 9.0000000000000001e33 or 1.39999999999999999e94 < c < 1.10000000000000003e105

   1. Initial program 88.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 88.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 88.0%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 91.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 91.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 91.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 91.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 91.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around 0 77.2%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - b \cdot \left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 77.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right) \cdot b} \]

      2. *-commutative 77.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(\color{blue}{z \cdot c} + -1 \cdot \left(i \cdot t\right)\right) \cdot b \]

      3. associate-*r* 77.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-1 \cdot i\right) \cdot t}\right) \cdot b \]

      4. neg-mul-1 77.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-i\right)} \cdot t\right) \cdot b \]

      5. *-commutative 77.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{t \cdot \left(-i\right)}\right) \cdot b \]

      6. fma-udef 77.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \cdot b \]

      7. *-commutative 77.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

      8. *-rgt-identity 77.2%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

      9. cancel-sign-sub-inv 77.2%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(-b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

   6. Simplified 80.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in i around inf 74.3%

      \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if -1.9e-94 < c < -1.2e-218 or 9.0000000000000001e33 < c < 1.39999999999999999e94

   1. Initial program 64.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 64.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 64.2%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 67.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 67.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 67.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 67.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 67.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in x around inf 73.2%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 73.2%

         \[\leadsto \left(y \cdot z - \color{blue}{t \cdot a}\right) \cdot x \]

      2. *-commutative 73.2%

         \[\leadsto \left(\color{blue}{z \cdot y} - t \cdot a\right) \cdot x \]

   6. Simplified 73.2%

      \[\leadsto \color{blue}{\left(z \cdot y - t \cdot a\right) \cdot x} \]

   if -8.9999999999999995e-304 < c < 7e-119

   1. Initial program 84.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 84.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 84.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 84.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 84.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 84.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in b around 0 75.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right)} \]

   5. Taylor expanded in z around 0 69.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot a - i \cdot y\right) \cdot j} \]
   6. Step-by-step derivation

      1. *-commutative 69.3%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right)} \]

      2. *-commutative 69.3%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot a - \color{blue}{y \cdot i}\right) \]

      3. sub-neg 69.3%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)} \]

      4. distribute-rgt-in 69.3%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{\left(\left(c \cdot a\right) \cdot j + \left(-y \cdot i\right) \cdot j\right)} \]

      5. associate-*r* 63.5%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\color{blue}{c \cdot \left(a \cdot j\right)} + \left(-y \cdot i\right) \cdot j\right) \]

      6. distribute-lft-neg-in 63.5%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) + \color{blue}{\left(-\left(y \cdot i\right) \cdot j\right)}\right) \]

      7. *-commutative 63.5%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) + \left(-\color{blue}{\left(i \cdot y\right)} \cdot j\right)\right) \]

      8. associate-*r* 51.7%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) + \left(-\color{blue}{i \cdot \left(y \cdot j\right)}\right)\right) \]

      9. mul-1-neg 51.7%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) + \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)}\right) \]

      10. *-commutative 51.7%

          \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \color{blue}{\left(j \cdot a\right)} + -1 \cdot \left(i \cdot \left(y \cdot j\right)\right)\right) \]

      11. associate-*r* 57.4%

          \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\color{blue}{\left(c \cdot j\right) \cdot a} + -1 \cdot \left(i \cdot \left(y \cdot j\right)\right)\right) \]

      12. associate-*r* 69.3%

          \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\left(c \cdot j\right) \cdot a + -1 \cdot \color{blue}{\left(\left(i \cdot y\right) \cdot j\right)}\right) \]

      13. *-commutative 69.3%

          \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\left(c \cdot j\right) \cdot a + -1 \cdot \left(\color{blue}{\left(y \cdot i\right)} \cdot j\right)\right) \]

      14. associate-*r* 66.4%

          \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\left(c \cdot j\right) \cdot a + -1 \cdot \color{blue}{\left(y \cdot \left(i \cdot j\right)\right)}\right) \]

      15. associate-+l+ 66.4%

          \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot j\right) \cdot a\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]

   7. Simplified 66.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right) - y \cdot \left(i \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+49}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-304}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-119}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+33}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+105}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 3: 58.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(t \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.2 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (- (* i (* t b)) (* y (- (* i j) (* x z)))))
        (t_3 (* c (- (* a j) (* z b)))))
   (if (<= c -1.2e+49)
     t_3
     (if (<= c -1.45e-94)
       t_2
       (if (<= c -2e-218)
         t_1
         (if (<= c 8e+39)
           t_2
           (if (<= c 2.7e+93) t_1 (if (<= c 1.6e+105) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.2e+49) {
		tmp = t_3;
	} else if (c <= -1.45e-94) {
		tmp = t_2;
	} else if (c <= -2e-218) {
		tmp = t_1;
	} else if (c <= 8e+39) {
		tmp = t_2;
	} else if (c <= 2.7e+93) {
		tmp = t_1;
	} else if (c <= 1.6e+105) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)))
    t_3 = c * ((a * j) - (z * b))
    if (c <= (-1.2d+49)) then
        tmp = t_3
    else if (c <= (-1.45d-94)) then
        tmp = t_2
    else if (c <= (-2d-218)) then
        tmp = t_1
    else if (c <= 8d+39) then
        tmp = t_2
    else if (c <= 2.7d+93) then
        tmp = t_1
    else if (c <= 1.6d+105) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.2e+49) {
		tmp = t_3;
	} else if (c <= -1.45e-94) {
		tmp = t_2;
	} else if (c <= -2e-218) {
		tmp = t_1;
	} else if (c <= 8e+39) {
		tmp = t_2;
	} else if (c <= 2.7e+93) {
		tmp = t_1;
	} else if (c <= 1.6e+105) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)))
	t_3 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -1.2e+49:
		tmp = t_3
	elif c <= -1.45e-94:
		tmp = t_2
	elif c <= -2e-218:
		tmp = t_1
	elif c <= 8e+39:
		tmp = t_2
	elif c <= 2.7e+93:
		tmp = t_1
	elif c <= 1.6e+105:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(i * Float64(t * b)) - Float64(y * Float64(Float64(i * j) - Float64(x * z))))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.2e+49)
		tmp = t_3;
	elseif (c <= -1.45e-94)
		tmp = t_2;
	elseif (c <= -2e-218)
		tmp = t_1;
	elseif (c <= 8e+39)
		tmp = t_2;
	elseif (c <= 2.7e+93)
		tmp = t_1;
	elseif (c <= 1.6e+105)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)));
	t_3 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.2e+49)
		tmp = t_3;
	elseif (c <= -1.45e-94)
		tmp = t_2;
	elseif (c <= -2e-218)
		tmp = t_1;
	elseif (c <= 8e+39)
		tmp = t_2;
	elseif (c <= 2.7e+93)
		tmp = t_1;
	elseif (c <= 1.6e+105)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.2e+49], t$95$3, If[LessEqual[c, -1.45e-94], t$95$2, If[LessEqual[c, -2e-218], t$95$1, If[LessEqual[c, 8e+39], t$95$2, If[LessEqual[c, 2.7e+93], t$95$1, If[LessEqual[c, 1.6e+105], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.2e49 or 1.6e105 < c

   1. Initial program 68.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 68.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 68.4%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 70.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 70.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 70.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 72.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 72.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 72.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 78.3%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -1.2e49 < c < -1.44999999999999998e-94 or -2.0000000000000001e-218 < c < 7.99999999999999952e39 or 2.6999999999999999e93 < c < 1.6e105

   1. Initial program 87.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 87.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 87.0%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 89.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 89.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 89.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 89.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 89.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 89.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around 0 71.9%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - b \cdot \left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 71.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right) \cdot b} \]

      2. *-commutative 71.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(\color{blue}{z \cdot c} + -1 \cdot \left(i \cdot t\right)\right) \cdot b \]

      3. associate-*r* 71.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-1 \cdot i\right) \cdot t}\right) \cdot b \]

      4. neg-mul-1 71.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-i\right)} \cdot t\right) \cdot b \]

      5. *-commutative 71.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{t \cdot \left(-i\right)}\right) \cdot b \]

      6. fma-udef 71.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \cdot b \]

      7. *-commutative 71.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

      8. *-rgt-identity 71.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

      9. cancel-sign-sub-inv 71.9%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(-b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

   6. Simplified 74.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in i around inf 68.2%

      \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if -1.44999999999999998e-94 < c < -2.0000000000000001e-218 or 7.99999999999999952e39 < c < 2.6999999999999999e93

   1. Initial program 64.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 64.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 64.2%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 67.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 67.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 67.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 67.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 67.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 67.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in x around inf 73.2%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 73.2%

         \[\leadsto \left(y \cdot z - \color{blue}{t \cdot a}\right) \cdot x \]

      2. *-commutative 73.2%

         \[\leadsto \left(\color{blue}{z \cdot y} - t \cdot a\right) \cdot x \]

   6. Simplified 73.2%

      \[\leadsto \color{blue}{\left(z \cdot y - t \cdot a\right) \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{+49}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+39}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+105}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 4: 58.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(t \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{if}\;c \leq -6.4 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-218}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b))))
        (t_2 (- (* i (* t b)) (* y (- (* i j) (* x z))))))
   (if (<= c -6.4e+47)
     t_1
     (if (<= c -3.4e+28)
       (* t (- (* b i) (* x a)))
       (if (<= c -3.4e-218)
         (- (* y (- (* x z) (* i j))) (* z (* b c)))
         (if (<= c 1.4e+39)
           t_2
           (if (<= c 1.75e+94)
             (* x (- (* y z) (* t a)))
             (if (<= c 1.1e+105) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)));
	double tmp;
	if (c <= -6.4e+47) {
		tmp = t_1;
	} else if (c <= -3.4e+28) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= -3.4e-218) {
		tmp = (y * ((x * z) - (i * j))) - (z * (b * c));
	} else if (c <= 1.4e+39) {
		tmp = t_2;
	} else if (c <= 1.75e+94) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 1.1e+105) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)))
    if (c <= (-6.4d+47)) then
        tmp = t_1
    else if (c <= (-3.4d+28)) then
        tmp = t * ((b * i) - (x * a))
    else if (c <= (-3.4d-218)) then
        tmp = (y * ((x * z) - (i * j))) - (z * (b * c))
    else if (c <= 1.4d+39) then
        tmp = t_2
    else if (c <= 1.75d+94) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 1.1d+105) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)));
	double tmp;
	if (c <= -6.4e+47) {
		tmp = t_1;
	} else if (c <= -3.4e+28) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= -3.4e-218) {
		tmp = (y * ((x * z) - (i * j))) - (z * (b * c));
	} else if (c <= 1.4e+39) {
		tmp = t_2;
	} else if (c <= 1.75e+94) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 1.1e+105) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)))
	tmp = 0
	if c <= -6.4e+47:
		tmp = t_1
	elif c <= -3.4e+28:
		tmp = t * ((b * i) - (x * a))
	elif c <= -3.4e-218:
		tmp = (y * ((x * z) - (i * j))) - (z * (b * c))
	elif c <= 1.4e+39:
		tmp = t_2
	elif c <= 1.75e+94:
		tmp = x * ((y * z) - (t * a))
	elif c <= 1.1e+105:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(Float64(i * Float64(t * b)) - Float64(y * Float64(Float64(i * j) - Float64(x * z))))
	tmp = 0.0
	if (c <= -6.4e+47)
		tmp = t_1;
	elseif (c <= -3.4e+28)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (c <= -3.4e-218)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(z * Float64(b * c)));
	elseif (c <= 1.4e+39)
		tmp = t_2;
	elseif (c <= 1.75e+94)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 1.1e+105)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)));
	tmp = 0.0;
	if (c <= -6.4e+47)
		tmp = t_1;
	elseif (c <= -3.4e+28)
		tmp = t * ((b * i) - (x * a));
	elseif (c <= -3.4e-218)
		tmp = (y * ((x * z) - (i * j))) - (z * (b * c));
	elseif (c <= 1.4e+39)
		tmp = t_2;
	elseif (c <= 1.75e+94)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 1.1e+105)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.4e+47], t$95$1, If[LessEqual[c, -3.4e+28], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.4e-218], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.4e+39], t$95$2, If[LessEqual[c, 1.75e+94], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.1e+105], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -6.4e47 or 1.10000000000000003e105 < c

