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

Percentage Accurate: 73.2% → 81.4%

Time: 31.4s

Alternatives: 26

Speedup: 0.5×

• 58.2% 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: 73.2% 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: 81.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t\_1 - b \cdot \left(z \cdot c - t \cdot i\right)\\ t_3 := a \cdot c - y \cdot i\\ \mathbf{if}\;t\_2 + j \cdot t\_3 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, t\_3, t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (- t_1 (* b (- (* z c) (* t i)))))
        (t_3 (- (* a c) (* y i))))
   (if (<= (+ t_2 (* j t_3)) INFINITY) (fma j t_3 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 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (b * ((z * c) - (t * i)));
	double t_3 = (a * c) - (y * i);
	double tmp;
	if ((t_2 + (j * t_3)) <= ((double) INFINITY)) {
		tmp = fma(j, t_3, t_2);
	} else {
		tmp = t_1;
	}
	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(t_1 - Float64(b * Float64(Float64(z * c) - Float64(t * i))))
	t_3 = Float64(Float64(a * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(t_2 + Float64(j * t_3)) <= Inf)
		tmp = fma(j, t_3, t_2);
	else
		tmp = t_1;
	end
	return 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[(t$95$1 - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 + N[(j * t$95$3), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$3 + t$95$2), $MachinePrecision], t$95$1]]]]

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 92.2%

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

      1. +-commutative 92.2%

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

      2. fma-define 92.2%

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

      3. *-commutative 92.2%

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

      4. *-commutative 92.2%

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

   3. Simplified 92.2%

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

   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. Add Preprocessing

   3. Taylor expanded in x around inf 50.5%

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

4. Final simplification 83.1%

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

Alternative 2: 55.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot b\right) \cdot \left(i - a \cdot \frac{x}{b}\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := t\_2 + x \cdot \left(y \cdot z\right)\\ t_4 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -13200000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-81}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-130}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-267}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-304}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-188}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-138}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-40}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+226}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* t b) (- i (* a (/ x b)))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (+ t_2 (* x (* y z))))
        (t_4 (* c (- (* a j) (* z b)))))
   (if (<= t -3.3e+95)
     (* t (- (* b i) (* x a)))
     (if (<= t -6.6e+65)
       t_2
       (if (<= t -13200000000000.0)
         t_1
         (if (<= t -1.8e-81)
           t_3
           (if (<= t -6.5e-130)
             (* z (- (* x y) (* b c)))
             (if (<= t -9.5e-267)
               t_3
               (if (<= t 1.65e-304)
                 t_4
                 (if (<= t 3.2e-188)
                   t_3
                   (if (<= t 1.12e-138)
                     t_4
                     (if (<= t 6.2e-40)
                       t_3
                       (if (<= t 1.56e+40)
                         (* x (- (* y z) (* t a)))
                         (if (<= t 1.85e+226)
                           (* i (- (* t b) (* y j)))
                           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 * b) * (i - (a * (x / b)));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_2 + (x * (y * z));
	double t_4 = c * ((a * j) - (z * b));
	double tmp;
	if (t <= -3.3e+95) {
		tmp = t * ((b * i) - (x * a));
	} else if (t <= -6.6e+65) {
		tmp = t_2;
	} else if (t <= -13200000000000.0) {
		tmp = t_1;
	} else if (t <= -1.8e-81) {
		tmp = t_3;
	} else if (t <= -6.5e-130) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= -9.5e-267) {
		tmp = t_3;
	} else if (t <= 1.65e-304) {
		tmp = t_4;
	} else if (t <= 3.2e-188) {
		tmp = t_3;
	} else if (t <= 1.12e-138) {
		tmp = t_4;
	} else if (t <= 6.2e-40) {
		tmp = t_3;
	} else if (t <= 1.56e+40) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 1.85e+226) {
		tmp = i * ((t * b) - (y * j));
	} 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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (t * b) * (i - (a * (x / b)))
    t_2 = j * ((a * c) - (y * i))
    t_3 = t_2 + (x * (y * z))
    t_4 = c * ((a * j) - (z * b))
    if (t <= (-3.3d+95)) then
        tmp = t * ((b * i) - (x * a))
    else if (t <= (-6.6d+65)) then
        tmp = t_2
    else if (t <= (-13200000000000.0d0)) then
        tmp = t_1
    else if (t <= (-1.8d-81)) then
        tmp = t_3
    else if (t <= (-6.5d-130)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= (-9.5d-267)) then
        tmp = t_3
    else if (t <= 1.65d-304) then
        tmp = t_4
    else if (t <= 3.2d-188) then
        tmp = t_3
    else if (t <= 1.12d-138) then
        tmp = t_4
    else if (t <= 6.2d-40) then
        tmp = t_3
    else if (t <= 1.56d+40) then
        tmp = x * ((y * z) - (t * a))
    else if (t <= 1.85d+226) then
        tmp = i * ((t * b) - (y * j))
    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 * b) * (i - (a * (x / b)));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_2 + (x * (y * z));
	double t_4 = c * ((a * j) - (z * b));
	double tmp;
	if (t <= -3.3e+95) {
		tmp = t * ((b * i) - (x * a));
	} else if (t <= -6.6e+65) {
		tmp = t_2;
	} else if (t <= -13200000000000.0) {
		tmp = t_1;
	} else if (t <= -1.8e-81) {
		tmp = t_3;
	} else if (t <= -6.5e-130) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= -9.5e-267) {
		tmp = t_3;
	} else if (t <= 1.65e-304) {
		tmp = t_4;
	} else if (t <= 3.2e-188) {
		tmp = t_3;
	} else if (t <= 1.12e-138) {
		tmp = t_4;
	} else if (t <= 6.2e-40) {
		tmp = t_3;
	} else if (t <= 1.56e+40) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 1.85e+226) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * b) * (i - (a * (x / b)))
	t_2 = j * ((a * c) - (y * i))
	t_3 = t_2 + (x * (y * z))
	t_4 = c * ((a * j) - (z * b))
	tmp = 0
	if t <= -3.3e+95:
		tmp = t * ((b * i) - (x * a))
	elif t <= -6.6e+65:
		tmp = t_2
	elif t <= -13200000000000.0:
		tmp = t_1
	elif t <= -1.8e-81:
		tmp = t_3
	elif t <= -6.5e-130:
		tmp = z * ((x * y) - (b * c))
	elif t <= -9.5e-267:
		tmp = t_3
	elif t <= 1.65e-304:
		tmp = t_4
	elif t <= 3.2e-188:
		tmp = t_3
	elif t <= 1.12e-138:
		tmp = t_4
	elif t <= 6.2e-40:
		tmp = t_3
	elif t <= 1.56e+40:
		tmp = x * ((y * z) - (t * a))
	elif t <= 1.85e+226:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * b) * Float64(i - Float64(a * Float64(x / b))))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(t_2 + Float64(x * Float64(y * z)))
	t_4 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (t <= -3.3e+95)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (t <= -6.6e+65)
		tmp = t_2;
	elseif (t <= -13200000000000.0)
		tmp = t_1;
	elseif (t <= -1.8e-81)
		tmp = t_3;
	elseif (t <= -6.5e-130)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= -9.5e-267)
		tmp = t_3;
	elseif (t <= 1.65e-304)
		tmp = t_4;
	elseif (t <= 3.2e-188)
		tmp = t_3;
	elseif (t <= 1.12e-138)
		tmp = t_4;
	elseif (t <= 6.2e-40)
		tmp = t_3;
	elseif (t <= 1.56e+40)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (t <= 1.85e+226)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	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 * b) * (i - (a * (x / b)));
	t_2 = j * ((a * c) - (y * i));
	t_3 = t_2 + (x * (y * z));
	t_4 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (t <= -3.3e+95)
		tmp = t * ((b * i) - (x * a));
	elseif (t <= -6.6e+65)
		tmp = t_2;
	elseif (t <= -13200000000000.0)
		tmp = t_1;
	elseif (t <= -1.8e-81)
		tmp = t_3;
	elseif (t <= -6.5e-130)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= -9.5e-267)
		tmp = t_3;
	elseif (t <= 1.65e-304)
		tmp = t_4;
	elseif (t <= 3.2e-188)
		tmp = t_3;
	elseif (t <= 1.12e-138)
		tmp = t_4;
	elseif (t <= 6.2e-40)
		tmp = t_3;
	elseif (t <= 1.56e+40)
		tmp = x * ((y * z) - (t * a));
	elseif (t <= 1.85e+226)
		tmp = i * ((t * b) - (y * j));
	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[(N[(t * b), $MachinePrecision] * N[(i - N[(a * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e+95], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.6e+65], t$95$2, If[LessEqual[t, -13200000000000.0], t$95$1, If[LessEqual[t, -1.8e-81], t$95$3, If[LessEqual[t, -6.5e-130], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.5e-267], t$95$3, If[LessEqual[t, 1.65e-304], t$95$4, If[LessEqual[t, 3.2e-188], t$95$3, If[LessEqual[t, 1.12e-138], t$95$4, If[LessEqual[t, 6.2e-40], t$95$3, If[LessEqual[t, 1.56e+40], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+226], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -3.2999999999999998e95

   1. Initial program 60.8%

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

   3. Taylor expanded in t around inf 71.6%

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

      1. distribute-lft-out-- 71.6%

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

      2. *-commutative 71.6%

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

   5. Simplified 71.6%

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

   if -3.2999999999999998e95 < t < -6.60000000000000046e65

   1. Initial program 34.0%

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

   3. Taylor expanded in j around inf 78.2%

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

   if -6.60000000000000046e65 < t < -1.32e13 or 1.84999999999999991e226 < t

   1. Initial program 70.3%

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

   3. Taylor expanded in b around inf 66.4%

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

      1. fma-define 70.1%

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

      2. associate-/l* 66.6%

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

   5. Simplified 66.6%

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

   6. Taylor expanded in t around inf 70.6%

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

      1. associate-*r* 74.2%

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

      2. *-commutative 74.2%

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

      3. mul-1-neg 74.2%

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

      4. unsub-neg 74.2%

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

      5. associate-/l* 77.8%

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

   8. Simplified 77.8%

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

   if -1.32e13 < t < -1.7999999999999999e-81 or -6.5000000000000002e-130 < t < -9.49999999999999985e-267 or 1.65000000000000006e-304 < t < 3.20000000000000022e-188 or 1.1199999999999999e-138 < t < 6.20000000000000021e-40

   1. Initial program 85.0%

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

   3. Taylor expanded in b around 0 86.1%

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

   4. Taylor expanded in y around inf 76.5%

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

   if -1.7999999999999999e-81 < t < -6.5000000000000002e-130

   1. Initial program 67.3%

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

   3. Taylor expanded in z around inf 89.6%

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

      1. *-commutative 89.6%

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

      2. *-commutative 89.6%

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

   5. Simplified 89.6%

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

   if -9.49999999999999985e-267 < t < 1.65000000000000006e-304 or 3.20000000000000022e-188 < t < 1.1199999999999999e-138

   1. Initial program 60.5%

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

   3. Taylor expanded in c around inf 85.8%

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

      1. *-commutative 85.8%

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

   5. Simplified 85.8%

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

   if 6.20000000000000021e-40 < t < 1.56e40

   1. Initial program 92.1%

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

   3. Taylor expanded in x around inf 77.3%

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

   if 1.56e40 < t < 1.84999999999999991e226

   1. Initial program 67.0%

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

   3. Taylor expanded in i around -inf 67.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{+65}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -13200000000000:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(i - a \cdot \frac{x}{b}\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-81}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-130}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-267}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-188}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-138}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-40}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+226}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(i - a \cdot \frac{x}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 55.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t\_1 + x \cdot \left(y \cdot z\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-81}:\\ \;\;\;\;t\_1 - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-130}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-264}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-304}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-188}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-139}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+226}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(i - a \cdot \frac{x}{b}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ t_1 (* x (* y z))))
        (t_3 (* c (- (* a j) (* z b)))))
   (if (<= t -6.8e+95)
     (* t (- (* b i) (* x a)))
     (if (<= t -7e+65)
       t_1
       (if (<= t -4.2e+23)
         (* b (- (* t i) (* z c)))
         (if (<= t -3.7e-81)
           (- t_1 (* a (* x t)))
           (if (<= t -1.05e-130)
             (* z (- (* x y) (* b c)))
             (if (<= t -8.5e-264)
               t_2
               (if (<= t 1.65e-304)
                 t_3
                 (if (<= t 1.7e-188)
                   t_2
                   (if (<= t 6e-139)
                     t_3
                     (if (<= t 7e-40)
                       t_2
                       (if (<= t 1.02e+39)
                         (* x (- (* y z) (* t a)))
                         (if (<= t 2.2e+226)
                           (* i (- (* t b) (* y j)))
                           (* (* t b) (- i (* a (/ x b))))))))))))))))))

