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

Percentage Accurate: 73.7% → 82.5%

Time: 21.4s

Alternatives: 19

Speedup: 0.5×

• 57.3% 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: 73.7% 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: 82.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.0%

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

   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 c around inf 65.6%

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

      1. *-commutative 65.6%

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

   5. Simplified 65.6%

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

4. Final simplification 86.7%

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

Alternative 2: 55.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t\_1 + b \cdot \left(t \cdot i\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+174}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-122}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-198}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-264}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-296}:\\ \;\;\;\;t\_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(\frac{a \cdot \left(c \cdot j - x \cdot t\right)}{y} - i \cdot j\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+132}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+181}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+196}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

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 (* t i))))
        (t_3 (+ (* j (- (* a c) (* y i))) (* x (* y z))))
        (t_4 (* z (- (* x y) (* b c)))))
   (if (<= z -1.85e+174)
     t_4
     (if (<= z -3e-122)
       t_3
       (if (<= z -2.8e-198)
         t_2
         (if (<= z -1.65e-264)
           t_3
           (if (<= z -2.7e-296)
             (- t_1 (* i (* y j)))
             (if (<= z 1.5e+46)
               (* y (- (/ (* a (- (* c j) (* x t))) y) (* i j)))
               (if (<= z 1.95e+132)
                 (* b (- (* t i) (* z c)))
                 (if (<= z 1.15e+181)
                   t_3
                   (if (<= z 3.9e+196) t_2 t_4)))))))))))

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 * (t * i));
	double t_3 = (j * ((a * c) - (y * i))) + (x * (y * z));
	double t_4 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.85e+174) {
		tmp = t_4;
	} else if (z <= -3e-122) {
		tmp = t_3;
	} else if (z <= -2.8e-198) {
		tmp = t_2;
	} else if (z <= -1.65e-264) {
		tmp = t_3;
	} else if (z <= -2.7e-296) {
		tmp = t_1 - (i * (y * j));
	} else if (z <= 1.5e+46) {
		tmp = y * (((a * ((c * j) - (x * t))) / y) - (i * j));
	} else if (z <= 1.95e+132) {
		tmp = b * ((t * i) - (z * c));
	} else if (z <= 1.15e+181) {
		tmp = t_3;
	} else if (z <= 3.9e+196) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	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 = x * ((y * z) - (t * a))
    t_2 = t_1 + (b * (t * i))
    t_3 = (j * ((a * c) - (y * i))) + (x * (y * z))
    t_4 = z * ((x * y) - (b * c))
    if (z <= (-1.85d+174)) then
        tmp = t_4
    else if (z <= (-3d-122)) then
        tmp = t_3
    else if (z <= (-2.8d-198)) then
        tmp = t_2
    else if (z <= (-1.65d-264)) then
        tmp = t_3
    else if (z <= (-2.7d-296)) then
        tmp = t_1 - (i * (y * j))
    else if (z <= 1.5d+46) then