   1. Initial program 68.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 68.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 68.4%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 70.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 70.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 70.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 72.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 72.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 72.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 78.3%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -6.4e47 < c < -3.4e28

   1. Initial program 85.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 85.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 85.2%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 85.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 85.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 85.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 85.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 85.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 85.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in t around inf 98.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 98.8%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \cdot t \]

      2. associate-*r* 98.8%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x - i \cdot b\right) \cdot t\right)} \]

      3. mul-1-neg 98.8%

         \[\leadsto \color{blue}{-\left(a \cdot x - i \cdot b\right) \cdot t} \]

      4. *-commutative 98.8%

         \[\leadsto -\color{blue}{t \cdot \left(a \cdot x - i \cdot b\right)} \]

      5. *-commutative 98.8%

         \[\leadsto -t \cdot \left(a \cdot x - \color{blue}{b \cdot i}\right) \]

   6. Simplified 98.8%

      \[\leadsto \color{blue}{-t \cdot \left(a \cdot x - b \cdot i\right)} \]

   if -3.4e28 < c < -3.39999999999999986e-218

   1. Initial program 81.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 81.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 81.3%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 83.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 83.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 83.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 83.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 83.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 83.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around 0 64.1%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - b \cdot \left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 64.1%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right) \cdot b} \]

      2. *-commutative 64.1%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(\color{blue}{z \cdot c} + -1 \cdot \left(i \cdot t\right)\right) \cdot b \]

      3. associate-*r* 64.1%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-1 \cdot i\right) \cdot t}\right) \cdot b \]

      4. neg-mul-1 64.1%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-i\right)} \cdot t\right) \cdot b \]

      5. *-commutative 64.1%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{t \cdot \left(-i\right)}\right) \cdot b \]

      6. fma-udef 64.1%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \cdot b \]

      7. *-commutative 64.1%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

      8. *-rgt-identity 64.1%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

      9. cancel-sign-sub-inv 64.1%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(-b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

   6. Simplified 64.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in t around 0 59.6%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right) + y \cdot \left(z \cdot x - i \cdot j\right)} \]
   8. Step-by-step derivation

      1. +-commutative 59.6%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + -1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} \]

      2. mul-1-neg 59.6%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} \]

      3. unsub-neg 59.6%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - c \cdot \left(b \cdot z\right)} \]

      4. *-commutative 59.6%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{\left(b \cdot z\right) \cdot c} \]

      5. *-commutative 59.6%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{\left(z \cdot b\right)} \cdot c \]

      6. associate-*l* 64.1%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{z \cdot \left(b \cdot c\right)} \]

      7. *-commutative 64.1%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - z \cdot \color{blue}{\left(c \cdot b\right)} \]

   9. Simplified 64.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - z \cdot \left(c \cdot b\right)} \]

   if -3.39999999999999986e-218 < c < 1.40000000000000001e39 or 1.7499999999999999e94 < c < 1.10000000000000003e105

   1. Initial program 86.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 86.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 86.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 90.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 90.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 90.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 90.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 90.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 90.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around 0 69.8%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - b \cdot \left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 69.8%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right) \cdot b} \]

      2. *-commutative 69.8%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(\color{blue}{z \cdot c} + -1 \cdot \left(i \cdot t\right)\right) \cdot b \]

      3. associate-*r* 69.8%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-1 \cdot i\right) \cdot t}\right) \cdot b \]

      4. neg-mul-1 69.8%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-i\right)} \cdot t\right) \cdot b \]

      5. *-commutative 69.8%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{t \cdot \left(-i\right)}\right) \cdot b \]

      6. fma-udef 69.8%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \cdot b \]

      7. *-commutative 69.8%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

      8. *-rgt-identity 69.8%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

      9. cancel-sign-sub-inv 69.8%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(-b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

   6. Simplified 73.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in i around inf 71.0%

      \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if 1.40000000000000001e39 < c < 1.7499999999999999e94

   1. Initial program 49.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 49.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 49.8%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 49.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 49.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 49.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 49.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 49.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 49.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in x around inf 74.1%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 74.1%

         \[\leadsto \left(y \cdot z - \color{blue}{t \cdot a}\right) \cdot x \]

      2. *-commutative 74.1%

         \[\leadsto \left(\color{blue}{z \cdot y} - t \cdot a\right) \cdot x \]

   6. Simplified 74.1%

      \[\leadsto \color{blue}{\left(z \cdot y - t \cdot a\right) \cdot x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.4 \cdot 10^{+47}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-218}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+39}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+105}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 5: 59.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ t_2 := i \cdot \left(t \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.5 \cdot 10^{+50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.06 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* x (- (* y z) (* t a))) (* c (* z b))))
        (t_2 (- (* i (* t b)) (* y (- (* i j) (* x z)))))
        (t_3 (* c (- (* a j) (* z b)))))
   (if (<= c -2.5e+50)
     t_3
     (if (<= c -3.1e-52)
       t_2
       (if (<= c -3.3e-219)
         t_1
         (if (<= c 1.06e+38)
           t_2
           (if (<= c 2.8e+95) t_1 (if (<= c 1.3e+105) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) - (c * (z * b));
	double t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -2.5e+50) {
		tmp = t_3;
	} else if (c <= -3.1e-52) {
		tmp = t_2;
	} else if (c <= -3.3e-219) {
		tmp = t_1;
	} else if (c <= 1.06e+38) {
		tmp = t_2;
	} else if (c <= 2.8e+95) {
		tmp = t_1;
	} else if (c <= 1.3e+105) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) - (c * (z * b))
    t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)))
    t_3 = c * ((a * j) - (z * b))
    if (c <= (-2.5d+50)) then
        tmp = t_3
    else if (c <= (-3.1d-52)) then
        tmp = t_2
    else if (c <= (-3.3d-219)) then
        tmp = t_1
    else if (c <= 1.06d+38) then
        tmp = t_2
    else if (c <= 2.8d+95) then
        tmp = t_1
    else if (c <= 1.3d+105) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) - (c * (z * b));
	double t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -2.5e+50) {
		tmp = t_3;
	} else if (c <= -3.1e-52) {
		tmp = t_2;
	} else if (c <= -3.3e-219) {
		tmp = t_1;
	} else if (c <= 1.06e+38) {
		tmp = t_2;
	} else if (c <= 2.8e+95) {
		tmp = t_1;
	} else if (c <= 1.3e+105) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) - (c * (z * b))
	t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)))
	t_3 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -2.5e+50:
		tmp = t_3
	elif c <= -3.1e-52:
		tmp = t_2
	elif c <= -3.3e-219:
		tmp = t_1
	elif c <= 1.06e+38:
		tmp = t_2
	elif c <= 2.8e+95:
		tmp = t_1
	elif c <= 1.3e+105:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(c * Float64(z * b)))
	t_2 = Float64(Float64(i * Float64(t * b)) - Float64(y * Float64(Float64(i * j) - Float64(x * z))))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.5e+50)
		tmp = t_3;
	elseif (c <= -3.1e-52)
		tmp = t_2;
	elseif (c <= -3.3e-219)
		tmp = t_1;
	elseif (c <= 1.06e+38)
		tmp = t_2;
	elseif (c <= 2.8e+95)
		tmp = t_1;
	elseif (c <= 1.3e+105)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) - (c * (z * b));
	t_2 = (i * (t * b)) - (y * ((i * j) - (x * z)));
	t_3 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.5e+50)
		tmp = t_3;
	elseif (c <= -3.1e-52)
		tmp = t_2;
	elseif (c <= -3.3e-219)
		tmp = t_1;
	elseif (c <= 1.06e+38)
		tmp = t_2;
	elseif (c <= 2.8e+95)
		tmp = t_1;
	elseif (c <= 1.3e+105)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.5e+50], t$95$3, If[LessEqual[c, -3.1e-52], t$95$2, If[LessEqual[c, -3.3e-219], t$95$1, If[LessEqual[c, 1.06e+38], t$95$2, If[LessEqual[c, 2.8e+95], t$95$1, If[LessEqual[c, 1.3e+105], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.5e50 or 1.3000000000000001e105 < c

   1. Initial program 68.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 68.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 68.4%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 70.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 70.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 70.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 72.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 72.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 72.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 78.3%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -2.5e50 < c < -3.0999999999999999e-52 or -3.3000000000000002e-219 < c < 1.06e38 or 2.7999999999999998e95 < c < 1.3000000000000001e105

   1. Initial program 87.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 87.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 87.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 89.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 89.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 89.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 89.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 89.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around 0 71.9%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - b \cdot \left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 71.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right) \cdot b} \]

      2. *-commutative 71.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(\color{blue}{z \cdot c} + -1 \cdot \left(i \cdot t\right)\right) \cdot b \]

      3. associate-*r* 71.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-1 \cdot i\right) \cdot t}\right) \cdot b \]

      4. neg-mul-1 71.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-i\right)} \cdot t\right) \cdot b \]

      5. *-commutative 71.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{t \cdot \left(-i\right)}\right) \cdot b \]

      6. fma-udef 71.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \cdot b \]

      7. *-commutative 71.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

      8. *-rgt-identity 71.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

      9. cancel-sign-sub-inv 71.9%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(-b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

   6. Simplified 74.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in i around inf 70.5%

      \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if -3.0999999999999999e-52 < c < -3.3000000000000002e-219 or 1.06e38 < c < 2.7999999999999998e95

   1. Initial program 68.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 68.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 68.4%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 71.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 71.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 71.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 71.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 71.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 71.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in i around 0 64.6%

      \[\leadsto \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)\right) - c \cdot \left(b \cdot z\right)} \]

   5. Taylor expanded in j around 0 73.1%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - c \cdot \left(z \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+50}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-52}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-219}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;c \leq 1.06 \cdot 10^{+38}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+105}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 6: 66.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -9.2 \cdot 10^{+173}:\\ \;\;\;\;t_1 - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{+26}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 6500000:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+172}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -9.2e+173)
     (- t_1 (* y (* i j)))
     (if (<= a -5.6e+26)
       (* c (- (* a j) (* z b)))
       (if (<= a 6500000.0)
         (+ (* y (- (* x z) (* i j))) (* b (- (* t i) (* z c))))
         (if (<= a 3.8e+172)
           (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -9.2e+173) {
		tmp = t_1 - (y * (i * j));
	} else if (a <= -5.6e+26) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= 6500000.0) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else if (a <= 3.8e+172) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-9.2d+173)) then
        tmp = t_1 - (y * (i * j))
    else if (a <= (-5.6d+26)) then
        tmp = c * ((a * j) - (z * b))
    else if (a <= 6500000.0d0) then
        tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
    else if (a <= 3.8d+172) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -9.2e+173) {
		tmp = t_1 - (y * (i * j));
	} else if (a <= -5.6e+26) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= 6500000.0) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else if (a <= 3.8e+172) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -9.2e+173:
		tmp = t_1 - (y * (i * j))
	elif a <= -5.6e+26:
		tmp = c * ((a * j) - (z * b))
	elif a <= 6500000.0:
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
	elif a <= 3.8e+172:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -9.2e+173)
		tmp = Float64(t_1 - Float64(y * Float64(i * j)));
	elseif (a <= -5.6e+26)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (a <= 6500000.0)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (a <= 3.8e+172)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -9.2e+173)
		tmp = t_1 - (y * (i * j));
	elseif (a <= -5.6e+26)
		tmp = c * ((a * j) - (z * b));
	elseif (a <= 6500000.0)
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	elseif (a <= 3.8e+172)
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.2e+173], N[(t$95$1 - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.6e+26], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6500000.0], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e+172], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -9.1999999999999998e173