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 * ((a * c) - (y * i));
	double t_2 = t_1 + (x * (y * z));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (t <= -6.8e+95) {
		tmp = t * ((b * i) - (x * a));
	} else if (t <= -7e+65) {
		tmp = t_1;
	} else if (t <= -4.2e+23) {
		tmp = b * ((t * i) - (z * c));
	} else if (t <= -3.7e-81) {
		tmp = t_1 - (a * (x * t));
	} else if (t <= -1.05e-130) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= -8.5e-264) {
		tmp = t_2;
	} else if (t <= 1.65e-304) {
		tmp = t_3;
	} else if (t <= 1.7e-188) {
		tmp = t_2;
	} else if (t <= 6e-139) {
		tmp = t_3;
	} else if (t <= 7e-40) {
		tmp = t_2;
	} else if (t <= 1.02e+39) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 2.2e+226) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (t * b) * (i - (a * (x / 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t_1 + (x * (y * z))
    t_3 = c * ((a * j) - (z * b))
    if (t <= (-6.8d+95)) then
        tmp = t * ((b * i) - (x * a))
    else if (t <= (-7d+65)) then
        tmp = t_1
    else if (t <= (-4.2d+23)) then
        tmp = b * ((t * i) - (z * c))
    else if (t <= (-3.7d-81)) then
        tmp = t_1 - (a * (x * t))
    else if (t <= (-1.05d-130)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= (-8.5d-264)) then
        tmp = t_2
    else if (t <= 1.65d-304) then
        tmp = t_3
    else if (t <= 1.7d-188) then
        tmp = t_2
    else if (t <= 6d-139) then
        tmp = t_3
    else if (t <= 7d-40) then
        tmp = t_2
    else if (t <= 1.02d+39) then
        tmp = x * ((y * z) - (t * a))
    else if (t <= 2.2d+226) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = (t * b) * (i - (a * (x / 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 t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 + (x * (y * z));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (t <= -6.8e+95) {
		tmp = t * ((b * i) - (x * a));
	} else if (t <= -7e+65) {
		tmp = t_1;
	} else if (t <= -4.2e+23) {
		tmp = b * ((t * i) - (z * c));
	} else if (t <= -3.7e-81) {
		tmp = t_1 - (a * (x * t));
	} else if (t <= -1.05e-130) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= -8.5e-264) {
		tmp = t_2;
	} else if (t <= 1.65e-304) {
		tmp = t_3;
	} else if (t <= 1.7e-188) {
		tmp = t_2;
	} else if (t <= 6e-139) {
		tmp = t_3;
	} else if (t <= 7e-40) {
		tmp = t_2;
	} else if (t <= 1.02e+39) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 2.2e+226) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (t * b) * (i - (a * (x / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t_1 + (x * (y * z))
	t_3 = c * ((a * j) - (z * b))
	tmp = 0
	if t <= -6.8e+95:
		tmp = t * ((b * i) - (x * a))
	elif t <= -7e+65:
		tmp = t_1
	elif t <= -4.2e+23:
		tmp = b * ((t * i) - (z * c))
	elif t <= -3.7e-81:
		tmp = t_1 - (a * (x * t))
	elif t <= -1.05e-130:
		tmp = z * ((x * y) - (b * c))
	elif t <= -8.5e-264:
		tmp = t_2
	elif t <= 1.65e-304:
		tmp = t_3
	elif t <= 1.7e-188:
		tmp = t_2
	elif t <= 6e-139:
		tmp = t_3
	elif t <= 7e-40:
		tmp = t_2
	elif t <= 1.02e+39:
		tmp = x * ((y * z) - (t * a))
	elif t <= 2.2e+226:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = (t * b) * (i - (a * (x / b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t_1 + Float64(x * Float64(y * z)))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (t <= -6.8e+95)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (t <= -7e+65)
		tmp = t_1;
	elseif (t <= -4.2e+23)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (t <= -3.7e-81)
		tmp = Float64(t_1 - Float64(a * Float64(x * t)));
	elseif (t <= -1.05e-130)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= -8.5e-264)
		tmp = t_2;
	elseif (t <= 1.65e-304)
		tmp = t_3;
	elseif (t <= 1.7e-188)
		tmp = t_2;
	elseif (t <= 6e-139)
		tmp = t_3;
	elseif (t <= 7e-40)
		tmp = t_2;
	elseif (t <= 1.02e+39)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (t <= 2.2e+226)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(t * b) * Float64(i - Float64(a * Float64(x / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t_1 + (x * (y * z));
	t_3 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (t <= -6.8e+95)
		tmp = t * ((b * i) - (x * a));
	elseif (t <= -7e+65)
		tmp = t_1;
	elseif (t <= -4.2e+23)
		tmp = b * ((t * i) - (z * c));
	elseif (t <= -3.7e-81)
		tmp = t_1 - (a * (x * t));
	elseif (t <= -1.05e-130)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= -8.5e-264)
		tmp = t_2;
	elseif (t <= 1.65e-304)
		tmp = t_3;
	elseif (t <= 1.7e-188)
		tmp = t_2;
	elseif (t <= 6e-139)
		tmp = t_3;
	elseif (t <= 7e-40)
		tmp = t_2;
	elseif (t <= 1.02e+39)
		tmp = x * ((y * z) - (t * a));
	elseif (t <= 2.2e+226)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = (t * b) * (i - (a * (x / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e+95], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7e+65], t$95$1, If[LessEqual[t, -4.2e+23], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.7e-81], N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.05e-130], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.5e-264], t$95$2, If[LessEqual[t, 1.65e-304], t$95$3, If[LessEqual[t, 1.7e-188], t$95$2, If[LessEqual[t, 6e-139], t$95$3, If[LessEqual[t, 7e-40], t$95$2, If[LessEqual[t, 1.02e+39], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e+226], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * b), $MachinePrecision] * N[(i - N[(a * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if t < -6.80000000000000043e95

   1. Initial program 60.8%

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

   3. Taylor expanded in t around inf 71.6%

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

      1. distribute-lft-out-- 71.6%

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

      2. *-commutative 71.6%

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

   5. Simplified 71.6%

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

   if -6.80000000000000043e95 < t < -7.0000000000000002e65

   1. Initial program 34.0%

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

   3. Taylor expanded in j around inf 78.2%

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

   if -7.0000000000000002e65 < t < -4.2000000000000003e23

   1. Initial program 79.4%

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

   3. Taylor expanded in b around inf 97.0%

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

   if -4.2000000000000003e23 < t < -3.69999999999999986e-81

   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. Add Preprocessing

   3. Taylor expanded in b around 0 88.0%

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

   4. Taylor expanded in z around 0 82.2%

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

      1. +-commutative 82.2%

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

      2. mul-1-neg 82.2%

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

      3. unsub-neg 82.2%

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

      4. *-commutative 82.2%

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

   6. Simplified 82.2%

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

   if -3.69999999999999986e-81 < t < -1.05000000000000001e-130

   1. Initial program 67.3%

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

   3. Taylor expanded in z around inf 89.6%

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

      1. *-commutative 89.6%

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

      2. *-commutative 89.6%

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

   5. Simplified 89.6%

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

   if -1.05000000000000001e-130 < t < -8.5000000000000001e-264 or 1.65000000000000006e-304 < t < 1.70000000000000014e-188 or 5.9999999999999998e-139 < t < 7.0000000000000003e-40

   1. Initial program 85.9%

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

   3. Taylor expanded in b around 0 85.9%

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

   4. Taylor expanded in y around inf 76.8%

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

   if -8.5000000000000001e-264 < t < 1.65000000000000006e-304 or 1.70000000000000014e-188 < t < 5.9999999999999998e-139

   1. Initial program 60.5%

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

   3. Taylor expanded in c around inf 85.8%

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

      1. *-commutative 85.8%

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

   5. Simplified 85.8%

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

   if 7.0000000000000003e-40 < t < 1.02e39

   1. Initial program 92.1%

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

   3. Taylor expanded in x around inf 77.3%

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

   if 1.02e39 < t < 2.19999999999999994e226

   1. Initial program 67.0%

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

   3. Taylor expanded in i around -inf 67.4%

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

   if 2.19999999999999994e226 < t

   1. Initial program 66.8%

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

   3. Taylor expanded in b around inf 61.9%

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

      1. fma-define 66.6%

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

      2. associate-/l* 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in t around inf 67.5%

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

      1. associate-*r* 71.9%

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

      2. *-commutative 71.9%

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

      3. mul-1-neg 71.9%

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

      4. unsub-neg 71.9%

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

      5. associate-/l* 76.5%

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

   8. Simplified 76.5%

      \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot \left(i - a \cdot \frac{x}{b}\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+65}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-81}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-130}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-264}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-188}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-139}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-40}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+226}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(i - a \cdot \frac{x}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;t \leq -4 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+26}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-129}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-258}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-304}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-190}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-138}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+226}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(i - a \cdot \frac{x}{b}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ (* x (- (* y z) (* t a))) t_1))
        (t_3 (* c (- (* a j) (* z b)))))
   (if (<= t -4e+95)
     (* t (- (* b i) (* x a)))
     (if (<= t -9e+65)
       t_1
       (if (<= t -2.7e+26)
         (* b (- (* t i) (* z c)))
         (if (<= t -2.9e-81)
           t_2
           (if (<= t -3.5e-129)
             (* z (- (* x y) (* b c)))
             (if (<= t -1.1e-258)
               t_2
               (if (<= t 1.55e-304)
                 t_3
                 (if (<= t 5.8e-190)
                   t_2
                   (if (<= t 2.2e-138)
                     t_3
                     (if (<= t 5.2e+40)
                       t_2
                       (if (<= t 1.85e+226)
                         (* i (- (* t b) (* y j)))
                         (* (* t b) (- i (* a (/ x b)))))))))))))))))

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 * ((a * c) - (y * i));
	double t_2 = (x * ((y * z) - (t * a))) + t_1;
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (t <= -4e+95) {
		tmp = t * ((b * i) - (x * a));
	} else if (t <= -9e+65) {
		tmp = t_1;
	} else if (t <= -2.7e+26) {
		tmp = b * ((t * i) - (z * c));
	} else if (t <= -2.9e-81) {
		tmp = t_2;
	} else if (t <= -3.5e-129) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= -1.1e-258) {
		tmp = t_2;
	} else if (t <= 1.55e-304) {
		tmp = t_3;
	} else if (t <= 5.8e-190) {
		tmp = t_2;
	} else if (t <= 2.2e-138) {
		tmp = t_3;
	} else if (t <= 5.2e+40) {
		tmp = t_2;
	} else if (t <= 1.85e+226) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (t * b) * (i - (a * (x / 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = (x * ((y * z) - (t * a))) + t_1
    t_3 = c * ((a * j) - (z * b))
    if (t <= (-4d+95)) then
        tmp = t * ((b * i) - (x * a))
    else if (t <= (-9d+65)) then
        tmp = t_1
    else if (t <= (-2.7d+26)) then
        tmp = b * ((t * i) - (z * c))
    else if (t <= (-2.9d-81)) then
        tmp = t_2
    else if (t <= (-3.5d-129)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= (-1.1d-258)) then
        tmp = t_2
    else if (t <= 1.55d-304) then
        tmp = t_3
    else if (t <= 5.8d-190) then
        tmp = t_2
    else if (t <= 2.2d-138) then
        tmp = t_3
    else if (t <= 5.2d+40) then
        tmp = t_2
    else if (t <= 1.85d+226) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = (t * b) * (i - (a * (x / 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 t_1 = j * ((a * c) - (y * i));
	double t_2 = (x * ((y * z) - (t * a))) + t_1;
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (t <= -4e+95) {
		tmp = t * ((b * i) - (x * a));
	} else if (t <= -9e+65) {
		tmp = t_1;
	} else if (t <= -2.7e+26) {
		tmp = b * ((t * i) - (z * c));
	} else if (t <= -2.9e-81) {
		tmp = t_2;
	} else if (t <= -3.5e-129) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= -1.1e-258) {
		tmp = t_2;
	} else if (t <= 1.55e-304) {
		tmp = t_3;
	} else if (t <= 5.8e-190) {
		tmp = t_2;
	} else if (t <= 2.2e-138) {
		tmp = t_3;
	} else if (t <= 5.2e+40) {
		tmp = t_2;
	} else if (t <= 1.85e+226) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (t * b) * (i - (a * (x / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = (x * ((y * z) - (t * a))) + t_1
	t_3 = c * ((a * j) - (z * b))
	tmp = 0
	if t <= -4e+95:
		tmp = t * ((b * i) - (x * a))
	elif t <= -9e+65:
		tmp = t_1
	elif t <= -2.7e+26:
		tmp = b * ((t * i) - (z * c))
	elif t <= -2.9e-81:
		tmp = t_2
	elif t <= -3.5e-129:
		tmp = z * ((x * y) - (b * c))
	elif t <= -1.1e-258:
		tmp = t_2
	elif t <= 1.55e-304:
		tmp = t_3
	elif t <= 5.8e-190:
		tmp = t_2
	elif t <= 2.2e-138:
		tmp = t_3
	elif t <= 5.2e+40:
		tmp = t_2
	elif t <= 1.85e+226:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = (t * b) * (i - (a * (x / b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1)
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (t <= -4e+95)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (t <= -9e+65)
		tmp = t_1;
	elseif (t <= -2.7e+26)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (t <= -2.9e-81)
		tmp = t_2;
	elseif (t <= -3.5e-129)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= -1.1e-258)
		tmp = t_2;
	elseif (t <= 1.55e-304)
		tmp = t_3;
	elseif (t <= 5.8e-190)
		tmp = t_2;
	elseif (t <= 2.2e-138)
		tmp = t_3;
	elseif (t <= 5.2e+40)
		tmp = t_2;
	elseif (t <= 1.85e+226)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(t * b) * Float64(i - Float64(a * Float64(x / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = (x * ((y * z) - (t * a))) + t_1;
	t_3 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (t <= -4e+95)
		tmp = t * ((b * i) - (x * a));
	elseif (t <= -9e+65)
		tmp = t_1;
	elseif (t <= -2.7e+26)
		tmp = b * ((t * i) - (z * c));
	elseif (t <= -2.9e-81)
		tmp = t_2;
	elseif (t <= -3.5e-129)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= -1.1e-258)
		tmp = t_2;
	elseif (t <= 1.55e-304)
		tmp = t_3;
	elseif (t <= 5.8e-190)
		tmp = t_2;
	elseif (t <= 2.2e-138)
		tmp = t_3;
	elseif (t <= 5.2e+40)
		tmp = t_2;
	elseif (t <= 1.85e+226)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = (t * b) * (i - (a * (x / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e+95], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e+65], t$95$1, If[LessEqual[t, -2.7e+26], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.9e-81], t$95$2, If[LessEqual[t, -3.5e-129], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.1e-258], t$95$2, If[LessEqual[t, 1.55e-304], t$95$3, If[LessEqual[t, 5.8e-190], t$95$2, If[LessEqual[t, 2.2e-138], t$95$3, If[LessEqual[t, 5.2e+40], t$95$2, If[LessEqual[t, 1.85e+226], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * b), $MachinePrecision] * N[(i - N[(a * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -4.00000000000000008e95

   1. Initial program 60.8%

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

   3. Taylor expanded in t around inf 71.6%

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

      1. distribute-lft-out-- 71.6%

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

      2. *-commutative 71.6%

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

   5. Simplified 71.6%

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

   if -4.00000000000000008e95 < t < -9e65

   1. Initial program 34.0%

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

   3. Taylor expanded in j around inf 78.2%

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

   if -9e65 < t < -2.7e26

   1. Initial program 79.4%

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

   3. Taylor expanded in b around inf 97.0%

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

   if -2.7e26 < t < -2.89999999999999989e-81 or -3.4999999999999997e-129 < t < -1.10000000000000008e-258 or 1.54999999999999992e-304 < t < 5.8000000000000004e-190 or 2.1999999999999999e-138 < t < 5.2000000000000001e40

   1. Initial program 86.1%

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

   3. Taylor expanded in b around 0 85.1%

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

   if -2.89999999999999989e-81 < t < -3.4999999999999997e-129

   1. Initial program 67.3%

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

   3. Taylor expanded in z around inf 89.6%

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

      1. *-commutative 89.6%

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

      2. *-commutative 89.6%

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

   5. Simplified 89.6%

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

   if -1.10000000000000008e-258 < t < 1.54999999999999992e-304 or 5.8000000000000004e-190 < t < 2.1999999999999999e-138

   1. Initial program 60.5%

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

   3. Taylor expanded in c around inf 85.8%

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

      1. *-commutative 85.8%

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

   5. Simplified 85.8%

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

   if 5.2000000000000001e40 < t < 1.84999999999999991e226

   1. Initial program 67.0%

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

   3. Taylor expanded in i around -inf 67.4%

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

   if 1.84999999999999991e226 < t

   1. Initial program 66.8%

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

   3. Taylor expanded in b around inf 61.9%

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

      1. fma-define 66.6%

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

      2. associate-/l* 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in t around inf 67.5%