        tmp = y * (((a * ((c * j) - (x * t))) / y) - (i * j))
    else if (z <= 1.95d+132) then
        tmp = b * ((t * i) - (z * c))
    else if (z <= 1.15d+181) then
        tmp = t_3
    else if (z <= 3.9d+196) then
        tmp = t_2
    else
        tmp = t_4
    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 = t_1 + (b * (t * i));
	double t_3 = (j * ((a * c) - (y * i))) + (x * (y * z));
	double t_4 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.85e+174) {
		tmp = t_4;
	} else if (z <= -3e-122) {
		tmp = t_3;
	} else if (z <= -2.8e-198) {
		tmp = t_2;
	} else if (z <= -1.65e-264) {
		tmp = t_3;
	} else if (z <= -2.7e-296) {
		tmp = t_1 - (i * (y * j));
	} else if (z <= 1.5e+46) {
		tmp = y * (((a * ((c * j) - (x * t))) / y) - (i * j));
	} else if (z <= 1.95e+132) {
		tmp = b * ((t * i) - (z * c));
	} else if (z <= 1.15e+181) {
		tmp = t_3;
	} else if (z <= 3.9e+196) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	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 * (t * i))
	t_3 = (j * ((a * c) - (y * i))) + (x * (y * z))
	t_4 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -1.85e+174:
		tmp = t_4
	elif z <= -3e-122:
		tmp = t_3
	elif z <= -2.8e-198:
		tmp = t_2
	elif z <= -1.65e-264:
		tmp = t_3
	elif z <= -2.7e-296:
		tmp = t_1 - (i * (y * j))
	elif z <= 1.5e+46:
		tmp = y * (((a * ((c * j) - (x * t))) / y) - (i * j))
	elif z <= 1.95e+132:
		tmp = b * ((t * i) - (z * c))
	elif z <= 1.15e+181:
		tmp = t_3
	elif z <= 3.9e+196:
		tmp = t_2
	else:
		tmp = t_4
	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(t * i)))
	t_3 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)))
	t_4 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -1.85e+174)
		tmp = t_4;
	elseif (z <= -3e-122)
		tmp = t_3;
	elseif (z <= -2.8e-198)
		tmp = t_2;
	elseif (z <= -1.65e-264)
		tmp = t_3;
	elseif (z <= -2.7e-296)
		tmp = Float64(t_1 - Float64(i * Float64(y * j)));
	elseif (z <= 1.5e+46)
		tmp = Float64(y * Float64(Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) / y) - Float64(i * j)));
	elseif (z <= 1.95e+132)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (z <= 1.15e+181)
		tmp = t_3;
	elseif (z <= 3.9e+196)
		tmp = t_2;
	else
		tmp = t_4;
	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 * (t * i));
	t_3 = (j * ((a * c) - (y * i))) + (x * (y * z));
	t_4 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -1.85e+174)
		tmp = t_4;
	elseif (z <= -3e-122)
		tmp = t_3;
	elseif (z <= -2.8e-198)
		tmp = t_2;
	elseif (z <= -1.65e-264)
		tmp = t_3;
	elseif (z <= -2.7e-296)
		tmp = t_1 - (i * (y * j));
	elseif (z <= 1.5e+46)
		tmp = y * (((a * ((c * j) - (x * t))) / y) - (i * j));
	elseif (z <= 1.95e+132)
		tmp = b * ((t * i) - (z * c));
	elseif (z <= 1.15e+181)
		tmp = t_3;
	elseif (z <= 3.9e+196)
		tmp = t_2;
	else
		tmp = t_4;
	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[(t$95$1 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e+174], t$95$4, If[LessEqual[z, -3e-122], t$95$3, If[LessEqual[z, -2.8e-198], t$95$2, If[LessEqual[z, -1.65e-264], t$95$3, If[LessEqual[z, -2.7e-296], N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+46], N[(y * N[(N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+132], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+181], t$95$3, If[LessEqual[z, 3.9e+196], t$95$2, t$95$4]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.8500000000000001e174 or 3.9e196 < z