   1. Initial program 69.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 69.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 69.3%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 69.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 69.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 69.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 69.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 69.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 69.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in b around 0 66.2%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right)} \]

   5. Taylor expanded in z around 0 69.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot a - i \cdot y\right) \cdot j} \]
   6. Step-by-step derivation

      1. *-commutative 69.6%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right)} \]

      2. *-commutative 69.6%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot a - \color{blue}{y \cdot i}\right) \]

      3. sub-neg 69.6%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)} \]

      4. distribute-rgt-in 69.6%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{\left(\left(c \cdot a\right) \cdot j + \left(-y \cdot i\right) \cdot j\right)} \]

      5. associate-*r* 63.0%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\color{blue}{c \cdot \left(a \cdot j\right)} + \left(-y \cdot i\right) \cdot j\right) \]

      6. distribute-lft-neg-in 63.0%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) + \color{blue}{\left(-\left(y \cdot i\right) \cdot j\right)}\right) \]

      7. *-commutative 63.0%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) + \left(-\color{blue}{\left(i \cdot y\right)} \cdot j\right)\right) \]

      8. associate-*r* 63.0%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) + \left(-\color{blue}{i \cdot \left(y \cdot j\right)}\right)\right) \]

      9. mul-1-neg 63.0%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) + \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)}\right) \]

      10. *-commutative 63.0%

          \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \color{blue}{\left(j \cdot a\right)} + -1 \cdot \left(i \cdot \left(y \cdot j\right)\right)\right) \]

      11. associate-*r* 76.1%

          \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\color{blue}{\left(c \cdot j\right) \cdot a} + -1 \cdot \left(i \cdot \left(y \cdot j\right)\right)\right) \]

      12. associate-*r* 76.1%

          \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\left(c \cdot j\right) \cdot a + -1 \cdot \color{blue}{\left(\left(i \cdot y\right) \cdot j\right)}\right) \]

      13. *-commutative 76.1%

          \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\left(c \cdot j\right) \cdot a + -1 \cdot \left(\color{blue}{\left(y \cdot i\right)} \cdot j\right)\right) \]

      14. associate-*r* 76.1%

          \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\left(c \cdot j\right) \cdot a + -1 \cdot \color{blue}{\left(y \cdot \left(i \cdot j\right)\right)}\right) \]

      15. associate-+l+ 76.1%

          \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot j\right) \cdot a\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]

   7. Simplified 76.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right) - y \cdot \left(i \cdot j\right)} \]

   if -9.1999999999999998e173 < a < -5.59999999999999999e26

   1. Initial program 61.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 61.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 61.3%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 71.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 71.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 71.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 71.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 71.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 71.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 81.1%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -5.59999999999999999e26 < a < 6.5e6

   1. Initial program 84.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 84.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 84.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 85.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 85.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 85.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 86.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 86.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around 0 75.3%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - b \cdot \left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 75.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right) \cdot b} \]

      2. *-commutative 75.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(\color{blue}{z \cdot c} + -1 \cdot \left(i \cdot t\right)\right) \cdot b \]

      3. associate-*r* 75.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-1 \cdot i\right) \cdot t}\right) \cdot b \]

      4. neg-mul-1 75.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-i\right)} \cdot t\right) \cdot b \]

      5. *-commutative 75.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{t \cdot \left(-i\right)}\right) \cdot b \]

      6. fma-udef 76.0%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \cdot b \]

      7. *-commutative 76.0%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

      8. *-rgt-identity 76.0%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

      9. cancel-sign-sub-inv 76.0%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(-b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

   6. Simplified 76.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if 6.5e6 < a < 3.7999999999999997e172

   1. Initial program 73.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 73.6%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 73.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 73.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 73.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 77.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 77.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in b around 0 74.2%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right)} \]

   if 3.7999999999999997e172 < a

   1. Initial program 67.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 67.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 67.4%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 71.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 71.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 71.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 71.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 71.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 92.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 92.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 92.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 92.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+173}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{+26}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 6500000:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+172}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 7: 65.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -9.2 \cdot 10^{+173}:\\ \;\;\;\;t_1 - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{+26}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -9.2e+173)
     (- t_1 (* y (* i j)))
     (if (<= a -2.55e+26)
       (* c (- (* a j) (* z b)))
       (if (<= a 1.5e+51)
         (+ (* y (- (* x z) (* i j))) (* b (- (* t i) (* z c))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -9.2e+173) {
		tmp = t_1 - (y * (i * j));
	} else if (a <= -2.55e+26) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= 1.5e+51) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-9.2d+173)) then
        tmp = t_1 - (y * (i * j))
    else if (a <= (-2.55d+26)) then
        tmp = c * ((a * j) - (z * b))
    else if (a <= 1.5d+51) then
        tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -9.2e+173) {
		tmp = t_1 - (y * (i * j));
	} else if (a <= -2.55e+26) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= 1.5e+51) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -9.2e+173:
		tmp = t_1 - (y * (i * j))
	elif a <= -2.55e+26:
		tmp = c * ((a * j) - (z * b))
	elif a <= 1.5e+51:
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -9.2e+173)
		tmp = Float64(t_1 - Float64(y * Float64(i * j)));
	elseif (a <= -2.55e+26)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (a <= 1.5e+51)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -9.2e+173)
		tmp = t_1 - (y * (i * j));
	elseif (a <= -2.55e+26)
		tmp = c * ((a * j) - (z * b));
	elseif (a <= 1.5e+51)
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.2e+173], N[(t$95$1 - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.55e+26], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+51], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.1999999999999998e173

   1. Initial program 69.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 69.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 69.3%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 69.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 69.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 69.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 69.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 69.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 69.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in b around 0 66.2%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x + j \cdot \left(c \cdot a - y \cdot i\right)} \]

   5. Taylor expanded in z around 0 69.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot a - i \cdot y\right) \cdot j} \]
   6. Step-by-step derivation

      1. *-commutative 69.6%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right)} \]

      2. *-commutative 69.6%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(c \cdot a - \color{blue}{y \cdot i}\right) \]

      3. sub-neg 69.6%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)} \]

      4. distribute-rgt-in 69.6%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \color{blue}{\left(\left(c \cdot a\right) \cdot j + \left(-y \cdot i\right) \cdot j\right)} \]

      5. associate-*r* 63.0%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\color{blue}{c \cdot \left(a \cdot j\right)} + \left(-y \cdot i\right) \cdot j\right) \]

      6. distribute-lft-neg-in 63.0%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) + \color{blue}{\left(-\left(y \cdot i\right) \cdot j\right)}\right) \]

      7. *-commutative 63.0%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) + \left(-\color{blue}{\left(i \cdot y\right)} \cdot j\right)\right) \]

      8. associate-*r* 63.0%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) + \left(-\color{blue}{i \cdot \left(y \cdot j\right)}\right)\right) \]

      9. mul-1-neg 63.0%

         \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(a \cdot j\right) + \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)}\right) \]

      10. *-commutative 63.0%

          \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \color{blue}{\left(j \cdot a\right)} + -1 \cdot \left(i \cdot \left(y \cdot j\right)\right)\right) \]

      11. associate-*r* 76.1%

          \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\color{blue}{\left(c \cdot j\right) \cdot a} + -1 \cdot \left(i \cdot \left(y \cdot j\right)\right)\right) \]

      12. associate-*r* 76.1%

          \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\left(c \cdot j\right) \cdot a + -1 \cdot \color{blue}{\left(\left(i \cdot y\right) \cdot j\right)}\right) \]

      13. *-commutative 76.1%

          \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\left(c \cdot j\right) \cdot a + -1 \cdot \left(\color{blue}{\left(y \cdot i\right)} \cdot j\right)\right) \]

      14. associate-*r* 76.1%

          \[\leadsto -1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(\left(c \cdot j\right) \cdot a + -1 \cdot \color{blue}{\left(y \cdot \left(i \cdot j\right)\right)}\right) \]

      15. associate-+l+ 76.1%

          \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot j\right) \cdot a\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]

   7. Simplified 76.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right) - y \cdot \left(i \cdot j\right)} \]

   if -9.1999999999999998e173 < a < -2.5499999999999999e26

   1. Initial program 61.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 61.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 61.3%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 71.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 71.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 71.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 71.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 71.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 71.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 81.1%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -2.5499999999999999e26 < a < 1.5e51

   1. Initial program 84.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 84.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 84.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 85.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 85.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 85.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 86.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 86.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 86.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around 0 74.3%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - b \cdot \left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 74.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right) \cdot b} \]

      2. *-commutative 74.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(\color{blue}{z \cdot c} + -1 \cdot \left(i \cdot t\right)\right) \cdot b \]

      3. associate-*r* 74.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-1 \cdot i\right) \cdot t}\right) \cdot b \]

      4. neg-mul-1 74.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-i\right)} \cdot t\right) \cdot b \]

      5. *-commutative 74.3%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{t \cdot \left(-i\right)}\right) \cdot b \]

      6. fma-udef 75.0%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \cdot b \]

      7. *-commutative 75.0%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

      8. *-rgt-identity 75.0%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

      9. cancel-sign-sub-inv 75.0%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(-b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

   6. Simplified 75.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if 1.5e51 < a

   1. Initial program 68.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 68.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 68.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 70.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 70.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 70.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 70.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 70.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 70.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 78.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 78.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 78.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 78.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+173}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{+26}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 8: 48.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.3 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -9.6 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -0.46:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-40}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-99}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -3.3e+93)
     t_2
     (if (<= c -9.6e+26)
       t_1
       (if (<= c -0.46)
         t_2
         (if (<= c -2.8e-40)
           (* z (* x y))
           (if (<= c -3.1e-288)
             t_1
             (if (<= c 3.2e-99)
               (* j (- (* a c) (* y i)))
               (if (<= c 9e+40) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -3.3e+93) {
		tmp = t_2;
	} else if (c <= -9.6e+26) {
		tmp = t_1;
	} else if (c <= -0.46) {
		tmp = t_2;
	} else if (c <= -2.8e-40) {
		tmp = z * (x * y);
	} else if (c <= -3.1e-288) {
		tmp = t_1;
	} else if (c <= 3.2e-99) {
		tmp = j * ((a * c) - (y * i));
	} else if (c <= 9e+40) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-3.3d+93)) then
        tmp = t_2
    else if (c <= (-9.6d+26)) then
        tmp = t_1
    else if (c <= (-0.46d0)) then
        tmp = t_2
    else if (c <= (-2.8d-40)) then
        tmp = z * (x * y)
    else if (c <= (-3.1d-288)) then
        tmp = t_1
    else if (c <= 3.2d-99) then
        tmp = j * ((a * c) - (y * i))
    else if (c <= 9d+40) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -3.3e+93) {
		tmp = t_2;
	} else if (c <= -9.6e+26) {
		tmp = t_1;
	} else if (c <= -0.46) {
		tmp = t_2;
	} else if (c <= -2.8e-40) {
		tmp = z * (x * y);
	} else if (c <= -3.1e-288) {
		tmp = t_1;
	} else if (c <= 3.2e-99) {
		tmp = j * ((a * c) - (y * i));
	} else if (c <= 9e+40) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -3.3e+93:
		tmp = t_2
	elif c <= -9.6e+26:
		tmp = t_1
	elif c <= -0.46:
		tmp = t_2
	elif c <= -2.8e-40:
		tmp = z * (x * y)
	elif c <= -3.1e-288:
		tmp = t_1
	elif c <= 3.2e-99:
		tmp = j * ((a * c) - (y * i))
	elif c <= 9e+40:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.3e+93)
		tmp = t_2;
	elseif (c <= -9.6e+26)
		tmp = t_1;
	elseif (c <= -0.46)
		tmp = t_2;
	elseif (c <= -2.8e-40)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= -3.1e-288)
		tmp = t_1;
	elseif (c <= 3.2e-99)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (c <= 9e+40)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.3e+93)
		tmp = t_2;
	elseif (c <= -9.6e+26)
		tmp = t_1;
	elseif (c <= -0.46)
		tmp = t_2;
	elseif (c <= -2.8e-40)
		tmp = z * (x * y);
	elseif (c <= -3.1e-288)
		tmp = t_1;
	elseif (c <= 3.2e-99)
		tmp = j * ((a * c) - (y * i));
	elseif (c <= 9e+40)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.3e+93], t$95$2, If[LessEqual[c, -9.6e+26], t$95$1, If[LessEqual[c, -0.46], t$95$2, If[LessEqual[c, -2.8e-40], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.1e-288], t$95$1, If[LessEqual[c, 3.2e-99], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9e+40], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.30000000000000009e93 or -9.60000000000000018e26 < c < -0.46000000000000002 or 9.00000000000000064e40 < c