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

      1. associate-*r* 71.9%

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

      2. *-commutative 71.9%

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

      3. mul-1-neg 71.9%

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

      4. unsub-neg 71.9%

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

      5. associate-/l* 76.5%

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

   8. Simplified 76.5%

      \[\leadsto \color{blue}{\left(t \cdot b\right) \cdot \left(i - a \cdot \frac{x}{b}\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+65}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+26}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-129}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-258}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-138}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+226}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot b\right) \cdot \left(i - a \cdot \frac{x}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := \left(t\_1 - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_2 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (- t_1 (* b (- (* z c) (* t i)))) (* j (- (* a c) (* y i))))))
   (if (<= t_2 INFINITY) 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 = x * ((y * z) - (t * a));
	double t_2 = (t_1 - (b * ((z * c) - (t * i)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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));
	double t_2 = (t_1 - (b * ((z * c) - (t * i)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = (t_1 - (b * ((z * c) - (t * i)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = t_1
	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(t_1 - Float64(b * Float64(Float64(z * c) - Float64(t * i)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_2 <= Inf)
		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 = x * ((y * z) - (t * a));
	t_2 = (t_1 - (b * ((z * c) - (t * i)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_2 <= Inf)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, t$95$1]]]

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 92.2%

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

   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. Add Preprocessing

   3. Taylor expanded in x around inf 50.5%

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

4. Final simplification 83.1%

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

Alternative 6: 50.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -5 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-62}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.26 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+152}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{+198}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+210}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -5e+35)
     t_2
     (if (<= j -1.25e-115)
       (* t (- (* b i) (* x a)))
       (if (<= j 2.3e-183)
         t_1
         (if (<= j 8.5e-62)
           (* b (- (* t i) (* z c)))
           (if (<= j 1.26e+56)
             t_1
             (if (<= j 8e+152)
               (* i (- (* t b) (* y j)))
               (if (<= j 3.9e+198)
                 (* z (- (* x y) (* b c)))
                 (if (<= j 1.6e+210) (* a (- (* c j) (* x t))) 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 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -5e+35) {
		tmp = t_2;
	} else if (j <= -1.25e-115) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 2.3e-183) {
		tmp = t_1;
	} else if (j <= 8.5e-62) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 1.26e+56) {
		tmp = t_1;
	} else if (j <= 8e+152) {
		tmp = i * ((t * b) - (y * j));
	} else if (j <= 3.9e+198) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 1.6e+210) {
		tmp = a * ((c * j) - (x * t));
	} 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 = x * ((y * z) - (t * a))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-5d+35)) then
        tmp = t_2
    else if (j <= (-1.25d-115)) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 2.3d-183) then
        tmp = t_1
    else if (j <= 8.5d-62) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 1.26d+56) then
        tmp = t_1
    else if (j <= 8d+152) then
        tmp = i * ((t * b) - (y * j))
    else if (j <= 3.9d+198) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 1.6d+210) then
        tmp = a * ((c * j) - (x * t))
    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 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -5e+35) {
		tmp = t_2;
	} else if (j <= -1.25e-115) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 2.3e-183) {
		tmp = t_1;
	} else if (j <= 8.5e-62) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 1.26e+56) {
		tmp = t_1;
	} else if (j <= 8e+152) {
		tmp = i * ((t * b) - (y * j));
	} else if (j <= 3.9e+198) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 1.6e+210) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -5e+35:
		tmp = t_2
	elif j <= -1.25e-115:
		tmp = t * ((b * i) - (x * a))
	elif j <= 2.3e-183:
		tmp = t_1
	elif j <= 8.5e-62:
		tmp = b * ((t * i) - (z * c))
	elif j <= 1.26e+56:
		tmp = t_1
	elif j <= 8e+152:
		tmp = i * ((t * b) - (y * j))
	elif j <= 3.9e+198:
		tmp = z * ((x * y) - (b * c))
	elif j <= 1.6e+210:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_2
	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(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -5e+35)
		tmp = t_2;
	elseif (j <= -1.25e-115)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 2.3e-183)
		tmp = t_1;
	elseif (j <= 8.5e-62)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 1.26e+56)
		tmp = t_1;
	elseif (j <= 8e+152)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (j <= 3.9e+198)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 1.6e+210)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_2;
	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 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -5e+35)
		tmp = t_2;
	elseif (j <= -1.25e-115)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 2.3e-183)
		tmp = t_1;
	elseif (j <= 8.5e-62)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 1.26e+56)
		tmp = t_1;
	elseif (j <= 8e+152)
		tmp = i * ((t * b) - (y * j));
	elseif (j <= 3.9e+198)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 1.6e+210)
		tmp = a * ((c * j) - (x * t));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5e+35], t$95$2, If[LessEqual[j, -1.25e-115], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e-183], t$95$1, If[LessEqual[j, 8.5e-62], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.26e+56], t$95$1, If[LessEqual[j, 8e+152], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.9e+198], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.6e+210], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -5.00000000000000021e35 or 1.6000000000000001e210 < j

   1. Initial program 69.4%

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

   3. Taylor expanded in j around inf 68.7%

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

   if -5.00000000000000021e35 < j < -1.2500000000000001e-115

   1. Initial program 82.4%

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

   3. Taylor expanded in t around inf 68.7%

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

      1. distribute-lft-out-- 68.7%

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

      2. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   if -1.2500000000000001e-115 < j < 2.30000000000000016e-183 or 8.4999999999999995e-62 < j < 1.2599999999999999e56

   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. Add Preprocessing

   3. Taylor expanded in x around inf 61.8%

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

   if 2.30000000000000016e-183 < j < 8.4999999999999995e-62

   1. Initial program 75.2%

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

   3. Taylor expanded in b around inf 64.7%

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

   if 1.2599999999999999e56 < j < 8.0000000000000004e152

   1. Initial program 68.5%

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

   3. Taylor expanded in i around -inf 56.3%

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

   if 8.0000000000000004e152 < j < 3.9e198

   1. Initial program 36.2%

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

   3. Taylor expanded in z around inf 72.9%

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

      1. *-commutative 72.9%

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

      2. *-commutative 72.9%

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

   5. Simplified 72.9%

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

   if 3.9e198 < j < 1.6000000000000001e210

   1. Initial program 59.7%

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

   3. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5 \cdot 10^{+35}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-62}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.26 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+152}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 3.9 \cdot 10^{+198}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+210}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 30.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := \left(x \cdot t\right) \cdot \left(-a\right)\\ t_3 := c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{-13}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-243}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{-294}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* (* x t) (- a))) (t_3 (* c (* z (- b)))))
   (if (<= b -3.4e-13)
     t_3
     (if (<= b -5.4e-167)
       (* a (* c j))
       (if (<= b -6.2e-243)
         t_2
         (if (<= b -1.2e-249)
           t_1
           (if (<= b 5.7e-294)
             (* j (- (* y i)))
             (if (<= b 7.2e-94)
               t_2
               (if (<= b 3.7e+40)
                 t_1
                 (if (<= b 1.3e+147) (* t (* b i)) 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 = z * (x * y);
	double t_2 = (x * t) * -a;
	double t_3 = c * (z * -b);
	double tmp;
	if (b <= -3.4e-13) {
		tmp = t_3;
	} else if (b <= -5.4e-167) {
		tmp = a * (c * j);
	} else if (b <= -6.2e-243) {
		tmp = t_2;
	} else if (b <= -1.2e-249) {
		tmp = t_1;
	} else if (b <= 5.7e-294) {
		tmp = j * -(y * i);
	} else if (b <= 7.2e-94) {
		tmp = t_2;
	} else if (b <= 3.7e+40) {
		tmp = t_1;
	} else if (b <= 1.3e+147) {
		tmp = t * (b * i);
	} 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 = z * (x * y)
    t_2 = (x * t) * -a
    t_3 = c * (z * -b)
    if (b <= (-3.4d-13)) then
        tmp = t_3
    else if (b <= (-5.4d-167)) then
        tmp = a * (c * j)
    else if (b <= (-6.2d-243)) then
        tmp = t_2
    else if (b <= (-1.2d-249)) then
        tmp = t_1
    else if (b <= 5.7d-294) then
        tmp = j * -(y * i)
    else if (b <= 7.2d-94) then
        tmp = t_2
    else if (b <= 3.7d+40) then
        tmp = t_1
    else if (b <= 1.3d+147) then
        tmp = t * (b * i)
    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 = z * (x * y);
	double t_2 = (x * t) * -a;
	double t_3 = c * (z * -b);
	double tmp;
	if (b <= -3.4e-13) {
		tmp = t_3;
	} else if (b <= -5.4e-167) {
		tmp = a * (c * j);
	} else if (b <= -6.2e-243) {
		tmp = t_2;
	} else if (b <= -1.2e-249) {
		tmp = t_1;
	} else if (b <= 5.7e-294) {
		tmp = j * -(y * i);
	} else if (b <= 7.2e-94) {
		tmp = t_2;
	} else if (b <= 3.7e+40) {
		tmp = t_1;
	} else if (b <= 1.3e+147) {
		tmp = t * (b * i);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = (x * t) * -a
	t_3 = c * (z * -b)
	tmp = 0
	if b <= -3.4e-13:
		tmp = t_3
	elif b <= -5.4e-167:
		tmp = a * (c * j)
	elif b <= -6.2e-243:
		tmp = t_2
	elif b <= -1.2e-249:
		tmp = t_1
	elif b <= 5.7e-294:
		tmp = j * -(y * i)
	elif b <= 7.2e-94:
		tmp = t_2
	elif b <= 3.7e+40:
		tmp = t_1
	elif b <= 1.3e+147:
		tmp = t * (b * i)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(Float64(x * t) * Float64(-a))
	t_3 = Float64(c * Float64(z * Float64(-b)))
	tmp = 0.0
	if (b <= -3.4e-13)
		tmp = t_3;
	elseif (b <= -5.4e-167)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= -6.2e-243)
		tmp = t_2;
	elseif (b <= -1.2e-249)
		tmp = t_1;
	elseif (b <= 5.7e-294)
		tmp = Float64(j * Float64(-Float64(y * i)));
	elseif (b <= 7.2e-94)
		tmp = t_2;
	elseif (b <= 3.7e+40)
		tmp = t_1;
	elseif (b <= 1.3e+147)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	t_2 = (x * t) * -a;
	t_3 = c * (z * -b);
	tmp = 0.0;
	if (b <= -3.4e-13)
		tmp = t_3;
	elseif (b <= -5.4e-167)
		tmp = a * (c * j);
	elseif (b <= -6.2e-243)
		tmp = t_2;
	elseif (b <= -1.2e-249)
		tmp = t_1;
	elseif (b <= 5.7e-294)
		tmp = j * -(y * i);
	elseif (b <= 7.2e-94)
		tmp = t_2;
	elseif (b <= 3.7e+40)
		tmp = t_1;
	elseif (b <= 1.3e+147)
		tmp = t * (b * i);
	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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.4e-13], t$95$3, If[LessEqual[b, -5.4e-167], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.2e-243], t$95$2, If[LessEqual[b, -1.2e-249], t$95$1, If[LessEqual[b, 5.7e-294], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, 7.2e-94], t$95$2, If[LessEqual[b, 3.7e+40], t$95$1, If[LessEqual[b, 1.3e+147], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -3.40000000000000015e-13 or 1.2999999999999999e147 < b

   1. Initial program 70.5%

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

   3. Taylor expanded in c around inf 52.8%

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

      1. *-commutative 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in j around 0 44.9%

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

      1. mul-1-neg 44.9%

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

      2. *-commutative 44.9%

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

      3. distribute-lft-neg-in 44.9%

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

   8. Simplified 44.9%

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

   if -3.40000000000000015e-13 < b < -5.4000000000000001e-167

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf 54.7%

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

      1. +-commutative 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

      4. *-commutative 54.7%

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

   5. Simplified 54.7%

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

   6. Taylor expanded in j around inf 37.6%

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

      1. *-commutative 37.6%

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

   8. Simplified 37.6%

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

   if -5.4000000000000001e-167 < b < -6.1999999999999999e-243 or 5.70000000000000032e-294 < b < 7.2e-94

   1. Initial program 72.4%

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

   3. Taylor expanded in a around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. mul-1-neg 60.6%

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

      3. unsub-neg 60.6%

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

      4. *-commutative 60.6%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in j around 0 39.8%

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

      1. neg-mul-1 39.8%

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

      2. distribute-lft-neg-in 39.8%

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

      3. *-commutative 39.8%

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

   8. Simplified 39.8%

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

   if -6.1999999999999999e-243 < b < -1.20000000000000006e-249 or 7.2e-94 < b < 3.7e40

   1. Initial program 73.2%

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

   3. Taylor expanded in z around inf 50.8%

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

      1. *-commutative 50.8%

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

      2. *-commutative 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in y around inf 44.3%

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

      1. *-commutative 44.3%

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

   8. Simplified 44.3%

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

   if -1.20000000000000006e-249 < b < 5.70000000000000032e-294

   1. Initial program 63.3%

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

   3. Taylor expanded in j around inf 69.3%

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

   4. Taylor expanded in a around 0 59.5%

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

      1. neg-mul-1 59.5%

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

      2. distribute-rgt-neg-in 59.5%

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

   6. Simplified 59.5%

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

   if 3.7e40 < b < 1.2999999999999999e147

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf 55.1%

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

   4. Taylor expanded in i around inf 46.5%

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

      1. associate-*r* 50.6%

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

      2. *-commutative 50.6%

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

   6. Simplified 50.6%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{-13}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-243}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-249}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{-294}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-94}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 30.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-245}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right)\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-298}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-94}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* c (* z (- b)))))
   (if (<= b -1.1e-13)
     t_2
     (if (<= b -3.4e-167)
       (* a (* c j))
       (if (<= b -7e-245)
         (* (* x a) (- t))
         (if (<= b -2.15e-249)
           t_1
           (if (<= b 9.2e-298)
             (* j (- (* y i)))
             (if (<= b 6.8e-94)
               (* (* x t) (- a))
               (if (<= b 6e+40)
                 t_1
                 (if (<= b 4e+146) (* t (* b 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 = z * (x * y);
	double t_2 = c * (z * -b);
	double tmp;
	if (b <= -1.1e-13) {
		tmp = t_2;
	} else if (b <= -3.4e-167) {
		tmp = a * (c * j);
	} else if (b <= -7e-245) {
		tmp = (x * a) * -t;
	} else if (b <= -2.15e-249) {
		tmp = t_1;
	} else if (b <= 9.2e-298) {
		tmp = j * -(y * i);
	} else if (b <= 6.8e-94) {
		tmp = (x * t) * -a;
	} else if (b <= 6e+40) {
		tmp = t_1;
	} else if (b <= 4e+146) {
		tmp = t * (b * 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 = z * (x * y)
    t_2 = c * (z * -b)
    if (b <= (-1.1d-13)) then
        tmp = t_2
    else if (b <= (-3.4d-167)) then
        tmp = a * (c * j)
    else if (b <= (-7d-245)) then
        tmp = (x * a) * -t
    else if (b <= (-2.15d-249)) then
        tmp = t_1
    else if (b <= 9.2d-298) then
        tmp = j * -(y * i)
    else if (b <= 6.8d-94) then
        tmp = (x * t) * -a
    else if (b <= 6d+40) then
        tmp = t_1
    else if (b <= 4d+146) then
        tmp = t * (b * 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 = z * (x * y);
	double t_2 = c * (z * -b);
	double tmp;
	if (b <= -1.1e-13) {
		tmp = t_2;
	} else if (b <= -3.4e-167) {
		tmp = a * (c * j);
	} else if (b <= -7e-245) {
		tmp = (x * a) * -t;
	} else if (b <= -2.15e-249) {
		tmp = t_1;
	} else if (b <= 9.2e-298) {
		tmp = j * -(y * i);
	} else if (b <= 6.8e-94) {
		tmp = (x * t) * -a;
	} else if (b <= 6e+40) {
		tmp = t_1;
	} else if (b <= 4e+146) {
		tmp = t * (b * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = c * (z * -b)
	tmp = 0
	if b <= -1.1e-13:
		tmp = t_2
	elif b <= -3.4e-167:
		tmp = a * (c * j)
	elif b <= -7e-245:
		tmp = (x * a) * -t
	elif b <= -2.15e-249:
		tmp = t_1
	elif b <= 9.2e-298:
		tmp = j * -(y * i)
	elif b <= 6.8e-94:
		tmp = (x * t) * -a
	elif b <= 6e+40:
		tmp = t_1
	elif b <= 4e+146:
		tmp = t * (b * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(c * Float64(z * Float64(-b)))
	tmp = 0.0
	if (b <= -1.1e-13)
		tmp = t_2;
	elseif (b <= -3.4e-167)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= -7e-245)
		tmp = Float64(Float64(x * a) * Float64(-t));
	elseif (b <= -2.15e-249)
		tmp = t_1;
	elseif (b <= 9.2e-298)
		tmp = Float64(j * Float64(-Float64(y * i)));
	elseif (b <= 6.8e-94)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (b <= 6e+40)
		tmp = t_1;
	elseif (b <= 4e+146)
		tmp = Float64(t * Float64(b * 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 = z * (x * y);
	t_2 = c * (z * -b);
	tmp = 0.0;
	if (b <= -1.1e-13)
		tmp = t_2;
	elseif (b <= -3.4e-167)
		tmp = a * (c * j);
	elseif (b <= -7e-245)
		tmp = (x * a) * -t;
	elseif (b <= -2.15e-249)
		tmp = t_1;
	elseif (b <= 9.2e-298)
		tmp = j * -(y * i);
	elseif (b <= 6.8e-94)
		tmp = (x * t) * -a;
	elseif (b <= 6e+40)
		tmp = t_1;
	elseif (b <= 4e+146)
		tmp = t * (b * 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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.1e-13], t$95$2, If[LessEqual[b, -3.4e-167], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7e-245], N[(N[(x * a), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[b, -2.15e-249], t$95$1, If[LessEqual[b, 9.2e-298], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, 6.8e-94], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[b, 6e+40], t$95$1, If[LessEqual[b, 4e+146], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -1.09999999999999998e-13 or 3.99999999999999973e146 < b

   1. Initial program 70.5%

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

   3. Taylor expanded in c around inf 52.8%

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

      1. *-commutative 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in j around 0 44.9%

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

      1. mul-1-neg 44.9%

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

      2. *-commutative 44.9%

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

      3. distribute-lft-neg-in 44.9%

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

   8. Simplified 44.9%

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

   if -1.09999999999999998e-13 < b < -3.3999999999999997e-167

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf 54.7%

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

      1. +-commutative 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

      4. *-commutative 54.7%

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

   5. Simplified 54.7%

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

   6. Taylor expanded in j around inf 37.6%

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

      1. *-commutative 37.6%

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

   8. Simplified 37.6%

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

   if -3.3999999999999997e-167 < b < -7.00000000000000033e-245

   1. Initial program 56.6%

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

   3. Taylor expanded in t around inf 56.9%

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

      1. distribute-lft-out-- 56.9%

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

      2. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in a around inf 39.6%

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

      1. mul-1-neg 39.6%

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

      2. *-commutative 39.6%

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

      3. associate-*l* 45.6%

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

      4. *-commutative 45.6%

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

      5. distribute-rgt-neg-out 45.6%

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

      6. distribute-rgt-neg-in 45.6%

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

   8. Simplified 45.6%

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

   if -7.00000000000000033e-245 < b < -2.1500000000000001e-249 or 6.7999999999999996e-94 < b < 6.0000000000000004e40

   1. Initial program 73.2%

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

   3. Taylor expanded in z around inf 50.8%

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

      1. *-commutative 50.8%

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

      2. *-commutative 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in y around inf 44.3%

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

      1. *-commutative 44.3%

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

   8. Simplified 44.3%

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

   if -2.1500000000000001e-249 < b < 9.2000000000000003e-298

   1. Initial program 63.3%

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

   3. Taylor expanded in j around inf 69.3%

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

   4. Taylor expanded in a around 0 59.5%

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

      1. neg-mul-1 59.5%

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

      2. distribute-rgt-neg-in 59.5%

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

   6. Simplified 59.5%

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

   if 9.2000000000000003e-298 < b < 6.7999999999999996e-94

   1. Initial program 80.5%

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

   3. Taylor expanded in a around inf 65.2%

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

      1. +-commutative 65.2%

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

      2. mul-1-neg 65.2%

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

      3. unsub-neg 65.2%

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

      4. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in j around 0 40.0%

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

      1. neg-mul-1 40.0%

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

      2. distribute-lft-neg-in 40.0%

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

      3. *-commutative 40.0%

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

   8. Simplified 40.0%

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

   if 6.0000000000000004e40 < b < 3.99999999999999973e146

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf 55.1%

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

   4. Taylor expanded in i around inf 46.5%

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

      1. associate-*r* 50.6%

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

      2. *-commutative 50.6%

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

   6. Simplified 50.6%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-13}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-245}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right)\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-249}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-298}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-94}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;b \leq -6.2 \cdot 10^{-15}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-243}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right)\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-296}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-94}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= b -6.2e-15)
     (* c (* z (- b)))
     (if (<= b -5.8e-167)
       (* a (* c j))
       (if (<= b -2.5e-243)
         (* (* x a) (- t))
         (if (<= b -3.1e-249)
           t_1
           (if (<= b 1.3e-296)
             (* j (- (* y i)))
             (if (<= b 4.7e-94)
               (* (* x t) (- a))
               (if (<= b 3.8e+40)
                 t_1
                 (if (<= b 5.5e+148) (* t (* b i)) (* b (* c (- z)))))))))))))

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);
	double tmp;
	if (b <= -6.2e-15) {
		tmp = c * (z * -b);
	} else if (b <= -5.8e-167) {
		tmp = a * (c * j);
	} else if (b <= -2.5e-243) {
		tmp = (x * a) * -t;
	} else if (b <= -3.1e-249) {
		tmp = t_1;
	} else if (b <= 1.3e-296) {
		tmp = j * -(y * i);
	} else if (b <= 4.7e-94) {
		tmp = (x * t) * -a;
	} else if (b <= 3.8e+40) {
		tmp = t_1;
	} else if (b <= 5.5e+148) {
		tmp = t * (b * i);
	} else {
		tmp = b * (c * -z);
	}
	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 = z * (x * y)
    if (b <= (-6.2d-15)) then
        tmp = c * (z * -b)
    else if (b <= (-5.8d-167)) then
        tmp = a * (c * j)
    else if (b <= (-2.5d-243)) then
        tmp = (x * a) * -t
    else if (b <= (-3.1d-249)) then
        tmp = t_1
    else if (b <= 1.3d-296) then
        tmp = j * -(y * i)
    else if (b <= 4.7d-94) then
        tmp = (x * t) * -a
    else if (b <= 3.8d+40) then
        tmp = t_1
    else if (b <= 5.5d+148) then
        tmp = t * (b * i)
    else
        tmp = b * (c * -z)
    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);
	double tmp;
	if (b <= -6.2e-15) {
		tmp = c * (z * -b);
	} else if (b <= -5.8e-167) {
		tmp = a * (c * j);
	} else if (b <= -2.5e-243) {
		tmp = (x * a) * -t;
	} else if (b <= -3.1e-249) {
		tmp = t_1;
	} else if (b <= 1.3e-296) {
		tmp = j * -(y * i);
	} else if (b <= 4.7e-94) {
		tmp = (x * t) * -a;
	} else if (b <= 3.8e+40) {
		tmp = t_1;
	} else if (b <= 5.5e+148) {
		tmp = t * (b * i);
	} else {
		tmp = b * (c * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if b <= -6.2e-15:
		tmp = c * (z * -b)
	elif b <= -5.8e-167:
		tmp = a * (c * j)
	elif b <= -2.5e-243:
		tmp = (x * a) * -t
	elif b <= -3.1e-249:
		tmp = t_1
	elif b <= 1.3e-296:
		tmp = j * -(y * i)
	elif b <= 4.7e-94:
		tmp = (x * t) * -a
	elif b <= 3.8e+40:
		tmp = t_1
	elif b <= 5.5e+148:
		tmp = t * (b * i)
	else:
		tmp = b * (c * -z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (b <= -6.2e-15)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (b <= -5.8e-167)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= -2.5e-243)
		tmp = Float64(Float64(x * a) * Float64(-t));
	elseif (b <= -3.1e-249)
		tmp = t_1;
	elseif (b <= 1.3e-296)
		tmp = Float64(j * Float64(-Float64(y * i)));
	elseif (b <= 4.7e-94)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (b <= 3.8e+40)
		tmp = t_1;
	elseif (b <= 5.5e+148)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(b * Float64(c * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	tmp = 0.0;
	if (b <= -6.2e-15)
		tmp = c * (z * -b);
	elseif (b <= -5.8e-167)
		tmp = a * (c * j);
	elseif (b <= -2.5e-243)
		tmp = (x * a) * -t;
	elseif (b <= -3.1e-249)
		tmp = t_1;
	elseif (b <= 1.3e-296)
		tmp = j * -(y * i);
	elseif (b <= 4.7e-94)
		tmp = (x * t) * -a;
	elseif (b <= 3.8e+40)
		tmp = t_1;
	elseif (b <= 5.5e+148)
		tmp = t * (b * i);
	else
		tmp = b * (c * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.2e-15], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.8e-167], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.5e-243], N[(N[(x * a), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[b, -3.1e-249], t$95$1, If[LessEqual[b, 1.3e-296], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, 4.7e-94], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[b, 3.8e+40], t$95$1, If[LessEqual[b, 5.5e+148], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(b * N[(c * (-z)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -6.1999999999999998e-15

   1. Initial program 76.0%

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

   3. Taylor expanded in c around inf 53.7%

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

      1. *-commutative 53.7%

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

   5. Simplified 53.7%

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

   6. Taylor expanded in j around 0 43.8%

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

      1. mul-1-neg 43.8%

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

      2. *-commutative 43.8%

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

      3. distribute-lft-neg-in 43.8%

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

   8. Simplified 43.8%

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

   if -6.1999999999999998e-15 < b < -5.80000000000000005e-167

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf 54.7%

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

      1. +-commutative 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

      4. *-commutative 54.7%

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

   5. Simplified 54.7%

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

   6. Taylor expanded in j around inf 37.6%

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

      1. *-commutative 37.6%

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

   8. Simplified 37.6%

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

   if -5.80000000000000005e-167 < b < -2.5e-243

   1. Initial program 56.6%

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

   3. Taylor expanded in t around inf 56.9%

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

      1. distribute-lft-out-- 56.9%

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

      2. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in a around inf 39.6%

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

      1. mul-1-neg 39.6%

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

      2. *-commutative 39.6%

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

      3. associate-*l* 45.6%

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

      4. *-commutative 45.6%

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

      5. distribute-rgt-neg-out 45.6%

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

      6. distribute-rgt-neg-in 45.6%

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

   8. Simplified 45.6%

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

   if -2.5e-243 < b < -3.09999999999999986e-249 or 4.70000000000000003e-94 < b < 3.80000000000000004e40

   1. Initial program 73.2%

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

   3. Taylor expanded in z around inf 50.8%

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

      1. *-commutative 50.8%

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

      2. *-commutative 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in y around inf 44.3%

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

      1. *-commutative 44.3%

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

   8. Simplified 44.3%

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

   if -3.09999999999999986e-249 < b < 1.3e-296

   1. Initial program 63.3%

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

   3. Taylor expanded in j around inf 69.3%

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

   4. Taylor expanded in a around 0 59.5%

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

      1. neg-mul-1 59.5%

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

      2. distribute-rgt-neg-in 59.5%

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

   6. Simplified 59.5%

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

   if 1.3e-296 < b < 4.70000000000000003e-94

   1. Initial program 80.5%

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

   3. Taylor expanded in a around inf 65.2%

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

      1. +-commutative 65.2%

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

      2. mul-1-neg 65.2%

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

      3. unsub-neg 65.2%

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

      4. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in j around 0 40.0%

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

      1. neg-mul-1 40.0%

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

      2. distribute-lft-neg-in 40.0%

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

      3. *-commutative 40.0%

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

   8. Simplified 40.0%

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

   if 3.80000000000000004e40 < b < 5.5e148

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf 55.1%

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

   4. Taylor expanded in i around inf 46.5%

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

      1. associate-*r* 50.6%

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

      2. *-commutative 50.6%

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

   6. Simplified 50.6%

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

   if 5.5e148 < b

   1. Initial program 62.5%

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

   3. Taylor expanded in z around inf 46.8%

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

      1. *-commutative 46.8%

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

      2. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in y around 0 48.6%

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

      1. associate-*r* 48.6%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 48.6%