   1. Initial program 67.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 67.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 67.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 69.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 69.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 69.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 71.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 71.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 71.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 75.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -3.30000000000000009e93 < c < -9.60000000000000018e26 or -2.8e-40 < c < -3.09999999999999983e-288 or 3.2000000000000001e-99 < c < 9.00000000000000064e40

   1. Initial program 83.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 83.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 83.6%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 86.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 86.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 86.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 86.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 86.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 86.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in i around inf 50.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 50.6%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + \left(--1 \cdot \left(t \cdot b\right)\right)\right)} \]

      2. mul-1-neg 50.6%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \left(-\color{blue}{\left(-t \cdot b\right)}\right)\right) \]

      3. remove-double-neg 50.6%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \color{blue}{t \cdot b}\right) \]

      4. +-commutative 50.6%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 50.6%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 50.6%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

      7. *-commutative 50.6%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot t} - y \cdot j\right) \]

   6. Simplified 50.6%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   if -0.46000000000000002 < c < -2.8e-40

   1. Initial program 83.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 83.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 83.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 83.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 83.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 83.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in z around inf 83.6%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 83.6%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if -3.09999999999999983e-288 < c < 3.2000000000000001e-99

   1. Initial program 85.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 85.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 85.8%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 88.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 88.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 88.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 88.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 88.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in j around inf 57.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.3 \cdot 10^{+93}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -9.6 \cdot 10^{+26}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -0.46:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-40}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-288}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-99}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+40}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 9: 50.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.95 \cdot 10^{+176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+43}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-140}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -1.95e+176)
     t_2
     (if (<= a -2e+43)
       (* c (- (* a j) (* z b)))
       (if (<= a -5.5e-120)
         t_1
         (if (<= a -4.6e-140)
           (* j (- (* a c) (* y i)))
           (if (<= a 7e-127)
             t_1
             (if (<= a 1.4e+51) (* y (- (* x z) (* i j))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.95e+176) {
		tmp = t_2;
	} else if (a <= -2e+43) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= -5.5e-120) {
		tmp = t_1;
	} else if (a <= -4.6e-140) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 7e-127) {
		tmp = t_1;
	} else if (a <= 1.4e+51) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-1.95d+176)) then
        tmp = t_2
    else if (a <= (-2d+43)) then
        tmp = c * ((a * j) - (z * b))
    else if (a <= (-5.5d-120)) then
        tmp = t_1
    else if (a <= (-4.6d-140)) then
        tmp = j * ((a * c) - (y * i))
    else if (a <= 7d-127) then
        tmp = t_1
    else if (a <= 1.4d+51) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.95e+176) {
		tmp = t_2;
	} else if (a <= -2e+43) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= -5.5e-120) {
		tmp = t_1;
	} else if (a <= -4.6e-140) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 7e-127) {
		tmp = t_1;
	} else if (a <= 1.4e+51) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.95e+176:
		tmp = t_2
	elif a <= -2e+43:
		tmp = c * ((a * j) - (z * b))
	elif a <= -5.5e-120:
		tmp = t_1
	elif a <= -4.6e-140:
		tmp = j * ((a * c) - (y * i))
	elif a <= 7e-127:
		tmp = t_1
	elif a <= 1.4e+51:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.95e+176)
		tmp = t_2;
	elseif (a <= -2e+43)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (a <= -5.5e-120)
		tmp = t_1;
	elseif (a <= -4.6e-140)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (a <= 7e-127)
		tmp = t_1;
	elseif (a <= 1.4e+51)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.95e+176)
		tmp = t_2;
	elseif (a <= -2e+43)
		tmp = c * ((a * j) - (z * b));
	elseif (a <= -5.5e-120)
		tmp = t_1;
	elseif (a <= -4.6e-140)
		tmp = j * ((a * c) - (y * i));
	elseif (a <= 7e-127)
		tmp = t_1;
	elseif (a <= 1.4e+51)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.95e+176], t$95$2, If[LessEqual[a, -2e+43], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.5e-120], t$95$1, If[LessEqual[a, -4.6e-140], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e-127], t$95$1, If[LessEqual[a, 1.4e+51], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.9500000000000001e176 or 1.40000000000000002e51 < a

   1. Initial program 68.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 68.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 68.2%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 69.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 69.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 69.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 69.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 69.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 69.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 74.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 74.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 74.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 74.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -1.9500000000000001e176 < a < -2.00000000000000003e43

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 73.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 80.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 80.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 80.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 80.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 80.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 80.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 77.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -2.00000000000000003e43 < a < -5.5000000000000001e-120 or -4.6000000000000002e-140 < a < 6.99999999999999979e-127

   1. Initial program 83.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 83.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 83.2%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 84.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 85.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 85.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 85.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in z around inf 65.1%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   if -5.5000000000000001e-120 < a < -4.6000000000000002e-140

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 78.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 78.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 78.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 78.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 78.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 78.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 78.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in j around inf 79.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right)} \]

   if 6.99999999999999979e-127 < a < 1.40000000000000002e51

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 77.7%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 82.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 82.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 82.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 85.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 85.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 85.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in y around inf 60.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 60.2%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 60.2%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 60.2%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 60.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+176}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+43}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-120}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-140}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-127}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 10: 30.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+226}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{+43}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -1.28 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-150}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+174}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* b (- z)))))
   (if (<= a -2.1e+226)
     (* t (* x (- a)))
     (if (<= a -7.5e+43)
       (* c (* a j))
       (if (<= a -1.28e-120)
         t_1
         (if (<= a -4.6e-150)
           (* j (* y (- i)))
           (if (<= a 1.55e-187)
             t_1
             (if (<= a 4.2e+30)
               (* z (* x y))
               (if (<= a 1.2e+174) (* j (* a c)) (* (* x t) (- a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (b * -z);
	double tmp;
	if (a <= -2.1e+226) {
		tmp = t * (x * -a);
	} else if (a <= -7.5e+43) {
		tmp = c * (a * j);
	} else if (a <= -1.28e-120) {
		tmp = t_1;
	} else if (a <= -4.6e-150) {
		tmp = j * (y * -i);
	} else if (a <= 1.55e-187) {
		tmp = t_1;
	} else if (a <= 4.2e+30) {
		tmp = z * (x * y);
	} else if (a <= 1.2e+174) {
		tmp = j * (a * c);
	} else {
		tmp = (x * t) * -a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (b * -z)
    if (a <= (-2.1d+226)) then
        tmp = t * (x * -a)
    else if (a <= (-7.5d+43)) then
        tmp = c * (a * j)
    else if (a <= (-1.28d-120)) then
        tmp = t_1
    else if (a <= (-4.6d-150)) then
        tmp = j * (y * -i)
    else if (a <= 1.55d-187) then
        tmp = t_1
    else if (a <= 4.2d+30) then
        tmp = z * (x * y)
    else if (a <= 1.2d+174) then
        tmp = j * (a * c)
    else
        tmp = (x * t) * -a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (b * -z);
	double tmp;
	if (a <= -2.1e+226) {
		tmp = t * (x * -a);
	} else if (a <= -7.5e+43) {
		tmp = c * (a * j);
	} else if (a <= -1.28e-120) {
		tmp = t_1;
	} else if (a <= -4.6e-150) {
		tmp = j * (y * -i);
	} else if (a <= 1.55e-187) {
		tmp = t_1;
	} else if (a <= 4.2e+30) {
		tmp = z * (x * y);
	} else if (a <= 1.2e+174) {
		tmp = j * (a * c);
	} else {
		tmp = (x * t) * -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (b * -z)
	tmp = 0
	if a <= -2.1e+226:
		tmp = t * (x * -a)
	elif a <= -7.5e+43:
		tmp = c * (a * j)
	elif a <= -1.28e-120:
		tmp = t_1
	elif a <= -4.6e-150:
		tmp = j * (y * -i)
	elif a <= 1.55e-187:
		tmp = t_1
	elif a <= 4.2e+30:
		tmp = z * (x * y)
	elif a <= 1.2e+174:
		tmp = j * (a * c)
	else:
		tmp = (x * t) * -a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(b * Float64(-z)))
	tmp = 0.0
	if (a <= -2.1e+226)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (a <= -7.5e+43)
		tmp = Float64(c * Float64(a * j));
	elseif (a <= -1.28e-120)
		tmp = t_1;
	elseif (a <= -4.6e-150)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (a <= 1.55e-187)
		tmp = t_1;
	elseif (a <= 4.2e+30)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 1.2e+174)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(Float64(x * t) * Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (b * -z);
	tmp = 0.0;
	if (a <= -2.1e+226)
		tmp = t * (x * -a);
	elseif (a <= -7.5e+43)
		tmp = c * (a * j);
	elseif (a <= -1.28e-120)
		tmp = t_1;
	elseif (a <= -4.6e-150)
		tmp = j * (y * -i);
	elseif (a <= 1.55e-187)
		tmp = t_1;
	elseif (a <= 4.2e+30)
		tmp = z * (x * y);
	elseif (a <= 1.2e+174)
		tmp = j * (a * c);
	else
		tmp = (x * t) * -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+226], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.5e+43], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.28e-120], t$95$1, If[LessEqual[a, -4.6e-150], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e-187], t$95$1, If[LessEqual[a, 4.2e+30], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+174], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -2.09999999999999993e226

   1. Initial program 66.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 66.5%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 66.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 66.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 66.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 66.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in t around inf 54.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 54.9%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \cdot t \]

      2. associate-*r* 54.9%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x - i \cdot b\right) \cdot t\right)} \]

      3. mul-1-neg 54.9%

         \[\leadsto \color{blue}{-\left(a \cdot x - i \cdot b\right) \cdot t} \]

      4. *-commutative 54.9%

         \[\leadsto -\color{blue}{t \cdot \left(a \cdot x - i \cdot b\right)} \]

      5. *-commutative 54.9%

         \[\leadsto -t \cdot \left(a \cdot x - \color{blue}{b \cdot i}\right) \]

   6. Simplified 54.9%

      \[\leadsto \color{blue}{-t \cdot \left(a \cdot x - b \cdot i\right)} \]

   7. Taylor expanded in a around inf 47.8%

      \[\leadsto -t \cdot \color{blue}{\left(a \cdot x\right)} \]

   if -2.09999999999999993e226 < a < -7.49999999999999967e43

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 71.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 71.4%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 76.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 76.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 76.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 76.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 76.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 64.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 64.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 64.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 64.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 56.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 56.4%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 56.4%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   if -7.49999999999999967e43 < a < -1.28000000000000008e-120 or -4.60000000000000006e-150 < a < 1.5500000000000001e-187