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

   8. Simplified 48.6%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{-15}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-243}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right)\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-249}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-296}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-94}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-238}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-259}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 10^{-290}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-94}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+145}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -3.9e-11)
   (* c (* z (- b)))
   (if (<= b -4e-167)
     (* a (* c j))
     (if (<= b -1.08e-238)
       (* (* x a) (- t))
       (if (<= b -1e-259)
         (* i (* y (- j)))
         (if (<= b 1e-290)
           (* y (* i (- j)))
           (if (<= b 5.5e-94)
             (* (* x t) (- a))
             (if (<= b 4.1e+40)
               (* z (* x y))
               (if (<= b 4.7e+145) (* t (* b i)) (* b (* c (- z))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3.9e-11) {
		tmp = c * (z * -b);
	} else if (b <= -4e-167) {
		tmp = a * (c * j);
	} else if (b <= -1.08e-238) {
		tmp = (x * a) * -t;
	} else if (b <= -1e-259) {
		tmp = i * (y * -j);
	} else if (b <= 1e-290) {
		tmp = y * (i * -j);
	} else if (b <= 5.5e-94) {
		tmp = (x * t) * -a;
	} else if (b <= 4.1e+40) {
		tmp = z * (x * y);
	} else if (b <= 4.7e+145) {
		tmp = t * (b * i);
	} else {
		tmp = b * (c * -z);
	}
	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 (b <= (-3.9d-11)) then
        tmp = c * (z * -b)
    else if (b <= (-4d-167)) then
        tmp = a * (c * j)
    else if (b <= (-1.08d-238)) then
        tmp = (x * a) * -t
    else if (b <= (-1d-259)) then
        tmp = i * (y * -j)
    else if (b <= 1d-290) then
        tmp = y * (i * -j)
    else if (b <= 5.5d-94) then
        tmp = (x * t) * -a
    else if (b <= 4.1d+40) then
        tmp = z * (x * y)
    else if (b <= 4.7d+145) then
        tmp = t * (b * i)
    else
        tmp = b * (c * -z)
    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 (b <= -3.9e-11) {
		tmp = c * (z * -b);
	} else if (b <= -4e-167) {
		tmp = a * (c * j);
	} else if (b <= -1.08e-238) {
		tmp = (x * a) * -t;
	} else if (b <= -1e-259) {
		tmp = i * (y * -j);
	} else if (b <= 1e-290) {
		tmp = y * (i * -j);
	} else if (b <= 5.5e-94) {
		tmp = (x * t) * -a;
	} else if (b <= 4.1e+40) {
		tmp = z * (x * y);
	} else if (b <= 4.7e+145) {
		tmp = t * (b * i);
	} else {
		tmp = b * (c * -z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -3.9e-11:
		tmp = c * (z * -b)
	elif b <= -4e-167:
		tmp = a * (c * j)
	elif b <= -1.08e-238:
		tmp = (x * a) * -t
	elif b <= -1e-259:
		tmp = i * (y * -j)
	elif b <= 1e-290:
		tmp = y * (i * -j)
	elif b <= 5.5e-94:
		tmp = (x * t) * -a
	elif b <= 4.1e+40:
		tmp = z * (x * y)
	elif b <= 4.7e+145:
		tmp = t * (b * i)
	else:
		tmp = b * (c * -z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -3.9e-11)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (b <= -4e-167)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= -1.08e-238)
		tmp = Float64(Float64(x * a) * Float64(-t));
	elseif (b <= -1e-259)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (b <= 1e-290)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (b <= 5.5e-94)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (b <= 4.1e+40)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 4.7e+145)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(b * Float64(c * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -3.9e-11)
		tmp = c * (z * -b);
	elseif (b <= -4e-167)
		tmp = a * (c * j);
	elseif (b <= -1.08e-238)
		tmp = (x * a) * -t;
	elseif (b <= -1e-259)
		tmp = i * (y * -j);
	elseif (b <= 1e-290)
		tmp = y * (i * -j);
	elseif (b <= 5.5e-94)
		tmp = (x * t) * -a;
	elseif (b <= 4.1e+40)
		tmp = z * (x * y);
	elseif (b <= 4.7e+145)
		tmp = t * (b * i);
	else
		tmp = b * (c * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -3.9e-11], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4e-167], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.08e-238], N[(N[(x * a), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[b, -1e-259], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-290], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e-94], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[b, 4.1e+40], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.7e+145], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(b * N[(c * (-z)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if b < -3.9000000000000001e-11

   1. Initial program 76.0%

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

   3. Taylor expanded in c around inf 53.7%

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

      1. *-commutative 53.7%

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

   5. Simplified 53.7%

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

   6. Taylor expanded in j around 0 43.8%

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

      1. mul-1-neg 43.8%

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

      2. *-commutative 43.8%

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

      3. distribute-lft-neg-in 43.8%

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

   8. Simplified 43.8%

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

   if -3.9000000000000001e-11 < b < -4.00000000000000001e-167

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf 54.7%

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

      1. +-commutative 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

      4. *-commutative 54.7%

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

   5. Simplified 54.7%

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

   6. Taylor expanded in j around inf 37.6%

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

      1. *-commutative 37.6%

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

   8. Simplified 37.6%

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

   if -4.00000000000000001e-167 < b < -1.08e-238

   1. Initial program 57.6%

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

   3. Taylor expanded in t around inf 64.8%

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

      1. distribute-lft-out-- 64.8%

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

      2. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in a around inf 44.6%

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

      1. mul-1-neg 44.6%

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

      2. *-commutative 44.6%

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

      3. associate-*l* 51.5%

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

      4. *-commutative 51.5%

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

      5. distribute-rgt-neg-out 51.5%

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

      6. distribute-rgt-neg-in 51.5%

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

   8. Simplified 51.5%

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

   if -1.08e-238 < b < -1.0000000000000001e-259

   1. Initial program 57.7%

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

   3. Taylor expanded in j around inf 45.9%

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

   4. Taylor expanded in a around 0 59.4%

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

      1. associate-*r* 59.4%

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

      2. neg-mul-1 59.4%

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

   6. Simplified 59.4%

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

   if -1.0000000000000001e-259 < b < 1.0000000000000001e-290

   1. Initial program 66.7%

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

   3. Taylor expanded in j around inf 72.4%

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

   4. Taylor expanded in a around 0 46.0%

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

      1. mul-1-neg 46.0%

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

      2. associate-*r* 56.6%

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

      3. distribute-rgt-neg-in 56.6%

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

      4. *-commutative 56.6%

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

   6. Simplified 56.6%

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

   if 1.0000000000000001e-290 < b < 5.49999999999999989e-94

   1. Initial program 79.2%

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

   3. Taylor expanded in a around inf 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in j around 0 42.5%

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

      1. neg-mul-1 42.5%

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

      2. distribute-lft-neg-in 42.5%

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

      3. *-commutative 42.5%

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

   8. Simplified 42.5%

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

   if 5.49999999999999989e-94 < b < 4.1000000000000002e40

   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. Add Preprocessing

   3. Taylor expanded in z around inf 47.3%

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

      1. *-commutative 47.3%

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

      2. *-commutative 47.3%

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

   5. Simplified 47.3%

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

   6. Taylor expanded in y around inf 40.4%

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

      1. *-commutative 40.4%

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

   8. Simplified 40.4%

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

   if 4.1000000000000002e40 < b < 4.7000000000000002e145

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf 55.1%

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

   4. Taylor expanded in i around inf 46.5%

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

      1. associate-*r* 50.6%

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

      2. *-commutative 50.6%

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

   6. Simplified 50.6%

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

   if 4.7000000000000002e145 < b

   1. Initial program 62.5%

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

   3. Taylor expanded in z around inf 46.8%

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

      1. *-commutative 46.8%

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

      2. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in y around 0 48.6%

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

      1. associate-*r* 48.6%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 48.6%

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

   8. Simplified 48.6%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-238}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(-t\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-259}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 10^{-290}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-94}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+145}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.56 \cdot 10^{+29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{-63}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+153}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+282}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -1.56e+29)
     t_2
     (if (<= j 3.6e-185)
       t_1
       (if (<= j 2.1e-63)
         (* b (- (* t i) (* z c)))
         (if (<= j 1.65e+14)
           t_1
           (if (<= j 1.15e+153)
             t_2
             (if (<= j 2.2e+198)
               t_1
               (if (<= j 8e+282) (* a (- (* c j) (* x t))) 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 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.56e+29) {
		tmp = t_2;
	} else if (j <= 3.6e-185) {
		tmp = t_1;
	} else if (j <= 2.1e-63) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 1.65e+14) {
		tmp = t_1;
	} else if (j <= 1.15e+153) {
		tmp = t_2;
	} else if (j <= 2.2e+198) {
		tmp = t_1;
	} else if (j <= 8e+282) {
		tmp = a * ((c * j) - (x * t));
	} 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 = x * ((y * z) - (t * a))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-1.56d+29)) then
        tmp = t_2
    else if (j <= 3.6d-185) then
        tmp = t_1
    else if (j <= 2.1d-63) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 1.65d+14) then
        tmp = t_1
    else if (j <= 1.15d+153) then
        tmp = t_2
    else if (j <= 2.2d+198) then
        tmp = t_1
    else if (j <= 8d+282) then
        tmp = a * ((c * j) - (x * t))
    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 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.56e+29) {
		tmp = t_2;
	} else if (j <= 3.6e-185) {
		tmp = t_1;
	} else if (j <= 2.1e-63) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 1.65e+14) {
		tmp = t_1;
	} else if (j <= 1.15e+153) {
		tmp = t_2;
	} else if (j <= 2.2e+198) {
		tmp = t_1;
	} else if (j <= 8e+282) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.56e+29:
		tmp = t_2
	elif j <= 3.6e-185:
		tmp = t_1
	elif j <= 2.1e-63:
		tmp = b * ((t * i) - (z * c))
	elif j <= 1.65e+14:
		tmp = t_1
	elif j <= 1.15e+153:
		tmp = t_2
	elif j <= 2.2e+198:
		tmp = t_1
	elif j <= 8e+282:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_2
	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(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.56e+29)
		tmp = t_2;
	elseif (j <= 3.6e-185)
		tmp = t_1;
	elseif (j <= 2.1e-63)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 1.65e+14)
		tmp = t_1;
	elseif (j <= 1.15e+153)
		tmp = t_2;
	elseif (j <= 2.2e+198)
		tmp = t_1;
	elseif (j <= 8e+282)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_2;
	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 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.56e+29)
		tmp = t_2;
	elseif (j <= 3.6e-185)
		tmp = t_1;
	elseif (j <= 2.1e-63)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 1.65e+14)
		tmp = t_1;
	elseif (j <= 1.15e+153)
		tmp = t_2;
	elseif (j <= 2.2e+198)
		tmp = t_1;
	elseif (j <= 8e+282)
		tmp = a * ((c * j) - (x * t));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.56e+29], t$95$2, If[LessEqual[j, 3.6e-185], t$95$1, If[LessEqual[j, 2.1e-63], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.65e+14], t$95$1, If[LessEqual[j, 1.15e+153], t$95$2, If[LessEqual[j, 2.2e+198], t$95$1, If[LessEqual[j, 8e+282], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.5599999999999999e29 or 1.65e14 < j < 1.1500000000000001e153 or 8.00000000000000026e282 < j

   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. Add Preprocessing

   3. Taylor expanded in j around inf 60.9%

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

   if -1.5599999999999999e29 < j < 3.5999999999999998e-185 or 2.1e-63 < j < 1.65e14 or 1.1500000000000001e153 < j < 2.2e198

   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. Add Preprocessing

   3. Taylor expanded in x around inf 61.3%

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

   if 3.5999999999999998e-185 < j < 2.1e-63

   1. Initial program 75.2%

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

   3. Taylor expanded in b around inf 64.7%

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

   if 2.2e198 < j < 8.00000000000000026e282

   1. Initial program 49.9%

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

   3. Taylor expanded in a around inf 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unsub-neg 73.1%

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

      4. *-commutative 73.1%

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

   5. Simplified 73.1%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.56 \cdot 10^{+29}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-185}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{-63}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+153}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+282}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.6 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.75 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+152}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+198}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.15 \cdot 10^{+211}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -2.6e+32)
     t_2
     (if (<= j 3.6e-186)
       t_1
       (if (<= j 1.1e-60)
         (* b (- (* t i) (* z c)))
         (if (<= j 4.75e+55)
           t_1
           (if (<= j 1.3e+152)
             (* i (- (* t b) (* y j)))
             (if (<= j 2e+198)
               (* z (- (* x y) (* b c)))
               (if (<= j 3.15e+211) (* a (- (* c j) (* x t))) 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 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.6e+32) {
		tmp = t_2;
	} else if (j <= 3.6e-186) {
		tmp = t_1;
	} else if (j <= 1.1e-60) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 4.75e+55) {
		tmp = t_1;
	} else if (j <= 1.3e+152) {
		tmp = i * ((t * b) - (y * j));
	} else if (j <= 2e+198) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 3.15e+211) {
		tmp = a * ((c * j) - (x * t));
	} 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 = x * ((y * z) - (t * a))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-2.6d+32)) then
        tmp = t_2
    else if (j <= 3.6d-186) then
        tmp = t_1
    else if (j <= 1.1d-60) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 4.75d+55) then
        tmp = t_1
    else if (j <= 1.3d+152) then
        tmp = i * ((t * b) - (y * j))
    else if (j <= 2d+198) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 3.15d+211) then
        tmp = a * ((c * j) - (x * t))
    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 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.6e+32) {
		tmp = t_2;
	} else if (j <= 3.6e-186) {
		tmp = t_1;
	} else if (j <= 1.1e-60) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 4.75e+55) {
		tmp = t_1;
	} else if (j <= 1.3e+152) {
		tmp = i * ((t * b) - (y * j));
	} else if (j <= 2e+198) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 3.15e+211) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.6e+32:
		tmp = t_2
	elif j <= 3.6e-186:
		tmp = t_1
	elif j <= 1.1e-60:
		tmp = b * ((t * i) - (z * c))
	elif j <= 4.75e+55:
		tmp = t_1
	elif j <= 1.3e+152:
		tmp = i * ((t * b) - (y * j))
	elif j <= 2e+198:
		tmp = z * ((x * y) - (b * c))
	elif j <= 3.15e+211:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_2
	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(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.6e+32)
		tmp = t_2;
	elseif (j <= 3.6e-186)
		tmp = t_1;
	elseif (j <= 1.1e-60)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 4.75e+55)
		tmp = t_1;
	elseif (j <= 1.3e+152)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (j <= 2e+198)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 3.15e+211)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_2;
	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 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.6e+32)
		tmp = t_2;
	elseif (j <= 3.6e-186)
		tmp = t_1;
	elseif (j <= 1.1e-60)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 4.75e+55)
		tmp = t_1;
	elseif (j <= 1.3e+152)
		tmp = i * ((t * b) - (y * j));
	elseif (j <= 2e+198)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 3.15e+211)
		tmp = a * ((c * j) - (x * t));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.6e+32], t$95$2, If[LessEqual[j, 3.6e-186], t$95$1, If[LessEqual[j, 1.1e-60], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.75e+55], t$95$1, If[LessEqual[j, 1.3e+152], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2e+198], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.15e+211], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.6000000000000002e32 or 3.1500000000000002e211 < j