   1. Initial program 81.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 81.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 81.6%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 82.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 82.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 82.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 83.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 83.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 45.3%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   5. Taylor expanded in a around 0 41.2%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 41.2%

         \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

      2. distribute-lft-neg-in 41.2%

         \[\leadsto c \cdot \color{blue}{\left(\left(-b\right) \cdot z\right)} \]

      3. *-commutative 41.2%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   7. Simplified 41.2%

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   if -1.28000000000000008e-120 < a < -4.60000000000000006e-150

   1. Initial program 82.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 82.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 82.6%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 82.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 82.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 82.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in j around inf 65.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right)} \]

   5. Taylor expanded in c around 0 56.6%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 56.6%

         \[\leadsto j \cdot \color{blue}{\left(-i \cdot y\right)} \]

      2. *-commutative 56.6%

         \[\leadsto j \cdot \left(-\color{blue}{y \cdot i}\right) \]

      3. distribute-rgt-neg-in 56.6%

         \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   7. Simplified 56.6%

      \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   if 1.5500000000000001e-187 < a < 4.2e30

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 80.2%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 84.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 84.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 84.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 86.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 86.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 86.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in z around inf 52.3%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 37.0%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if 4.2e30 < a < 1.1999999999999999e174

   1. Initial program 74.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 74.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 74.6%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 74.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 74.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 74.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 74.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 74.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 74.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 58.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 58.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 58.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 58.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 45.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 50.0%

         \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

      2. *-commutative 50.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]

   9. Simplified 50.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]

   if 1.1999999999999999e174 < a

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 66.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 70.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 70.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 70.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 70.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 70.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 70.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 92.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 92.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 92.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 92.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 73.5%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 73.5%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-out 73.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 73.5%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 73.5%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+226}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{+43}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -1.28 \cdot 10^{-120}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-150}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-187}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+174}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \end{array} \]

Alternative 11: 30.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{+223}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+43}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-153}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{+174}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* b (- z)))))
   (if (<= a -1.65e+223)
     (* t (* x (- a)))
     (if (<= a -5.2e+43)
       (* c (* a j))
       (if (<= a -8e-121)
         t_1
         (if (<= a -6.2e-153)
           (* j (* y (- i)))
           (if (<= a 3.5e-187)
             t_1
             (if (<= a 3.1e+46)
               (* y (* j (- i)))
               (if (<= a 1.16e+174) (* j (* a c)) (* (* x t) (- a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (b * -z);
	double tmp;
	if (a <= -1.65e+223) {
		tmp = t * (x * -a);
	} else if (a <= -5.2e+43) {
		tmp = c * (a * j);
	} else if (a <= -8e-121) {
		tmp = t_1;
	} else if (a <= -6.2e-153) {
		tmp = j * (y * -i);
	} else if (a <= 3.5e-187) {
		tmp = t_1;
	} else if (a <= 3.1e+46) {
		tmp = y * (j * -i);
	} else if (a <= 1.16e+174) {
		tmp = j * (a * c);
	} else {
		tmp = (x * t) * -a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (b * -z)
    if (a <= (-1.65d+223)) then
        tmp = t * (x * -a)
    else if (a <= (-5.2d+43)) then
        tmp = c * (a * j)
    else if (a <= (-8d-121)) then
        tmp = t_1
    else if (a <= (-6.2d-153)) then
        tmp = j * (y * -i)
    else if (a <= 3.5d-187) then
        tmp = t_1
    else if (a <= 3.1d+46) then
        tmp = y * (j * -i)
    else if (a <= 1.16d+174) then
        tmp = j * (a * c)
    else
        tmp = (x * t) * -a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (b * -z);
	double tmp;
	if (a <= -1.65e+223) {
		tmp = t * (x * -a);
	} else if (a <= -5.2e+43) {
		tmp = c * (a * j);
	} else if (a <= -8e-121) {
		tmp = t_1;
	} else if (a <= -6.2e-153) {
		tmp = j * (y * -i);
	} else if (a <= 3.5e-187) {
		tmp = t_1;
	} else if (a <= 3.1e+46) {
		tmp = y * (j * -i);
	} else if (a <= 1.16e+174) {
		tmp = j * (a * c);
	} else {
		tmp = (x * t) * -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (b * -z)
	tmp = 0
	if a <= -1.65e+223:
		tmp = t * (x * -a)
	elif a <= -5.2e+43:
		tmp = c * (a * j)
	elif a <= -8e-121:
		tmp = t_1
	elif a <= -6.2e-153:
		tmp = j * (y * -i)
	elif a <= 3.5e-187:
		tmp = t_1
	elif a <= 3.1e+46:
		tmp = y * (j * -i)
	elif a <= 1.16e+174:
		tmp = j * (a * c)
	else:
		tmp = (x * t) * -a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(b * Float64(-z)))
	tmp = 0.0
	if (a <= -1.65e+223)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (a <= -5.2e+43)
		tmp = Float64(c * Float64(a * j));
	elseif (a <= -8e-121)
		tmp = t_1;
	elseif (a <= -6.2e-153)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (a <= 3.5e-187)
		tmp = t_1;
	elseif (a <= 3.1e+46)
		tmp = Float64(y * Float64(j * Float64(-i)));
	elseif (a <= 1.16e+174)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(Float64(x * t) * Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (b * -z);
	tmp = 0.0;
	if (a <= -1.65e+223)
		tmp = t * (x * -a);
	elseif (a <= -5.2e+43)
		tmp = c * (a * j);
	elseif (a <= -8e-121)
		tmp = t_1;
	elseif (a <= -6.2e-153)
		tmp = j * (y * -i);
	elseif (a <= 3.5e-187)
		tmp = t_1;
	elseif (a <= 3.1e+46)
		tmp = y * (j * -i);
	elseif (a <= 1.16e+174)
		tmp = j * (a * c);
	else
		tmp = (x * t) * -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e+223], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.2e+43], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8e-121], t$95$1, If[LessEqual[a, -6.2e-153], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-187], t$95$1, If[LessEqual[a, 3.1e+46], N[(y * N[(j * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.16e+174], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -1.65e223

   1. Initial program 66.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 66.5%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 66.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 66.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 66.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 66.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in t around inf 54.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 54.9%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \cdot t \]

      2. associate-*r* 54.9%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x - i \cdot b\right) \cdot t\right)} \]

      3. mul-1-neg 54.9%

         \[\leadsto \color{blue}{-\left(a \cdot x - i \cdot b\right) \cdot t} \]

      4. *-commutative 54.9%

         \[\leadsto -\color{blue}{t \cdot \left(a \cdot x - i \cdot b\right)} \]

      5. *-commutative 54.9%

         \[\leadsto -t \cdot \left(a \cdot x - \color{blue}{b \cdot i}\right) \]

   6. Simplified 54.9%

      \[\leadsto \color{blue}{-t \cdot \left(a \cdot x - b \cdot i\right)} \]

   7. Taylor expanded in a around inf 47.8%

      \[\leadsto -t \cdot \color{blue}{\left(a \cdot x\right)} \]

   if -1.65e223 < a < -5.20000000000000042e43

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 71.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 71.4%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 76.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 76.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 76.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 76.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 76.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 64.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 64.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 64.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 64.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 56.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 56.4%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 56.4%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   if -5.20000000000000042e43 < a < -7.9999999999999998e-121 or -6.1999999999999999e-153 < a < 3.49999999999999979e-187

   1. Initial program 81.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 81.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 81.6%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 82.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 82.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 82.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 83.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 83.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 45.3%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   5. Taylor expanded in a around 0 41.2%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 41.2%

         \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

      2. distribute-lft-neg-in 41.2%

         \[\leadsto c \cdot \color{blue}{\left(\left(-b\right) \cdot z\right)} \]

      3. *-commutative 41.2%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   7. Simplified 41.2%

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   if -7.9999999999999998e-121 < a < -6.1999999999999999e-153

   1. Initial program 82.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 82.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 82.6%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 82.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 82.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 82.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in j around inf 65.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right)} \]

   5. Taylor expanded in c around 0 56.6%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 56.6%

         \[\leadsto j \cdot \color{blue}{\left(-i \cdot y\right)} \]

      2. *-commutative 56.6%

         \[\leadsto j \cdot \left(-\color{blue}{y \cdot i}\right) \]

      3. distribute-rgt-neg-in 56.6%

         \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   7. Simplified 56.6%

      \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   if 3.49999999999999979e-187 < a < 3.09999999999999975e46

   1. Initial program 81.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 81.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 81.0%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 85.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 87.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 87.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 87.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around 0 76.6%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - b \cdot \left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 76.6%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right) \cdot b} \]

      2. *-commutative 76.6%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(\color{blue}{z \cdot c} + -1 \cdot \left(i \cdot t\right)\right) \cdot b \]

      3. associate-*r* 76.6%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-1 \cdot i\right) \cdot t}\right) \cdot b \]

      4. neg-mul-1 76.6%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-i\right)} \cdot t\right) \cdot b \]

      5. *-commutative 76.6%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{t \cdot \left(-i\right)}\right) \cdot b \]

      6. fma-udef 76.6%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \cdot b \]

      7. *-commutative 76.6%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

      8. *-rgt-identity 76.6%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

      9. cancel-sign-sub-inv 76.6%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(-b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

   6. Simplified 78.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in t around 0 62.0%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right) + y \cdot \left(z \cdot x - i \cdot j\right)} \]
   8. Step-by-step derivation

      1. +-commutative 62.0%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + -1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} \]

      2. mul-1-neg 62.0%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} \]

      3. unsub-neg 62.0%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - c \cdot \left(b \cdot z\right)} \]

      4. *-commutative 62.0%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{\left(b \cdot z\right) \cdot c} \]

      5. *-commutative 62.0%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{\left(z \cdot b\right)} \cdot c \]

      6. associate-*l* 64.1%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{z \cdot \left(b \cdot c\right)} \]

      7. *-commutative 64.1%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - z \cdot \color{blue}{\left(c \cdot b\right)} \]

   9. Simplified 64.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - z \cdot \left(c \cdot b\right)} \]

   10. Taylor expanded in z around 0 36.8%

       \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 36.8%

          \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

       2. distribute-rgt-neg-in 36.8%

          \[\leadsto \color{blue}{y \cdot \left(-i \cdot j\right)} \]

       3. *-commutative 36.8%

          \[\leadsto y \cdot \left(-\color{blue}{j \cdot i}\right) \]

       4. distribute-rgt-neg-in 36.8%

          \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   12. Simplified 36.8%

       \[\leadsto \color{blue}{y \cdot \left(j \cdot \left(-i\right)\right)} \]

   if 3.09999999999999975e46 < a < 1.16000000000000003e174

   1. Initial program 72.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 72.2%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 72.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 72.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 72.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 72.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 72.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 72.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 58.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 58.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 58.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 58.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 49.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 54.0%

         \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

      2. *-commutative 54.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]

   9. Simplified 54.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]

   if 1.16000000000000003e174 < a

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 66.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 70.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 70.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 70.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 70.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 70.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 70.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 92.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 92.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 92.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 92.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 73.5%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 73.5%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-out 73.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 73.5%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 73.5%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+223}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+43}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-121}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-153}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-187}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{+174}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \end{array} \]