   1. Initial program 69.8%

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

   3. Taylor expanded in j around inf 69.1%

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

   if -2.6000000000000002e32 < j < 3.5999999999999998e-186 or 1.0999999999999999e-60 < j < 4.74999999999999995e55

   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. Add Preprocessing

   3. Taylor expanded in x around inf 58.9%

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

   if 3.5999999999999998e-186 < j < 1.0999999999999999e-60

   1. Initial program 75.2%

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

   3. Taylor expanded in b around inf 64.7%

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

   if 4.74999999999999995e55 < j < 1.3e152

   1. Initial program 68.5%

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

   3. Taylor expanded in i around -inf 56.3%

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

   if 1.3e152 < j < 2.00000000000000004e198

   1. Initial program 36.2%

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

   3. Taylor expanded in z around inf 72.9%

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

      1. *-commutative 72.9%

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

      2. *-commutative 72.9%

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

   5. Simplified 72.9%

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

   if 2.00000000000000004e198 < j < 3.1500000000000002e211

   1. Initial program 59.7%

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

   3. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.6 \cdot 10^{+32}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.75 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+152}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+198}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.15 \cdot 10^{+211}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -6 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 3.45 \cdot 10^{-183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{-62}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+198}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - j \cdot \frac{y}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -6e+35)
     t_2
     (if (<= j -8.2e-116)
       (* t (- (* b i) (* x a)))
       (if (<= j 3.45e-183)
         t_1
         (if (<= j 4.3e-62)
           (* b (- (* t i) (* z c)))
           (if (<= j 9.5e+55)
             t_1
             (if (<= j 4.5e+198) (* (* b i) (- t (* j (/ y b)))) 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 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -6e+35) {
		tmp = t_2;
	} else if (j <= -8.2e-116) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 3.45e-183) {
		tmp = t_1;
	} else if (j <= 4.3e-62) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 9.5e+55) {
		tmp = t_1;
	} else if (j <= 4.5e+198) {
		tmp = (b * i) * (t - (j * (y / b)));
	} 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 = x * ((y * z) - (t * a))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-6d+35)) then
        tmp = t_2
    else if (j <= (-8.2d-116)) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 3.45d-183) then
        tmp = t_1
    else if (j <= 4.3d-62) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 9.5d+55) then
        tmp = t_1
    else if (j <= 4.5d+198) then
        tmp = (b * i) * (t - (j * (y / b)))
    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 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -6e+35) {
		tmp = t_2;
	} else if (j <= -8.2e-116) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 3.45e-183) {
		tmp = t_1;
	} else if (j <= 4.3e-62) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 9.5e+55) {
		tmp = t_1;
	} else if (j <= 4.5e+198) {
		tmp = (b * i) * (t - (j * (y / b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -6e+35:
		tmp = t_2
	elif j <= -8.2e-116:
		tmp = t * ((b * i) - (x * a))
	elif j <= 3.45e-183:
		tmp = t_1
	elif j <= 4.3e-62:
		tmp = b * ((t * i) - (z * c))
	elif j <= 9.5e+55:
		tmp = t_1
	elif j <= 4.5e+198:
		tmp = (b * i) * (t - (j * (y / b)))
	else:
		tmp = t_2
	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(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -6e+35)
		tmp = t_2;
	elseif (j <= -8.2e-116)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 3.45e-183)
		tmp = t_1;
	elseif (j <= 4.3e-62)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 9.5e+55)
		tmp = t_1;
	elseif (j <= 4.5e+198)
		tmp = Float64(Float64(b * i) * Float64(t - Float64(j * Float64(y / b))));
	else
		tmp = t_2;
	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 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -6e+35)
		tmp = t_2;
	elseif (j <= -8.2e-116)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 3.45e-183)
		tmp = t_1;
	elseif (j <= 4.3e-62)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 9.5e+55)
		tmp = t_1;
	elseif (j <= 4.5e+198)
		tmp = (b * i) * (t - (j * (y / b)));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6e+35], t$95$2, If[LessEqual[j, -8.2e-116], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.45e-183], t$95$1, If[LessEqual[j, 4.3e-62], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.5e+55], t$95$1, If[LessEqual[j, 4.5e+198], N[(N[(b * i), $MachinePrecision] * N[(t - N[(j * N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -5.99999999999999981e35 or 4.50000000000000001e198 < j

   1. Initial program 68.8%

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

   3. Taylor expanded in j around inf 68.2%

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

   if -5.99999999999999981e35 < j < -8.1999999999999998e-116

   1. Initial program 82.4%

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

   3. Taylor expanded in t around inf 68.7%

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

      1. distribute-lft-out-- 68.7%

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

      2. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   if -8.1999999999999998e-116 < j < 3.45e-183 or 4.2999999999999997e-62 < j < 9.49999999999999989e55

   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. Add Preprocessing

   3. Taylor expanded in x around inf 61.8%

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

   if 3.45e-183 < j < 4.2999999999999997e-62

   1. Initial program 75.2%

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

   3. Taylor expanded in b around inf 64.7%

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

   if 9.49999999999999989e55 < j < 4.50000000000000001e198

   1. Initial program 57.8%

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

   3. Taylor expanded in b around inf 54.6%

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

      1. fma-define 57.6%

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

      2. associate-/l* 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in i around inf 53.4%

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

      1. associate-*r* 56.0%

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

      2. *-commutative 56.0%

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

      3. mul-1-neg 56.0%

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

      4. unsub-neg 56.0%

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

      5. associate-/l* 61.9%

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

   8. Simplified 61.9%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6 \cdot 10^{+35}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 3.45 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{-62}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+198}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - j \cdot \frac{y}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.8 \cdot 10^{+29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+149} \lor \neg \left(j \leq 1.8 \cdot 10^{+198}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -3.8e+29)
     t_2
     (if (<= j 3.1e-187)
       t_1
       (if (<= j 1.5e-60)
         (* b (- (* t i) (* z c)))
         (if (<= j 1.9e+16)
           t_1
           (if (or (<= j 3.6e+149) (not (<= j 1.8e+198)))
             t_2
             (* 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));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.8e+29) {
		tmp = t_2;
	} else if (j <= 3.1e-187) {
		tmp = t_1;
	} else if (j <= 1.5e-60) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 1.9e+16) {
		tmp = t_1;
	} else if ((j <= 3.6e+149) || !(j <= 1.8e+198)) {
		tmp = t_2;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	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 = x * ((y * z) - (t * a))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-3.8d+29)) then
        tmp = t_2
    else if (j <= 3.1d-187) then
        tmp = t_1
    else if (j <= 1.5d-60) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 1.9d+16) then
        tmp = t_1
    else if ((j <= 3.6d+149) .or. (.not. (j <= 1.8d+198))) then
        tmp = t_2
    else
        tmp = z * ((x * y) - (b * c))
    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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.8e+29) {
		tmp = t_2;
	} else if (j <= 3.1e-187) {
		tmp = t_1;
	} else if (j <= 1.5e-60) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 1.9e+16) {
		tmp = t_1;
	} else if ((j <= 3.6e+149) || !(j <= 1.8e+198)) {
		tmp = t_2;
	} 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))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -3.8e+29:
		tmp = t_2
	elif j <= 3.1e-187:
		tmp = t_1
	elif j <= 1.5e-60:
		tmp = b * ((t * i) - (z * c))
	elif j <= 1.9e+16:
		tmp = t_1
	elif (j <= 3.6e+149) or not (j <= 1.8e+198):
		tmp = t_2
	else:
		tmp = z * ((x * y) - (b * c))
	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(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3.8e+29)
		tmp = t_2;
	elseif (j <= 3.1e-187)
		tmp = t_1;
	elseif (j <= 1.5e-60)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 1.9e+16)
		tmp = t_1;
	elseif ((j <= 3.6e+149) || !(j <= 1.8e+198))
		tmp = t_2;
	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));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -3.8e+29)
		tmp = t_2;
	elseif (j <= 3.1e-187)
		tmp = t_1;
	elseif (j <= 1.5e-60)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 1.9e+16)
		tmp = t_1;
	elseif ((j <= 3.6e+149) || ~((j <= 1.8e+198)))
		tmp = t_2;
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.8e+29], t$95$2, If[LessEqual[j, 3.1e-187], t$95$1, If[LessEqual[j, 1.5e-60], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.9e+16], t$95$1, If[Or[LessEqual[j, 3.6e+149], N[Not[LessEqual[j, 1.8e+198]], $MachinePrecision]], t$95$2, N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.79999999999999971e29 or 1.9e16 < j < 3.59999999999999995e149 or 1.8000000000000001e198 < j

   1. Initial program 71.1%

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

   3. Taylor expanded in j around inf 61.9%

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

   if -3.79999999999999971e29 < j < 3.10000000000000019e-187 or 1.50000000000000009e-60 < j < 1.9e16

   1. Initial program 76.3%

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

   3. Taylor expanded in x around inf 61.0%

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

   if 3.10000000000000019e-187 < j < 1.50000000000000009e-60

   1. Initial program 75.2%

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

   3. Taylor expanded in b around inf 64.7%

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

   if 3.59999999999999995e149 < j < 1.8000000000000001e198

   1. Initial program 36.2%

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

   3. Taylor expanded in z around inf 72.9%

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

      1. *-commutative 72.9%

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

      2. *-commutative 72.9%

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

   5. Simplified 72.9%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.8 \cdot 10^{+29}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-187}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+149} \lor \neg \left(j \leq 1.8 \cdot 10^{+198}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.1 \cdot 10^{+28}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{-186}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.06 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{+63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -2.1e+28)
     t_3
     (if (<= j 2.45e-186)
       t_2
       (if (<= j 1.06e-61)
         t_1
         (if (<= j 6.4e+63)
           t_2
           (if (<= j 1.75e+145)
             t_1
             (if (<= j 2.15e+198) (* y (- (* x z) (* i j))) 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 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.1e+28) {
		tmp = t_3;
	} else if (j <= 2.45e-186) {
		tmp = t_2;
	} else if (j <= 1.06e-61) {
		tmp = t_1;
	} else if (j <= 6.4e+63) {
		tmp = t_2;
	} else if (j <= 1.75e+145) {
		tmp = t_1;
	} else if (j <= 2.15e+198) {
		tmp = y * ((x * z) - (i * j));
	} 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 = b * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-2.1d+28)) then
        tmp = t_3
    else if (j <= 2.45d-186) then
        tmp = t_2
    else if (j <= 1.06d-61) then
        tmp = t_1
    else if (j <= 6.4d+63) then
        tmp = t_2
    else if (j <= 1.75d+145) then
        tmp = t_1
    else if (j <= 2.15d+198) then
        tmp = y * ((x * z) - (i * j))
    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 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.1e+28) {
		tmp = t_3;
	} else if (j <= 2.45e-186) {
		tmp = t_2;
	} else if (j <= 1.06e-61) {
		tmp = t_1;
	} else if (j <= 6.4e+63) {
		tmp = t_2;
	} else if (j <= 1.75e+145) {
		tmp = t_1;
	} else if (j <= 2.15e+198) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.1e+28:
		tmp = t_3
	elif j <= 2.45e-186:
		tmp = t_2
	elif j <= 1.06e-61:
		tmp = t_1
	elif j <= 6.4e+63:
		tmp = t_2
	elif j <= 1.75e+145:
		tmp = t_1
	elif j <= 2.15e+198:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.1e+28)
		tmp = t_3;
	elseif (j <= 2.45e-186)
		tmp = t_2;
	elseif (j <= 1.06e-61)
		tmp = t_1;
	elseif (j <= 6.4e+63)
		tmp = t_2;
	elseif (j <= 1.75e+145)
		tmp = t_1;
	elseif (j <= 2.15e+198)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.1e+28)
		tmp = t_3;
	elseif (j <= 2.45e-186)
		tmp = t_2;
	elseif (j <= 1.06e-61)
		tmp = t_1;
	elseif (j <= 6.4e+63)
		tmp = t_2;
	elseif (j <= 1.75e+145)
		tmp = t_1;
	elseif (j <= 2.15e+198)
		tmp = y * ((x * z) - (i * j));
	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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.1e+28], t$95$3, If[LessEqual[j, 2.45e-186], t$95$2, If[LessEqual[j, 1.06e-61], t$95$1, If[LessEqual[j, 6.4e+63], t$95$2, If[LessEqual[j, 1.75e+145], t$95$1, If[LessEqual[j, 2.15e+198], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.09999999999999989e28 or 2.14999999999999991e198 < j

   1. Initial program 69.2%

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

   3. Taylor expanded in j around inf 68.5%

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

   if -2.09999999999999989e28 < j < 2.4499999999999998e-186 or 1.0599999999999999e-61 < j < 6.40000000000000022e63

   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. Add Preprocessing

   3. Taylor expanded in x around inf 58.2%

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

   if 2.4499999999999998e-186 < j < 1.0599999999999999e-61 or 6.40000000000000022e63 < j < 1.7500000000000001e145

   1. Initial program 74.1%

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

   3. Taylor expanded in b around inf 58.8%

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

   if 1.7500000000000001e145 < j < 2.14999999999999991e198

   1. Initial program 33.2%

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

   3. Taylor expanded in y around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. unsub-neg 67.1%

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

      4. *-commutative 67.1%

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

      5. *-commutative 67.1%

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

   5. Simplified 67.1%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.1 \cdot 10^{+28}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.06 \cdot 10^{-61}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{if}\;b \leq -1.12 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.3 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-240}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-59}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+145}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))))
   (if (<= b -1.12e-10)
     t_1
     (if (<= b -6.3e-167)
       (* a (* c j))
       (if (<= b -1.2e-240)
         (* (* x t) (- a))
         (if (<= b 1.65e-59)
           (* c (* a j))
           (if (<= b 3.8e+40)
             (* z (* x y))
             (if (<= b 8.6e+145) (* t (* b i)) 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 * (z * -b);
	double tmp;
	if (b <= -1.12e-10) {
		tmp = t_1;
	} else if (b <= -6.3e-167) {
		tmp = a * (c * j);
	} else if (b <= -1.2e-240) {
		tmp = (x * t) * -a;
	} else if (b <= 1.65e-59) {
		tmp = c * (a * j);
	} else if (b <= 3.8e+40) {
		tmp = z * (x * y);
	} else if (b <= 8.6e+145) {
		tmp = t * (b * i);
	} 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 = c * (z * -b)
    if (b <= (-1.12d-10)) then
        tmp = t_1
    else if (b <= (-6.3d-167)) then
        tmp = a * (c * j)
    else if (b <= (-1.2d-240)) then
        tmp = (x * t) * -a
    else if (b <= 1.65d-59) then
        tmp = c * (a * j)
    else if (b <= 3.8d+40) then
        tmp = z * (x * y)
    else if (b <= 8.6d+145) then
        tmp = t * (b * i)
    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 * (z * -b);
	double tmp;
	if (b <= -1.12e-10) {
		tmp = t_1;
	} else if (b <= -6.3e-167) {
		tmp = a * (c * j);
	} else if (b <= -1.2e-240) {
		tmp = (x * t) * -a;
	} else if (b <= 1.65e-59) {
		tmp = c * (a * j);
	} else if (b <= 3.8e+40) {
		tmp = z * (x * y);
	} else if (b <= 8.6e+145) {
		tmp = t * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * -b)
	tmp = 0
	if b <= -1.12e-10:
		tmp = t_1
	elif b <= -6.3e-167:
		tmp = a * (c * j)
	elif b <= -1.2e-240:
		tmp = (x * t) * -a
	elif b <= 1.65e-59:
		tmp = c * (a * j)
	elif b <= 3.8e+40:
		tmp = z * (x * y)
	elif b <= 8.6e+145:
		tmp = t * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	tmp = 0.0
	if (b <= -1.12e-10)
		tmp = t_1;
	elseif (b <= -6.3e-167)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= -1.2e-240)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (b <= 1.65e-59)
		tmp = Float64(c * Float64(a * j));
	elseif (b <= 3.8e+40)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 8.6e+145)
		tmp = Float64(t * Float64(b * i));
	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 * (z * -b);
	tmp = 0.0;
	if (b <= -1.12e-10)
		tmp = t_1;
	elseif (b <= -6.3e-167)
		tmp = a * (c * j);
	elseif (b <= -1.2e-240)
		tmp = (x * t) * -a;
	elseif (b <= 1.65e-59)
		tmp = c * (a * j);
	elseif (b <= 3.8e+40)
		tmp = z * (x * y);
	elseif (b <= 8.6e+145)
		tmp = t * (b * i);
	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[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.12e-10], t$95$1, If[LessEqual[b, -6.3e-167], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.2e-240], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[b, 1.65e-59], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e+40], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.6e+145], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.12e-10 or 8.59999999999999996e145 < b

   1. Initial program 70.5%

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

   3. Taylor expanded in c around inf 52.8%

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

      1. *-commutative 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in j around 0 44.9%

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

      1. mul-1-neg 44.9%

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

      2. *-commutative 44.9%

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

      3. distribute-lft-neg-in 44.9%

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

   8. Simplified 44.9%

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

   if -1.12e-10 < b < -6.3000000000000001e-167

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf 54.7%

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

      1. +-commutative 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

      4. *-commutative 54.7%

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

   5. Simplified 54.7%

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

   6. Taylor expanded in j around inf 37.6%

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

      1. *-commutative 37.6%

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

   8. Simplified 37.6%

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

   if -6.3000000000000001e-167 < b < -1.2e-240

   1. Initial program 57.6%

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

   3. Taylor expanded in a around inf 51.4%

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

      1. +-commutative 51.4%

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

      2. mul-1-neg 51.4%

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

      3. unsub-neg 51.4%

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

      4. *-commutative 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in j around 0 44.6%

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

      1. neg-mul-1 44.6%

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

      2. distribute-lft-neg-in 44.6%

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

      3. *-commutative 44.6%

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

   8. Simplified 44.6%

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

   if -1.2e-240 < b < 1.64999999999999991e-59

   1. Initial program 75.4%

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

   3. Taylor expanded in c around inf 37.6%

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

      1. *-commutative 37.6%

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

   5. Simplified 37.6%

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

   6. Taylor expanded in j around inf 32.8%

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

      1. *-commutative 32.8%

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

   8. Simplified 32.8%

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

   if 1.64999999999999991e-59 < b < 3.80000000000000004e40

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 48.3%

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

      1. *-commutative 48.3%

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

      2. *-commutative 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in y around inf 43.9%

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

      1. *-commutative 43.9%

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

   8. Simplified 43.9%

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

   if 3.80000000000000004e40 < b < 8.59999999999999996e145

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf 55.1%

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

   4. Taylor expanded in i around inf 46.5%

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

      1. associate-*r* 50.6%

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

      2. *-commutative 50.6%

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

   6. Simplified 50.6%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.12 \cdot 10^{-10}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -6.3 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-240}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-59}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+145}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 42.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.15 \cdot 10^{-110}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-264}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-213}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.9 \cdot 10^{-100}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* b i))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -2.15e-110)
     t_2
     (if (<= a -1.8e-264)
       (* j (- (* y i)))
       (if (<= a 2.95e-213)
         t_1
         (if (<= a 6.9e-100)
           (* c (* z (- b)))
           (if (<= a 1.8e+49) 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 = t * (b * i);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.15e-110) {
		tmp = t_2;
	} else if (a <= -1.8e-264) {
		tmp = j * -(y * i);
	} else if (a <= 2.95e-213) {
		tmp = t_1;
	} else if (a <= 6.9e-100) {
		tmp = c * (z * -b);
	} else if (a <= 1.8e+49) {
		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 = t * (b * i)
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-2.15d-110)) then
        tmp = t_2
    else if (a <= (-1.8d-264)) then
        tmp = j * -(y * i)
    else if (a <= 2.95d-213) then
        tmp = t_1
    else if (a <= 6.9d-100) then
        tmp = c * (z * -b)
    else if (a <= 1.8d+49) 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 = t * (b * i);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.15e-110) {
		tmp = t_2;
	} else if (a <= -1.8e-264) {
		tmp = j * -(y * i);
	} else if (a <= 2.95e-213) {
		tmp = t_1;
	} else if (a <= 6.9e-100) {
		tmp = c * (z * -b);
	} else if (a <= 1.8e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (b * i)
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.15e-110:
		tmp = t_2
	elif a <= -1.8e-264:
		tmp = j * -(y * i)
	elif a <= 2.95e-213:
		tmp = t_1
	elif a <= 6.9e-100:
		tmp = c * (z * -b)
	elif a <= 1.8e+49:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(b * i))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.15e-110)
		tmp = t_2;
	elseif (a <= -1.8e-264)
		tmp = Float64(j * Float64(-Float64(y * i)));
	elseif (a <= 2.95e-213)
		tmp = t_1;
	elseif (a <= 6.9e-100)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (a <= 1.8e+49)
		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 = t * (b * i);
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.15e-110)
		tmp = t_2;
	elseif (a <= -1.8e-264)
		tmp = j * -(y * i);
	elseif (a <= 2.95e-213)
		tmp = t_1;
	elseif (a <= 6.9e-100)
		tmp = c * (z * -b);
	elseif (a <= 1.8e+49)
		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[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.15e-110], t$95$2, If[LessEqual[a, -1.8e-264], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision], If[LessEqual[a, 2.95e-213], t$95$1, If[LessEqual[a, 6.9e-100], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+49], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.15000000000000012e-110 or 1.79999999999999998e49 < a

   1. Initial program 67.3%

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

   3. Taylor expanded in a around inf 64.9%

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

      1. +-commutative 64.9%

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

      2. mul-1-neg 64.9%

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

      3. unsub-neg 64.9%

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

      4. *-commutative 64.9%

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

   5. Simplified 64.9%

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

   if -2.15000000000000012e-110 < a < -1.8000000000000001e-264

   1. Initial program 82.0%

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

   3. Taylor expanded in j around inf 47.7%

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

   4. Taylor expanded in a around 0 39.6%

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

      1. neg-mul-1 39.6%

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

      2. distribute-rgt-neg-in 39.6%

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

   6. Simplified 39.6%

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

   if -1.8000000000000001e-264 < a < 2.9499999999999999e-213 or 6.9e-100 < a < 1.79999999999999998e49

   1. Initial program 69.0%

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

   3. Taylor expanded in b around inf 42.6%

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

   4. Taylor expanded in i around inf 33.8%

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

      1. associate-*r* 38.9%

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

      2. *-commutative 38.9%

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

   6. Simplified 38.9%

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

   if 2.9499999999999999e-213 < a < 6.9e-100

   1. Initial program 87.9%

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

   3. Taylor expanded in c around inf 53.0%

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

      1. *-commutative 53.0%

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

   5. Simplified 53.0%

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

   6. Taylor expanded in j around 0 41.4%

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

      1. mul-1-neg 41.4%

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

      2. *-commutative 41.4%

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

      3. distribute-lft-neg-in 41.4%

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

   8. Simplified 41.4%

      \[\leadsto c \cdot \color{blue}{\left(\left(-z\right) \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{-110}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-264}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-213}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 6.9 \cdot 10^{-100}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 1.46 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -5.2e-11)
     t_2
     (if (<= b -1.8e-240)
       t_1
       (if (<= b 2.1e-306)
         (* y (* i (- j)))
         (if (<= b 1.46e-59) t_1 (if (<= b 3.7e+40) (* z (* x y)) 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 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.2e-11) {
		tmp = t_2;
	} else if (b <= -1.8e-240) {
		tmp = t_1;
	} else if (b <= 2.1e-306) {
		tmp = y * (i * -j);
	} else if (b <= 1.46e-59) {
		tmp = t_1;
	} else if (b <= 3.7e+40) {
		tmp = z * (x * y);
	} 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 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-5.2d-11)) then
        tmp = t_2
    else if (b <= (-1.8d-240)) then
        tmp = t_1
    else if (b <= 2.1d-306) then
        tmp = y * (i * -j)
    else if (b <= 1.46d-59) then
        tmp = t_1
    else if (b <= 3.7d+40) then
        tmp = z * (x * y)
    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 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.2e-11) {
		tmp = t_2;
	} else if (b <= -1.8e-240) {
		tmp = t_1;
	} else if (b <= 2.1e-306) {
		tmp = y * (i * -j);
	} else if (b <= 1.46e-59) {
		tmp = t_1;
	} else if (b <= 3.7e+40) {
		tmp = z * (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -5.2e-11:
		tmp = t_2
	elif b <= -1.8e-240:
		tmp = t_1
	elif b <= 2.1e-306:
		tmp = y * (i * -j)
	elif b <= 1.46e-59:
		tmp = t_1
	elif b <= 3.7e+40:
		tmp = z * (x * y)
	else:
		tmp = t_2
	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)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.2e-11)
		tmp = t_2;
	elseif (b <= -1.8e-240)
		tmp = t_1;
	elseif (b <= 2.1e-306)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (b <= 1.46e-59)
		tmp = t_1;
	elseif (b <= 3.7e+40)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_2;
	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));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.2e-11)
		tmp = t_2;
	elseif (b <= -1.8e-240)
		tmp = t_1;
	elseif (b <= 2.1e-306)
		tmp = y * (i * -j);
	elseif (b <= 1.46e-59)
		tmp = t_1;
	elseif (b <= 3.7e+40)
		tmp = z * (x * y);
	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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e-11], t$95$2, If[LessEqual[b, -1.8e-240], t$95$1, If[LessEqual[b, 2.1e-306], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.46e-59], t$95$1, If[LessEqual[b, 3.7e+40], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.2000000000000001e-11 or 3.7e40 < b

   1. Initial program 71.1%

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

   3. Taylor expanded in b around inf 63.2%

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

   if -5.2000000000000001e-11 < b < -1.7999999999999999e-240 or 2.1000000000000001e-306 < b < 1.45999999999999994e-59

   1. Initial program 76.9%

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

   3. Taylor expanded in a around inf 57.3%

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

      1. +-commutative 57.3%

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

      2. mul-1-neg 57.3%

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

      3. unsub-neg 57.3%

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

      4. *-commutative 57.3%

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

   5. Simplified 57.3%

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

   if -1.7999999999999999e-240 < b < 2.1000000000000001e-306

   1. Initial program 60.2%

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

   3. Taylor expanded in j around inf 56.2%

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

   4. Taylor expanded in a around 0 51.9%

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

      1. mul-1-neg 51.9%

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

      2. associate-*r* 61.0%

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

      3. distribute-rgt-neg-in 61.0%

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

      4. *-commutative 61.0%

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

   6. Simplified 61.0%

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

   if 1.45999999999999994e-59 < b < 3.7e40

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 48.3%

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

      1. *-commutative 48.3%

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

      2. *-commutative 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in y around inf 43.9%

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

      1. *-commutative 43.9%

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

   8. Simplified 43.9%

      \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-240}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 1.46 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 50.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.6 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-243}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-292}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -5.6e-11)
     t_2
     (if (<= b -5e-243)
       t_1
       (if (<= b 4.4e-292)
         (* j (- (* a c) (* y i)))
         (if (<= b 2.3e-59) t_1 (if (<= b 4.8e+40) (* z (* x y)) 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 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.6e-11) {
		tmp = t_2;
	} else if (b <= -5e-243) {
		tmp = t_1;
	} else if (b <= 4.4e-292) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 2.3e-59) {
		tmp = t_1;
	} else if (b <= 4.8e+40) {
		tmp = z * (x * y);
	} 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 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-5.6d-11)) then
        tmp = t_2
    else if (b <= (-5d-243)) then
        tmp = t_1
    else if (b <= 4.4d-292) then
        tmp = j * ((a * c) - (y * i))
    else if (b <= 2.3d-59) then
        tmp = t_1
    else if (b <= 4.8d+40) then
        tmp = z * (x * y)
    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 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.6e-11) {
		tmp = t_2;
	} else if (b <= -5e-243) {
		tmp = t_1;
	} else if (b <= 4.4e-292) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 2.3e-59) {
		tmp = t_1;
	} else if (b <= 4.8e+40) {
		tmp = z * (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -5.6e-11:
		tmp = t_2
	elif b <= -5e-243:
		tmp = t_1
	elif b <= 4.4e-292:
		tmp = j * ((a * c) - (y * i))
	elif b <= 2.3e-59:
		tmp = t_1
	elif b <= 4.8e+40:
		tmp = z * (x * y)
	else:
		tmp = t_2
	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)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.6e-11)
		tmp = t_2;
	elseif (b <= -5e-243)
		tmp = t_1;
	elseif (b <= 4.4e-292)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (b <= 2.3e-59)
		tmp = t_1;
	elseif (b <= 4.8e+40)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_2;
	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));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.6e-11)
		tmp = t_2;
	elseif (b <= -5e-243)
		tmp = t_1;
	elseif (b <= 4.4e-292)
		tmp = j * ((a * c) - (y * i));
	elseif (b <= 2.3e-59)
		tmp = t_1;
	elseif (b <= 4.8e+40)
		tmp = z * (x * y);
	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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.6e-11], t$95$2, If[LessEqual[b, -5e-243], t$95$1, If[LessEqual[b, 4.4e-292], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-59], t$95$1, If[LessEqual[b, 4.8e+40], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.6e-11 or 4.8e40 < b

   1. Initial program 71.1%

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

   3. Taylor expanded in b around inf 63.2%

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

   if -5.6e-11 < b < -5e-243 or 4.40000000000000023e-292 < b < 2.29999999999999979e-59