Alternative 12: 42.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(b \cdot \left(-z\right)\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-151}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* b (- z)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -4.2e+43)
     t_2
     (if (<= a -5.6e-121)
       t_1
       (if (<= a -7.8e-151)
         (* j (* y (- i)))
         (if (<= a 3.5e-186)
           t_1
           (if (<= a 9.8e-14) (* y (* j (- i))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (b * -z);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.2e+43) {
		tmp = t_2;
	} else if (a <= -5.6e-121) {
		tmp = t_1;
	} else if (a <= -7.8e-151) {
		tmp = j * (y * -i);
	} else if (a <= 3.5e-186) {
		tmp = t_1;
	} else if (a <= 9.8e-14) {
		tmp = y * (j * -i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (b * -z)
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-4.2d+43)) then
        tmp = t_2
    else if (a <= (-5.6d-121)) then
        tmp = t_1
    else if (a <= (-7.8d-151)) then
        tmp = j * (y * -i)
    else if (a <= 3.5d-186) then
        tmp = t_1
    else if (a <= 9.8d-14) then
        tmp = y * (j * -i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (b * -z);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.2e+43) {
		tmp = t_2;
	} else if (a <= -5.6e-121) {
		tmp = t_1;
	} else if (a <= -7.8e-151) {
		tmp = j * (y * -i);
	} else if (a <= 3.5e-186) {
		tmp = t_1;
	} else if (a <= 9.8e-14) {
		tmp = y * (j * -i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (b * -z)
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -4.2e+43:
		tmp = t_2
	elif a <= -5.6e-121:
		tmp = t_1
	elif a <= -7.8e-151:
		tmp = j * (y * -i)
	elif a <= 3.5e-186:
		tmp = t_1
	elif a <= 9.8e-14:
		tmp = y * (j * -i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(b * Float64(-z)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.2e+43)
		tmp = t_2;
	elseif (a <= -5.6e-121)
		tmp = t_1;
	elseif (a <= -7.8e-151)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (a <= 3.5e-186)
		tmp = t_1;
	elseif (a <= 9.8e-14)
		tmp = Float64(y * Float64(j * Float64(-i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (b * -z);
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -4.2e+43)
		tmp = t_2;
	elseif (a <= -5.6e-121)
		tmp = t_1;
	elseif (a <= -7.8e-151)
		tmp = j * (y * -i);
	elseif (a <= 3.5e-186)
		tmp = t_1;
	elseif (a <= 9.8e-14)
		tmp = y * (j * -i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e+43], t$95$2, If[LessEqual[a, -5.6e-121], t$95$1, If[LessEqual[a, -7.8e-151], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-186], t$95$1, If[LessEqual[a, 9.8e-14], N[(y * N[(j * (-i)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.20000000000000003e43 or 9.79999999999999989e-14 < a

   1. Initial program 71.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 71.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 71.5%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 74.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 74.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 74.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 75.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 75.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 75.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 66.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 66.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 66.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 66.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -4.20000000000000003e43 < a < -5.6000000000000002e-121 or -7.80000000000000013e-151 < a < 3.49999999999999989e-186

   1. Initial program 81.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 81.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 81.6%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 82.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 82.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 82.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 83.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 83.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 45.3%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   5. Taylor expanded in a around 0 41.2%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 41.2%

         \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

      2. distribute-lft-neg-in 41.2%

         \[\leadsto c \cdot \color{blue}{\left(\left(-b\right) \cdot z\right)} \]

      3. *-commutative 41.2%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   7. Simplified 41.2%

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   if -5.6000000000000002e-121 < a < -7.80000000000000013e-151

   1. Initial program 82.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 82.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 82.6%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 82.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 82.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 82.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in j around inf 65.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right)} \]

   5. Taylor expanded in c around 0 56.6%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 56.6%

         \[\leadsto j \cdot \color{blue}{\left(-i \cdot y\right)} \]

      2. *-commutative 56.6%

         \[\leadsto j \cdot \left(-\color{blue}{y \cdot i}\right) \]

      3. distribute-rgt-neg-in 56.6%

         \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   7. Simplified 56.6%

      \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   if 3.49999999999999989e-186 < a < 9.79999999999999989e-14

   1. Initial program 78.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 78.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 78.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 83.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 83.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 83.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 83.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 83.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 83.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around 0 80.9%

      \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - b \cdot \left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 80.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(c \cdot z + -1 \cdot \left(i \cdot t\right)\right) \cdot b} \]

      2. *-commutative 80.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(\color{blue}{z \cdot c} + -1 \cdot \left(i \cdot t\right)\right) \cdot b \]

      3. associate-*r* 80.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-1 \cdot i\right) \cdot t}\right) \cdot b \]

      4. neg-mul-1 80.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{\left(-i\right)} \cdot t\right) \cdot b \]

      5. *-commutative 80.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \left(z \cdot c + \color{blue}{t \cdot \left(-i\right)}\right) \cdot b \]

      6. fma-udef 80.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \cdot b \]

      7. *-commutative 80.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

      8. *-rgt-identity 80.9%

         \[\leadsto \left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) - \color{blue}{\left(b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

      9. cancel-sign-sub-inv 80.9%

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j\right)\right)\right) + \left(-b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right) \cdot 1} \]

   6. Simplified 83.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in t around 0 64.7%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right) + y \cdot \left(z \cdot x - i \cdot j\right)} \]
   8. Step-by-step derivation

      1. +-commutative 64.7%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + -1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} \]

      2. mul-1-neg 64.7%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) + \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} \]

      3. unsub-neg 64.7%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - c \cdot \left(b \cdot z\right)} \]

      4. *-commutative 64.7%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{\left(b \cdot z\right) \cdot c} \]

      5. *-commutative 64.7%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{\left(z \cdot b\right)} \cdot c \]

      6. associate-*l* 67.5%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{z \cdot \left(b \cdot c\right)} \]

      7. *-commutative 67.5%

         \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - z \cdot \color{blue}{\left(c \cdot b\right)} \]

   9. Simplified 67.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - z \cdot \left(c \cdot b\right)} \]

   10. Taylor expanded in z around 0 42.6%

       \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 42.6%

          \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

       2. distribute-rgt-neg-in 42.6%

          \[\leadsto \color{blue}{y \cdot \left(-i \cdot j\right)} \]

       3. *-commutative 42.6%

          \[\leadsto y \cdot \left(-\color{blue}{j \cdot i}\right) \]

       4. distribute-rgt-neg-in 42.6%

          \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   12. Simplified 42.6%

       \[\leadsto \color{blue}{y \cdot \left(j \cdot \left(-i\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+43}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-121}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-151}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-186}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 13: 51.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -5.4 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -0.0065:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.45 \cdot 10^{-40}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -5.4e+90)
     t_2
     (if (<= c -1.45e+25)
       t_1
       (if (<= c -0.0065)
         t_2
         (if (<= c -3.45e-40) (* z (* x y)) (if (<= c 3.6e+45) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -5.4e+90) {
		tmp = t_2;
	} else if (c <= -1.45e+25) {
		tmp = t_1;
	} else if (c <= -0.0065) {
		tmp = t_2;
	} else if (c <= -3.45e-40) {
		tmp = z * (x * y);
	} else if (c <= 3.6e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-5.4d+90)) then
        tmp = t_2
    else if (c <= (-1.45d+25)) then
        tmp = t_1
    else if (c <= (-0.0065d0)) then
        tmp = t_2
    else if (c <= (-3.45d-40)) then
        tmp = z * (x * y)
    else if (c <= 3.6d+45) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -5.4e+90) {
		tmp = t_2;
	} else if (c <= -1.45e+25) {
		tmp = t_1;
	} else if (c <= -0.0065) {
		tmp = t_2;
	} else if (c <= -3.45e-40) {
		tmp = z * (x * y);
	} else if (c <= 3.6e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -5.4e+90:
		tmp = t_2
	elif c <= -1.45e+25:
		tmp = t_1
	elif c <= -0.0065:
		tmp = t_2
	elif c <= -3.45e-40:
		tmp = z * (x * y)
	elif c <= 3.6e+45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -5.4e+90)
		tmp = t_2;
	elseif (c <= -1.45e+25)
		tmp = t_1;
	elseif (c <= -0.0065)
		tmp = t_2;
	elseif (c <= -3.45e-40)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 3.6e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -5.4e+90)
		tmp = t_2;
	elseif (c <= -1.45e+25)
		tmp = t_1;
	elseif (c <= -0.0065)
		tmp = t_2;
	elseif (c <= -3.45e-40)
		tmp = z * (x * y);
	elseif (c <= 3.6e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.4e+90], t$95$2, If[LessEqual[c, -1.45e+25], t$95$1, If[LessEqual[c, -0.0065], t$95$2, If[LessEqual[c, -3.45e-40], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.6e+45], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.4e90 or -1.44999999999999995e25 < c < -0.0064999999999999997 or 3.6e45 < c

   1. Initial program 67.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 67.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 67.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 69.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 69.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 69.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 71.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 71.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 71.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 75.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -5.4e90 < c < -1.44999999999999995e25 or -3.4499999999999998e-40 < c < 3.6e45

   1. Initial program 84.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 84.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 84.3%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 87.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 87.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 87.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 87.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 87.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in i around inf 48.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 48.5%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + \left(--1 \cdot \left(t \cdot b\right)\right)\right)} \]

      2. mul-1-neg 48.5%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \left(-\color{blue}{\left(-t \cdot b\right)}\right)\right) \]

      3. remove-double-neg 48.5%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \color{blue}{t \cdot b}\right) \]

      4. +-commutative 48.5%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 48.5%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 48.5%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

      7. *-commutative 48.5%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot t} - y \cdot j\right) \]

   6. Simplified 48.5%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   if -0.0064999999999999997 < c < -3.4499999999999998e-40

   1. Initial program 83.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 83.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 83.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 83.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 83.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 83.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in z around inf 83.6%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 83.6%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.4 \cdot 10^{+90}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{+25}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -0.0065:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.45 \cdot 10^{-40}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{+45}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 14: 51.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-140}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-90}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -1.8e+38)
     t_1
     (if (<= y 2.5e-140)
       (* c (- (* a j) (* z b)))
       (if (<= y 3.4e-90)
         (* i (- (* t b) (* y j)))
         (if (<= y 1.08e-63) (* a (- (* c j) (* x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.8e+38) {
		tmp = t_1;
	} else if (y <= 2.5e-140) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 3.4e-90) {
		tmp = i * ((t * b) - (y * j));
	} else if (y <= 1.08e-63) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (y <= (-1.8d+38)) then
        tmp = t_1
    else if (y <= 2.5d-140) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= 3.4d-90) then
        tmp = i * ((t * b) - (y * j))
    else if (y <= 1.08d-63) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.8e+38) {
		tmp = t_1;
	} else if (y <= 2.5e-140) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 3.4e-90) {
		tmp = i * ((t * b) - (y * j));
	} else if (y <= 1.08e-63) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.8e+38:
		tmp = t_1
	elif y <= 2.5e-140:
		tmp = c * ((a * j) - (z * b))
	elif y <= 3.4e-90:
		tmp = i * ((t * b) - (y * j))
	elif y <= 1.08e-63:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.8e+38)
		tmp = t_1;
	elseif (y <= 2.5e-140)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= 3.4e-90)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (y <= 1.08e-63)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.8e+38)
		tmp = t_1;
	elseif (y <= 2.5e-140)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= 3.4e-90)
		tmp = i * ((t * b) - (y * j));
	elseif (y <= 1.08e-63)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+38], t$95$1, If[LessEqual[y, 2.5e-140], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-90], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.08e-63], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.79999999999999985e38 or 1.07999999999999994e-63 < y

   1. Initial program 72.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 72.3%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 75.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 76.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 76.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 76.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in y around inf 65.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 65.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 65.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 65.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 65.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -1.79999999999999985e38 < y < 2.50000000000000007e-140

   1. Initial program 82.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 82.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 82.2%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 84.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 84.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 84.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 84.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 61.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if 2.50000000000000007e-140 < y < 3.39999999999999994e-90

   1. Initial program 74.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 74.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 74.9%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 74.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 83.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 83.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 83.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in i around inf 67.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(t \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 67.1%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + \left(--1 \cdot \left(t \cdot b\right)\right)\right)} \]

      2. mul-1-neg 67.1%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \left(-\color{blue}{\left(-t \cdot b\right)}\right)\right) \]

      3. remove-double-neg 67.1%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) + \color{blue}{t \cdot b}\right) \]

      4. +-commutative 67.1%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      5. mul-1-neg 67.1%

         \[\leadsto i \cdot \left(t \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      6. unsub-neg 67.1%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b - y \cdot j\right)} \]

      7. *-commutative 67.1%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot t} - y \cdot j\right) \]

   6. Simplified 67.1%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   if 3.39999999999999994e-90 < y < 1.07999999999999994e-63

   1. Initial program 83.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 83.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 83.3%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 83.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 83.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 83.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 83.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 83.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 68.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 68.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 68.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 68.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-140}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-90}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 15: 30.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+226}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+43}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-186}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+174}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.9e+226)
   (* t (* x (- a)))
   (if (<= a -4.2e+43)
     (* c (* a j))
     (if (<= a 1.65e-186)
       (* c (* b (- z)))
       (if (<= a 1.1e+36)
         (* z (* x y))
         (if (<= a 1.05e+174) (* j (* a c)) (* (* x t) (- a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.9e+226) {
		tmp = t * (x * -a);
	} else if (a <= -4.2e+43) {
		tmp = c * (a * j);
	} else if (a <= 1.65e-186) {
		tmp = c * (b * -z);
	} else if (a <= 1.1e+36) {
		tmp = z * (x * y);
	} else if (a <= 1.05e+174) {
		tmp = j * (a * c);
	} else {
		tmp = (x * t) * -a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.9d+226)) then
        tmp = t * (x * -a)
    else if (a <= (-4.2d+43)) then
        tmp = c * (a * j)
    else if (a <= 1.65d-186) then
        tmp = c * (b * -z)
    else if (a <= 1.1d+36) then
        tmp = z * (x * y)
    else if (a <= 1.05d+174) then
        tmp = j * (a * c)
    else
        tmp = (x * t) * -a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.9e+226) {
		tmp = t * (x * -a);
	} else if (a <= -4.2e+43) {
		tmp = c * (a * j);
	} else if (a <= 1.65e-186) {
		tmp = c * (b * -z);
	} else if (a <= 1.1e+36) {
		tmp = z * (x * y);
	} else if (a <= 1.05e+174) {
		tmp = j * (a * c);
	} else {
		tmp = (x * t) * -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.9e+226:
		tmp = t * (x * -a)
	elif a <= -4.2e+43:
		tmp = c * (a * j)
	elif a <= 1.65e-186:
		tmp = c * (b * -z)
	elif a <= 1.1e+36:
		tmp = z * (x * y)
	elif a <= 1.05e+174:
		tmp = j * (a * c)
	else:
		tmp = (x * t) * -a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.9e+226)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (a <= -4.2e+43)
		tmp = Float64(c * Float64(a * j));
	elseif (a <= 1.65e-186)
		tmp = Float64(c * Float64(b * Float64(-z)));
	elseif (a <= 1.1e+36)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 1.05e+174)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(Float64(x * t) * Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.9e+226)
		tmp = t * (x * -a);
	elseif (a <= -4.2e+43)
		tmp = c * (a * j);
	elseif (a <= 1.65e-186)
		tmp = c * (b * -z);
	elseif (a <= 1.1e+36)
		tmp = z * (x * y);
	elseif (a <= 1.05e+174)
		tmp = j * (a * c);
	else
		tmp = (x * t) * -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.9e+226], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.2e+43], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-186], N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e+36], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+174], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.89999999999999991e226

   1. Initial program 66.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 66.5%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 66.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 66.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 66.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 66.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in t around inf 54.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 54.9%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \cdot t \]

      2. associate-*r* 54.9%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x - i \cdot b\right) \cdot t\right)} \]

      3. mul-1-neg 54.9%

         \[\leadsto \color{blue}{-\left(a \cdot x - i \cdot b\right) \cdot t} \]

      4. *-commutative 54.9%

         \[\leadsto -\color{blue}{t \cdot \left(a \cdot x - i \cdot b\right)} \]

      5. *-commutative 54.9%

         \[\leadsto -t \cdot \left(a \cdot x - \color{blue}{b \cdot i}\right) \]

   6. Simplified 54.9%

      \[\leadsto \color{blue}{-t \cdot \left(a \cdot x - b \cdot i\right)} \]

   7. Taylor expanded in a around inf 47.8%

      \[\leadsto -t \cdot \color{blue}{\left(a \cdot x\right)} \]

   if -1.89999999999999991e226 < a < -4.20000000000000003e43

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 71.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 71.4%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 76.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 76.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 76.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 76.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 76.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 64.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 64.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 64.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 64.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 56.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 56.4%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 56.4%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   if -4.20000000000000003e43 < a < 1.65e-186

   1. Initial program 81.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 81.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 81.7%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 82.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 82.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 82.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 83.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 83.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 83.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 43.6%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   5. Taylor expanded in a around 0 38.1%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 38.1%

         \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

      2. distribute-lft-neg-in 38.1%

         \[\leadsto c \cdot \color{blue}{\left(\left(-b\right) \cdot z\right)} \]

      3. *-commutative 38.1%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   7. Simplified 38.1%

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   if 1.65e-186 < a < 1.1e36

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 80.2%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 84.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 84.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 84.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 86.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 86.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 86.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in z around inf 52.3%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 37.0%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if 1.1e36 < a < 1.05000000000000008e174

   1. Initial program 74.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 74.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 74.6%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 74.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 74.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 74.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 74.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 74.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 74.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 58.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 58.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 58.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 58.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 45.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 50.0%

         \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

      2. *-commutative 50.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]

   9. Simplified 50.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]

   if 1.05000000000000008e174 < a

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 66.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 70.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 70.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 70.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 70.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 70.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 70.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 92.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 92.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 92.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 92.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 73.5%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 73.5%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-out 73.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 73.5%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 73.5%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+226}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+43}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-186}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+174}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \end{array} \]

Alternative 16: 39.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+145} \lor \neg \left(x \leq 5.6 \cdot 10^{+32}\right) \land x \leq 1.05 \cdot 10^{+192}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -9.5e+145) (and (not (<= x 5.6e+32)) (<= x 1.05e+192)))
   (* z (* x y))
   (* c (- (* a j) (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -9.5e+145) || (!(x <= 5.6e+32) && (x <= 1.05e+192))) {
		tmp = z * (x * y);
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((x <= (-9.5d+145)) .or. (.not. (x <= 5.6d+32)) .and. (x <= 1.05d+192)) then
        tmp = z * (x * y)
    else
        tmp = c * ((a * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -9.5e+145) || (!(x <= 5.6e+32) && (x <= 1.05e+192))) {
		tmp = z * (x * y);
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -9.5e+145) or (not (x <= 5.6e+32) and (x <= 1.05e+192)):
		tmp = z * (x * y)
	else:
		tmp = c * ((a * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -9.5e+145) || (!(x <= 5.6e+32) && (x <= 1.05e+192)))
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -9.5e+145) || (~((x <= 5.6e+32)) && (x <= 1.05e+192)))
		tmp = z * (x * y);
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -9.5e+145], And[N[Not[LessEqual[x, 5.6e+32]], $MachinePrecision], LessEqual[x, 1.05e+192]]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.49999999999999948e145 or 5.6e32 < x < 1.04999999999999997e192

   1. Initial program 73.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 73.0%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 76.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 76.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 76.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 77.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 77.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in z around inf 72.0%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 69.0%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if -9.49999999999999948e145 < x < 5.6e32 or 1.04999999999999997e192 < x

   1. Initial program 78.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 78.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 78.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 80.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 80.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 80.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 80.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 80.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 80.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 52.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+145} \lor \neg \left(x \leq 5.6 \cdot 10^{+32}\right) \land x \leq 1.05 \cdot 10^{+192}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 17: 51.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-288}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.76 \cdot 10^{+19}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -1.25e+37)
     t_1
     (if (<= y 5.3e-288)
       (* c (- (* a j) (* z b)))
       (if (<= y 1.76e+19) (* b (- (* t i) (* z c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.25e+37) {
		tmp = t_1;
	} else if (y <= 5.3e-288) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 1.76e+19) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (y <= (-1.25d+37)) then
        tmp = t_1
    else if (y <= 5.3d-288) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= 1.76d+19) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.25e+37) {
		tmp = t_1;
	} else if (y <= 5.3e-288) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 1.76e+19) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.25e+37:
		tmp = t_1
	elif y <= 5.3e-288:
		tmp = c * ((a * j) - (z * b))
	elif y <= 1.76e+19:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.25e+37)
		tmp = t_1;
	elseif (y <= 5.3e-288)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= 1.76e+19)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.25e+37)
		tmp = t_1;
	elseif (y <= 5.3e-288)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= 1.76e+19)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+37], t$95$1, If[LessEqual[y, 5.3e-288], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.76e+19], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.24999999999999997e37 or 1.76e19 < y

   1. Initial program 71.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 71.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 71.6%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 75.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 75.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 75.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 75.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in y around inf 67.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 67.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 67.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 67.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 67.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -1.24999999999999997e37 < y < 5.3000000000000004e-288

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 80.2%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 82.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 82.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 82.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 82.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 82.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 82.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in c around inf 63.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if 5.3000000000000004e-288 < y < 1.76e19

   1. Initial program 82.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) - \left(-j\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      2. cancel-sign-sub-inv 82.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right)} \]

      3. *-commutative 82.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot a - y \cdot i\right) \]

      4. remove-double-neg 82.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 82.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 82.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 61.1%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-288}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.76 \cdot 10^{+19}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 18: 30.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+42}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{+173}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* x (- a)))))
   (if (<= a -1.55e+227)
     t_1
     (if (<= a -4.2e+42)
       (* c (* a j))
       (if (<= a 1.05e+34)
         (* z (* x y))
         (if (<= a 9.4e+173) (* j (* a c)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (x * -a);
	double tmp;
	if (a <= -1.55e+227) {
		tmp = t_1;
	} else if (a <= -4.2e+42) {
		tmp = c * (a * j);
	} else if (a <= 1.05e+34) {
		tmp = z * (x * y);
	} else if (a <= 9.4e+173) {
		tmp = j * (a * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x * -a)
    if (a <= (-1.55d+227)) then
        tmp = t_1
    else if (a <= (-4.2d+42)) then
        tmp = c * (a * j)
    else if (a <= 1.05d+34) then
        tmp = z * (x * y)
    else if (a <= 9.4d+173) then
        tmp = j * (a * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (x * -a);
	double tmp;
	if (a <= -1.55e+227) {
		tmp = t_1;
	} else if (a <= -4.2e+42) {
		tmp = c * (a * j);
	} else if (a <= 1.05e+34) {
		tmp = z * (x * y);
	} else if (a <= 9.4e+173) {
		tmp = j * (a * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (x * -a)
	tmp = 0
	if a <= -1.55e+227:
		tmp = t_1
	elif a <= -4.2e+42:
		tmp = c * (a * j)
	elif a <= 1.05e+34:
		tmp = z * (x * y)
	elif a <= 9.4e+173:
		tmp = j * (a * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(x * Float64(-a)))
	tmp = 0.0
	if (a <= -1.55e+227)
		tmp = t_1;
	elseif (a <= -4.2e+42)
		tmp = Float64(c * Float64(a * j));
	elseif (a <= 1.05e+34)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 9.4e+173)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (x * -a);
	tmp = 0.0;
	if (a <= -1.55e+227)
		tmp = t_1;
	elseif (a <= -4.2e+42)
		tmp = c * (a * j);
	elseif (a <= 1.05e+34)
		tmp = z * (x * y);
	elseif (a <= 9.4e+173)
		tmp = j * (a * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e+227], t$95$1, If[LessEqual[a, -4.2e+42], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+34], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.4e+173], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.5499999999999999e227 or 9.4000000000000003e173 < a