   1. Initial program 76.3%

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

   3. Taylor expanded in a around inf 56.4%

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

      1. +-commutative 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

      4. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   if -5e-243 < b < 4.40000000000000023e-292

   1. Initial program 63.8%

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

   3. Taylor expanded in j around inf 64.5%

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

   if 2.29999999999999979e-59 < b < 4.8e40

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 48.3%

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

      1. *-commutative 48.3%

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

      2. *-commutative 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in y around inf 43.9%

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

      1. *-commutative 43.9%

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

   8. Simplified 43.9%

      \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-243}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-292}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 68.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-49} \lor \neg \left(z \leq 2 \cdot 10^{-57}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + z \cdot \left(b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - \left(a \cdot \left(x \cdot t\right) + j \cdot \left(y \cdot i - a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -1.2e-49) (not (<= z 2e-57)))
   (+ (* x (- (* y z) (* t a))) (* z (* b (- (* i (/ t z)) c))))
   (- (* b (* t i)) (+ (* a (* x t)) (* j (- (* y i) (* a c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -1.2e-49) || !(z <= 2e-57)) {
		tmp = (x * ((y * z) - (t * a))) + (z * (b * ((i * (t / z)) - c)));
	} else {
		tmp = (b * (t * i)) - ((a * (x * t)) + (j * ((y * i) - (a * c))));
	}
	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 ((z <= (-1.2d-49)) .or. (.not. (z <= 2d-57))) then
        tmp = (x * ((y * z) - (t * a))) + (z * (b * ((i * (t / z)) - c)))
    else
        tmp = (b * (t * i)) - ((a * (x * t)) + (j * ((y * i) - (a * c))))
    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 ((z <= -1.2e-49) || !(z <= 2e-57)) {
		tmp = (x * ((y * z) - (t * a))) + (z * (b * ((i * (t / z)) - c)));
	} else {
		tmp = (b * (t * i)) - ((a * (x * t)) + (j * ((y * i) - (a * c))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -1.2e-49) or not (z <= 2e-57):
		tmp = (x * ((y * z) - (t * a))) + (z * (b * ((i * (t / z)) - c)))
	else:
		tmp = (b * (t * i)) - ((a * (x * t)) + (j * ((y * i) - (a * c))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -1.2e-49) || !(z <= 2e-57))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(z * Float64(b * Float64(Float64(i * Float64(t / z)) - c))));
	else
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(Float64(a * Float64(x * t)) + Float64(j * Float64(Float64(y * i) - Float64(a * c)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -1.2e-49) || ~((z <= 2e-57)))
		tmp = (x * ((y * z) - (t * a))) + (z * (b * ((i * (t / z)) - c)));
	else
		tmp = (b * (t * i)) - ((a * (x * t)) + (j * ((y * i) - (a * c))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -1.2e-49], N[Not[LessEqual[z, 2e-57]], $MachinePrecision]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(b * N[(N[(i * N[(t / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.19999999999999996e-49 or 1.99999999999999991e-57 < z

   1. Initial program 64.4%

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

   3. Taylor expanded in z around inf 65.7%

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

      1. +-commutative 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

      4. *-commutative 65.7%

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

      5. associate-/l* 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in j around 0 65.7%

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

      1. *-commutative 65.7%

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

      2. *-commutative 65.7%

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

      3. sub-neg 65.7%

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

      4. sub-neg 65.7%

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

      5. associate-/l* 65.7%

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

      6. associate-*r/ 69.5%

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

      7. distribute-lft-out-- 71.5%

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

   8. Simplified 71.5%

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

   if -1.19999999999999996e-49 < z < 1.99999999999999991e-57

   1. Initial program 83.8%

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

   3. Taylor expanded in z around 0 79.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + j \cdot \left(a \cdot c - i \cdot y\right)\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-49} \lor \neg \left(z \leq 2 \cdot 10^{-57}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + z \cdot \left(b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - \left(a \cdot \left(x \cdot t\right) + j \cdot \left(y \cdot i - a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-52}:\\ \;\;\;\;t\_1 + z \cdot \left(b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+86}:\\ \;\;\;\;t\_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= z -4.8e-52)
     (+ t_1 (* z (* b (- (* i (/ t z)) c))))
     (if (<= z 9e+86)
       (+ t_1 (* j (- (* a c) (* y i))))
       (* 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));
	double tmp;
	if (z <= -4.8e-52) {
		tmp = t_1 + (z * (b * ((i * (t / z)) - c)));
	} else if (z <= 9e+86) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	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 = x * ((y * z) - (t * a))
    if (z <= (-4.8d-52)) then
        tmp = t_1 + (z * (b * ((i * (t / z)) - c)))
    else if (z <= 9d+86) then
        tmp = t_1 + (j * ((a * c) - (y * i)))
    else
        tmp = z * ((x * y) - (b * c))
    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 tmp;
	if (z <= -4.8e-52) {
		tmp = t_1 + (z * (b * ((i * (t / z)) - c)));
	} else if (z <= 9e+86) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} 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))
	tmp = 0
	if z <= -4.8e-52:
		tmp = t_1 + (z * (b * ((i * (t / z)) - c)))
	elif z <= 9e+86:
		tmp = t_1 + (j * ((a * c) - (y * i)))
	else:
		tmp = z * ((x * y) - (b * c))
	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)))
	tmp = 0.0
	if (z <= -4.8e-52)
		tmp = Float64(t_1 + Float64(z * Float64(b * Float64(Float64(i * Float64(t / z)) - c))));
	elseif (z <= 9e+86)
		tmp = Float64(t_1 + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	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));
	tmp = 0.0;
	if (z <= -4.8e-52)
		tmp = t_1 + (z * (b * ((i * (t / z)) - c)));
	elseif (z <= 9e+86)
		tmp = t_1 + (j * ((a * c) - (y * i)));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-52], N[(t$95$1 + N[(z * N[(b * N[(N[(i * N[(t / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+86], N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8000000000000003e-52

   1. Initial program 64.0%

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

   3. Taylor expanded in z around inf 66.3%

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

      1. +-commutative 66.3%

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

      2. mul-1-neg 66.3%

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

      3. unsub-neg 66.3%

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

      4. *-commutative 66.3%

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

      5. associate-/l* 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in j around 0 66.6%

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

      1. *-commutative 66.6%

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

      2. *-commutative 66.6%

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

      3. sub-neg 66.6%

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

      4. sub-neg 66.6%

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

      5. associate-/l* 66.5%

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

      6. associate-*r/ 72.2%

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

      7. distribute-lft-out-- 74.6%

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

   8. Simplified 74.6%

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

   if -4.8000000000000003e-52 < z < 8.99999999999999986e86

   1. Initial program 81.8%

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

   3. Taylor expanded in b around 0 67.6%

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

   if 8.99999999999999986e86 < z

   1. Initial program 59.4%

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

   3. Taylor expanded in z around inf 72.1%

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

      1. *-commutative 72.1%

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

      2. *-commutative 72.1%

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

   5. Simplified 72.1%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + z \cdot \left(b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{-108} \lor \neg \left(c \leq 8.6 \cdot 10^{+67}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -3.2e-108) (not (<= c 8.6e+67))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.2e-108) || !(c <= 8.6e+67)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	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 ((c <= (-3.2d-108)) .or. (.not. (c <= 8.6d+67))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    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 ((c <= -3.2e-108) || !(c <= 8.6e+67)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -3.2e-108) or not (c <= 8.6e+67):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -3.2e-108) || !(c <= 8.6e+67))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -3.2e-108) || ~((c <= 8.6e+67)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -3.2e-108], N[Not[LessEqual[c, 8.6e+67]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.2e-108 or 8.6000000000000002e67 < c

   1. Initial program 67.2%

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

   3. Taylor expanded in a around inf 49.7%

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

      1. +-commutative 49.7%

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

      2. mul-1-neg 49.7%

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

      3. unsub-neg 49.7%

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

      4. *-commutative 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in j around inf 36.2%

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

      1. *-commutative 36.2%

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

   8. Simplified 36.2%

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

   if -3.2e-108 < c < 8.6000000000000002e67

   1. Initial program 77.0%

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

   3. Taylor expanded in b around inf 36.7%

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

   4. Taylor expanded in i around inf 31.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{-108} \lor \neg \left(c \leq 8.6 \cdot 10^{+67}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{-108}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -3.2e-108)
   (* c (* a j))
   (if (<= c 5.1e+68) (* b (* t i)) (* a (* c 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 (c <= -3.2e-108) {
		tmp = c * (a * j);
	} else if (c <= 5.1e+68) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * 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 (c <= (-3.2d-108)) then
        tmp = c * (a * j)
    else if (c <= 5.1d+68) then
        tmp = b * (t * i)
    else
        tmp = a * (c * 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 (c <= -3.2e-108) {
		tmp = c * (a * j);
	} else if (c <= 5.1e+68) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -3.2e-108:
		tmp = c * (a * j)
	elif c <= 5.1e+68:
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -3.2e-108)
		tmp = Float64(c * Float64(a * j));
	elseif (c <= 5.1e+68)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -3.2e-108)
		tmp = c * (a * j);
	elseif (c <= 5.1e+68)
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -3.2e-108], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.1e+68], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.2e-108

   1. Initial program 69.7%

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

   3. Taylor expanded in c around inf 55.7%

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

      1. *-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in j around inf 33.6%

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

      1. *-commutative 33.6%

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

   8. Simplified 33.6%

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

   if -3.2e-108 < c < 5.1e68

   1. Initial program 77.0%

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

   3. Taylor expanded in b around inf 36.7%

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

   4. Taylor expanded in i around inf 31.3%

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

   if 5.1e68 < c

   1. Initial program 63.9%

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

   3. Taylor expanded in a around inf 49.5%

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

      1. +-commutative 49.5%

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

      2. mul-1-neg 49.5%

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

      3. unsub-neg 49.5%

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

      4. *-commutative 49.5%

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

   5. Simplified 49.5%

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

   6. Taylor expanded in j around inf 39.5%

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

      1. *-commutative 39.5%

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

   8. Simplified 39.5%

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

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{-108}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{-112}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -2.5e-112)
   (* c (* a j))
   (if (<= c 5.6e+68) (* t (* b i)) (* a (* c 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 (c <= -2.5e-112) {
		tmp = c * (a * j);
	} else if (c <= 5.6e+68) {
		tmp = t * (b * i);
	} else {
		tmp = a * (c * 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 (c <= (-2.5d-112)) then
        tmp = c * (a * j)
    else if (c <= 5.6d+68) then
        tmp = t * (b * i)
    else
        tmp = a * (c * 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 (c <= -2.5e-112) {
		tmp = c * (a * j);
	} else if (c <= 5.6e+68) {
		tmp = t * (b * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -2.5e-112:
		tmp = c * (a * j)
	elif c <= 5.6e+68:
		tmp = t * (b * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -2.5e-112)
		tmp = Float64(c * Float64(a * j));
	elseif (c <= 5.6e+68)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -2.5e-112)
		tmp = c * (a * j);
	elseif (c <= 5.6e+68)
		tmp = t * (b * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -2.5e-112], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.6e+68], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.50000000000000022e-112

   1. Initial program 69.7%

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

   3. Taylor expanded in c around inf 55.7%

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

      1. *-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in j around inf 33.6%

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

      1. *-commutative 33.6%

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

   8. Simplified 33.6%

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

   if -2.50000000000000022e-112 < c < 5.6e68

   1. Initial program 77.0%

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

   3. Taylor expanded in b around inf 36.7%

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

   4. Taylor expanded in i around inf 31.3%

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

      1. associate-*r* 33.1%

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

      2. *-commutative 33.1%

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

   6. Simplified 33.1%

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

   if 5.6e68 < c

   1. Initial program 63.9%

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

   3. Taylor expanded in a around inf 49.5%

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

      1. +-commutative 49.5%

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

      2. mul-1-neg 49.5%

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

      3. unsub-neg 49.5%

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

      4. *-commutative 49.5%

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

   5. Simplified 49.5%

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

   6. Taylor expanded in j around inf 39.5%

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

      1. *-commutative 39.5%

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

   8. Simplified 39.5%

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

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{-112}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{-108}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -2.5e-108)
   (* j (* a c))
   (if (<= c 5.8e+68) (* t (* b i)) (* a (* c 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 (c <= -2.5e-108) {
		tmp = j * (a * c);
	} else if (c <= 5.8e+68) {
		tmp = t * (b * i);
	} else {
		tmp = a * (c * 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 (c <= (-2.5d-108)) then
        tmp = j * (a * c)
    else if (c <= 5.8d+68) then
        tmp = t * (b * i)
    else
        tmp = a * (c * 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 (c <= -2.5e-108) {
		tmp = j * (a * c);
	} else if (c <= 5.8e+68) {
		tmp = t * (b * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -2.5e-108:
		tmp = j * (a * c)
	elif c <= 5.8e+68:
		tmp = t * (b * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -2.5e-108)
		tmp = Float64(j * Float64(a * c));
	elseif (c <= 5.8e+68)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -2.5e-108)
		tmp = j * (a * c);
	elseif (c <= 5.8e+68)
		tmp = t * (b * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -2.5e-108], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.8e+68], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.5e-108

   1. Initial program 69.7%

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

   3. Taylor expanded in a around inf 49.8%

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

      1. +-commutative 49.8%

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

      2. mul-1-neg 49.8%

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

      3. unsub-neg 49.8%

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

      4. *-commutative 49.8%

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

   5. Simplified 49.8%

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

   6. Taylor expanded in j around inf 33.5%

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

      1. associate-*r* 36.2%

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

   8. Simplified 36.2%

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

   if -2.5e-108 < c < 5.80000000000000023e68

   1. Initial program 77.0%

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

   3. Taylor expanded in b around inf 36.7%

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

   4. Taylor expanded in i around inf 31.3%

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

      1. associate-*r* 33.1%

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

      2. *-commutative 33.1%

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

   6. Simplified 33.1%

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

   if 5.80000000000000023e68 < c

   1. Initial program 63.9%

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

   3. Taylor expanded in a around inf 49.5%

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

      1. +-commutative 49.5%

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

      2. mul-1-neg 49.5%

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

      3. unsub-neg 49.5%

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

      4. *-commutative 49.5%

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

   5. Simplified 49.5%

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

   6. Taylor expanded in j around inf 39.5%

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

      1. *-commutative 39.5%

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

   8. Simplified 39.5%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{-108}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.4% 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 72.0%

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

3. Taylor expanded in a around inf 39.3%

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

   1. +-commutative 39.3%

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

   2. mul-1-neg 39.3%

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

   3. unsub-neg 39.3%

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

   4. *-commutative 39.3%

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

5. Simplified 39.3%

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

6. Taylor expanded in j around inf 23.0%

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

   1. *-commutative 23.0%

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

8. Simplified 23.0%

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

9. Final simplification 23.0%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer target: 59.2% 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 2024067 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (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)))))