   1. Initial program 66.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 66.2%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 68.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 68.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 68.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 68.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 68.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 68.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in t around inf 69.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 69.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \cdot t \]

      2. associate-*r* 69.0%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x - i \cdot b\right) \cdot t\right)} \]

      3. mul-1-neg 69.0%

         \[\leadsto \color{blue}{-\left(a \cdot x - i \cdot b\right) \cdot t} \]

      4. *-commutative 69.0%

         \[\leadsto -\color{blue}{t \cdot \left(a \cdot x - i \cdot b\right)} \]

      5. *-commutative 69.0%

         \[\leadsto -t \cdot \left(a \cdot x - \color{blue}{b \cdot i}\right) \]

   6. Simplified 69.0%

      \[\leadsto \color{blue}{-t \cdot \left(a \cdot x - b \cdot i\right)} \]

   7. Taylor expanded in a around inf 64.0%

      \[\leadsto -t \cdot \color{blue}{\left(a \cdot x\right)} \]

   if -1.5499999999999999e227 < a < -4.19999999999999991e42

   1. Initial program 72.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 72.8%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 77.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 77.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 77.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 77.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 77.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 77.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 61.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 61.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 61.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 61.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 53.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 53.8%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 53.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   if -4.19999999999999991e42 < a < 1.05000000000000009e34

   1. Initial program 81.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 81.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 81.0%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 83.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 83.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 83.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 84.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 84.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 84.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in z around inf 58.2%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 32.9%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if 1.05000000000000009e34 < a < 9.4000000000000003e173

   1. Initial program 74.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 74.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 74.6%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 74.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 74.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 74.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 74.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 74.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 74.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 58.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 58.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 58.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 58.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 45.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 50.0%

         \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

      2. *-commutative 50.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]

   9. Simplified 50.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+227}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+42}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{+173}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]

Alternative 19: 30.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+224}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{+42}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{+174}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -4e+224)
   (* t (* x (- a)))
   (if (<= a -1.25e+42)
     (* c (* a j))
     (if (<= a 9e+33)
       (* z (* x y))
       (if (<= a 1.16e+174) (* j (* a c)) (* (* x t) (- a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -4e+224) {
		tmp = t * (x * -a);
	} else if (a <= -1.25e+42) {
		tmp = c * (a * j);
	} else if (a <= 9e+33) {
		tmp = z * (x * y);
	} else if (a <= 1.16e+174) {
		tmp = j * (a * c);
	} else {
		tmp = (x * t) * -a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-4d+224)) then
        tmp = t * (x * -a)
    else if (a <= (-1.25d+42)) then
        tmp = c * (a * j)
    else if (a <= 9d+33) then
        tmp = z * (x * y)
    else if (a <= 1.16d+174) then
        tmp = j * (a * c)
    else
        tmp = (x * t) * -a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -4e+224) {
		tmp = t * (x * -a);
	} else if (a <= -1.25e+42) {
		tmp = c * (a * j);
	} else if (a <= 9e+33) {
		tmp = z * (x * y);
	} else if (a <= 1.16e+174) {
		tmp = j * (a * c);
	} else {
		tmp = (x * t) * -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -4e+224:
		tmp = t * (x * -a)
	elif a <= -1.25e+42:
		tmp = c * (a * j)
	elif a <= 9e+33:
		tmp = z * (x * y)
	elif a <= 1.16e+174:
		tmp = j * (a * c)
	else:
		tmp = (x * t) * -a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -4e+224)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (a <= -1.25e+42)
		tmp = Float64(c * Float64(a * j));
	elseif (a <= 9e+33)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 1.16e+174)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(Float64(x * t) * Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -4e+224)
		tmp = t * (x * -a);
	elseif (a <= -1.25e+42)
		tmp = c * (a * j);
	elseif (a <= 9e+33)
		tmp = z * (x * y);
	elseif (a <= 1.16e+174)
		tmp = j * (a * c);
	else
		tmp = (x * t) * -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -4e+224], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.25e+42], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+33], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.16e+174], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.99999999999999988e224

   1. Initial program 66.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 66.5%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 66.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 66.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 66.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 66.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 66.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in t around inf 54.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 54.9%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \cdot t \]

      2. associate-*r* 54.9%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot x - i \cdot b\right) \cdot t\right)} \]

      3. mul-1-neg 54.9%

         \[\leadsto \color{blue}{-\left(a \cdot x - i \cdot b\right) \cdot t} \]

      4. *-commutative 54.9%

         \[\leadsto -\color{blue}{t \cdot \left(a \cdot x - i \cdot b\right)} \]

      5. *-commutative 54.9%

         \[\leadsto -t \cdot \left(a \cdot x - \color{blue}{b \cdot i}\right) \]

   6. Simplified 54.9%

      \[\leadsto \color{blue}{-t \cdot \left(a \cdot x - b \cdot i\right)} \]

   7. Taylor expanded in a around inf 47.8%

      \[\leadsto -t \cdot \color{blue}{\left(a \cdot x\right)} \]

   if -3.99999999999999988e224 < a < -1.25000000000000002e42

   1. Initial program 72.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 72.8%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 77.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 77.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 77.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 77.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 77.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 77.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 61.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 61.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 61.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 61.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 53.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 53.8%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 53.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   if -1.25000000000000002e42 < a < 9.0000000000000001e33

   1. Initial program 81.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 81.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 81.0%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 83.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 83.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 83.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 84.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 84.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 84.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in z around inf 58.2%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 32.9%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if 9.0000000000000001e33 < a < 1.16000000000000003e174

   1. Initial program 74.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 74.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 74.6%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 74.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 74.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 74.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 74.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 74.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 74.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 58.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 58.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 58.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 58.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 45.9%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 50.0%

         \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

      2. *-commutative 50.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]

   9. Simplified 50.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]

   if 1.16000000000000003e174 < a

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 66.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 70.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 70.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 70.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 70.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 70.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 70.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 92.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 92.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 92.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 92.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 73.5%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 73.5%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-out 73.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 73.5%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 73.5%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+224}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{+42}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{+174}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \end{array} \]

Alternative 20: 30.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+71} \lor \neg \left(x \leq 7.8 \cdot 10^{+24}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -6.8e+71) (not (<= x 7.8e+24))) (* y (* x z)) (* c (* a j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -6.8e+71) || !(x <= 7.8e+24)) {
		tmp = y * (x * z);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((x <= (-6.8d+71)) .or. (.not. (x <= 7.8d+24))) then
        tmp = y * (x * z)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -6.8e+71) || !(x <= 7.8e+24)) {
		tmp = y * (x * z);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -6.8e+71) or not (x <= 7.8e+24):
		tmp = y * (x * z)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -6.8e+71) || !(x <= 7.8e+24))
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -6.8e+71) || ~((x <= 7.8e+24)))
		tmp = y * (x * z);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -6.8e+71], N[Not[LessEqual[x, 7.8e+24]], $MachinePrecision]], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.7999999999999997e71 or 7.7999999999999995e24 < x

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 74.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 74.8%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 78.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 79.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 79.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in i around 0 66.4%

      \[\leadsto \color{blue}{\left(\left(y \cdot z - a \cdot t\right) \cdot x + c \cdot \left(a \cdot j\right)\right) - c \cdot \left(b \cdot z\right)} \]

   5. Taylor expanded in y around inf 48.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -6.7999999999999997e71 < x < 7.7999999999999995e24

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 78.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 78.3%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 79.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 80.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 80.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 80.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 38.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 38.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 38.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 38.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 30.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 30.8%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 30.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+71} \lor \neg \left(x \leq 7.8 \cdot 10^{+24}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 21: 30.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-15} \lor \neg \left(y \leq 1.35 \cdot 10^{-64}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -1.6e-15) (not (<= y 1.35e-64))) (* z (* x y)) (* c (* a j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -1.6e-15) || !(y <= 1.35e-64)) {
		tmp = z * (x * y);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-1.6d-15)) .or. (.not. (y <= 1.35d-64))) then
        tmp = z * (x * y)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -1.6e-15) || !(y <= 1.35e-64)) {
		tmp = z * (x * y);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -1.6e-15) or not (y <= 1.35e-64):
		tmp = z * (x * y)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -1.6e-15) || !(y <= 1.35e-64))
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -1.6e-15) || ~((y <= 1.35e-64)))
		tmp = z * (x * y);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -1.6e-15], N[Not[LessEqual[y, 1.35e-64]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e-15 or 1.34999999999999993e-64 < y

   1. Initial program 72.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 72.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 72.7%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 76.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 76.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 76.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 77.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 77.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in z around inf 57.5%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 43.5%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if -1.6e-15 < y < 1.34999999999999993e-64

   1. Initial program 82.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 82.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 82.1%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 82.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 82.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 82.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 83.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 83.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 45.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 45.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 45.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 45.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 32.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 32.4%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 32.4%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-15} \lor \neg \left(y \leq 1.35 \cdot 10^{-64}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 22: 22.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-221}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -3.7e-221) (* j (* a c)) (* c (* a j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -3.7e-221) {
		tmp = j * (a * c);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-3.7d-221)) then
        tmp = j * (a * c)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -3.7e-221) {
		tmp = j * (a * c);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -3.7e-221:
		tmp = j * (a * c)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -3.7e-221)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -3.7e-221)
		tmp = j * (a * c);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -3.7e-221], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.69999999999999985e-221

   1. Initial program 77.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 77.4%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 80.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 80.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 80.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 81.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 81.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 39.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 39.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 39.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 39.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 19.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 23.5%

         \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

      2. *-commutative 23.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]

   9. Simplified 23.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a\right)} \]

   if -3.69999999999999985e-221 < x

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. associate-+r- 76.4%

         \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

      3. fma-def 78.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

      4. *-commutative 78.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

      5. *-commutative 78.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

      6. fma-neg 79.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

      7. distribute-rgt-neg-in 79.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

   4. Taylor expanded in a around inf 36.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 36.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      2. unsub-neg 36.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 36.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 27.6%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 27.6%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 27.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-221}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 23: 22.6% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.8%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. +-commutative 76.8%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

   2. associate-+r- 76.8%

      \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

   3. fma-def 79.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

   4. *-commutative 79.1%

      \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

   5. *-commutative 79.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

   6. fma-neg 79.9%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

   7. distribute-rgt-neg-in 79.9%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

3. Simplified 79.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

4. Taylor expanded in a around inf 37.3%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
5. Step-by-step derivation

   1. mul-1-neg 37.3%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   2. unsub-neg 37.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

6. Simplified 37.3%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

7. Taylor expanded in c around inf 22.7%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
8. Step-by-step derivation

   1. *-commutative 22.7%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

9. Simplified 22.7%

   \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

10. Final simplification 22.7%

    \[\leadsto a \cdot \left(c \cdot j\right) \]

Alternative 24: 22.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ c \cdot \left(a \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* c (* a j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return c * (a * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = c * (a * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return c * (a * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return c * (a * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(c * Float64(a * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = c * (a * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.8%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. +-commutative 76.8%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

   2. associate-+r- 76.8%

      \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot a - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

   3. fma-def 79.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right) \]

   4. *-commutative 79.1%

      \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right) \]

   5. *-commutative 79.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) \]

   6. fma-neg 79.9%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)} \]

   7. distribute-rgt-neg-in 79.9%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{t \cdot \left(-i\right)}\right) \]

3. Simplified 79.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)} \]

4. Taylor expanded in a around inf 37.3%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]
5. Step-by-step derivation

   1. mul-1-neg 37.3%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   2. unsub-neg 37.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

6. Simplified 37.3%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

7. Taylor expanded in c around inf 24.2%

   \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
8. Step-by-step derivation

   1. *-commutative 24.2%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

9. Simplified 24.2%

   \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

10. Final simplification 24.2%

    \[\leadsto c \cdot \left(a \cdot j\right) \]

Developer target: 60.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023176 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))