   1. Initial program 67.9%

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

   3. Taylor expanded in z around inf 84.6%

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

      1. *-commutative 84.6%

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

   5. Simplified 84.6%

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

   if -1.8500000000000001e174 < z < -3.00000000000000004e-122 or -2.7999999999999999e-198 < z < -1.65000000000000006e-264 or 1.95000000000000001e132 < z < 1.1499999999999999e181

   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 b around 0 73.4%

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

   4. Taylor expanded in t around 0 70.2%

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

   if -3.00000000000000004e-122 < z < -2.7999999999999999e-198 or 1.1499999999999999e181 < z < 3.9e196

   1. Initial program 89.6%

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

   3. Taylor expanded in c around 0 84.3%

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

   4. Taylor expanded in i around 0 84.2%

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

   if -1.65000000000000006e-264 < z < -2.69999999999999999e-296

   1. Initial program 57.2%

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

   3. Taylor expanded in b around 0 71.4%

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

   4. Taylor expanded in a around 0 85.7%

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

      1. associate-*r* 85.7%

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

      2. neg-mul-1 85.7%

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

   6. Simplified 85.7%

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

   if -2.69999999999999999e-296 < z < 1.50000000000000012e46

   1. Initial program 78.2%

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

   3. Taylor expanded in b around 0 67.0%

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

   4. Taylor expanded in y around -inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. *-commutative 71.0%

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

      3. distribute-rgt-neg-in 71.0%

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

   6. Simplified 73.7%

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

   7. Taylor expanded in z around 0 69.9%

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

   if 1.50000000000000012e46 < z < 1.95000000000000001e132

   1. Initial program 72.5%

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

   3. Taylor expanded in b around inf 67.2%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+174}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-122}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-264}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(\frac{a \cdot \left(c \cdot j - x \cdot t\right)}{y} - i \cdot j\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+132}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+181}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{+146}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{+29} \lor \neg \left(b \leq -170000000\right) \land b \leq 1.8 \cdot 10^{+141}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -3.1e+224)
     t_1
     (if (<= b -7.4e+178)
       (+ (* x (- (* y z) (* t a))) (* b (* t i)))
       (if (<= b -5.2e+146)
         (* c (- (* a j) (* z b)))
         (if (or (<= b -5.5e+29)
                 (and (not (<= b -170000000.0)) (<= b 1.8e+141)))
           (- (* j (- (* a c) (* y i))) (* x (- (* t a) (* y z))))
           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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.1e+224) {
		tmp = t_1;
	} else if (b <= -7.4e+178) {
		tmp = (x * ((y * z) - (t * a))) + (b * (t * i));
	} else if (b <= -5.2e+146) {
		tmp = c * ((a * j) - (z * b));
	} else if ((b <= -5.5e+29) || (!(b <= -170000000.0) && (b <= 1.8e+141))) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} 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 = b * ((t * i) - (z * c))
    if (b <= (-3.1d+224)) then
        tmp = t_1
    else if (b <= (-7.4d+178)) then
        tmp = (x * ((y * z) - (t * a))) + (b * (t * i))
    else if (b <= (-5.2d+146)) then
        tmp = c * ((a * j) - (z * b))
    else if ((b <= (-5.5d+29)) .or. (.not. (b <= (-170000000.0d0))) .and. (b <= 1.8d+141)) then
        tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
    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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.1e+224) {
		tmp = t_1;
	} else if (b <= -7.4e+178) {
		tmp = (x * ((y * z) - (t * a))) + (b * (t * i));
	} else if (b <= -5.2e+146) {
		tmp = c * ((a * j) - (z * b));
	} else if ((b <= -5.5e+29) || (!(b <= -170000000.0) && (b <= 1.8e+141))) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3.1e+224:
		tmp = t_1
	elif b <= -7.4e+178:
		tmp = (x * ((y * z) - (t * a))) + (b * (t * i))
	elif b <= -5.2e+146:
		tmp = c * ((a * j) - (z * b))
	elif (b <= -5.5e+29) or (not (b <= -170000000.0) and (b <= 1.8e+141)):
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (b <= -3.1e+224)
		tmp = t_1;
	elseif (b <= -7.4e+178)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(t * i)));
	elseif (b <= -5.2e+146)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif ((b <= -5.5e+29) || (!(b <= -170000000.0) && (b <= 1.8e+141)))
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	else
		tmp = t_1;
	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));
	tmp = 0.0;
	if (b <= -3.1e+224)
		tmp = t_1;
	elseif (b <= -7.4e+178)
		tmp = (x * ((y * z) - (t * a))) + (b * (t * i));
	elseif (b <= -5.2e+146)
		tmp = c * ((a * j) - (z * b));
	elseif ((b <= -5.5e+29) || (~((b <= -170000000.0)) && (b <= 1.8e+141)))
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e+224], t$95$1, If[LessEqual[b, -7.4e+178], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.2e+146], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -5.5e+29], And[N[Not[LessEqual[b, -170000000.0]], $MachinePrecision], LessEqual[b, 1.8e+141]]], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.0999999999999999e224 or -5.5e29 < b < -1.7e8 or 1.8000000000000001e141 < b

   1. Initial program 67.9%

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

   3. Taylor expanded in b around inf 84.9%

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

   if -3.0999999999999999e224 < b < -7.4000000000000005e178

   1. Initial program 90.6%

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

   3. Taylor expanded in c around 0 99.7%

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

   4. Taylor expanded in i around 0 99.7%

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

   if -7.4000000000000005e178 < b < -5.20000000000000028e146

   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 c around inf 79.2%

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

      1. *-commutative 79.2%

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

   5. Simplified 79.2%

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

   if -5.20000000000000028e146 < b < -5.5e29 or -1.7e8 < b < 1.8000000000000001e141

   1. Initial program 77.8%

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

   3. Taylor expanded in b around 0 72.9%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+224}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{+146}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{+29} \lor \neg \left(b \leq -170000000\right) \land b \leq 1.8 \cdot 10^{+141}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.7 \cdot 10^{+223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-59}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+105}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -3.7e+223)
     t_1
     (if (<= b -7.5e+196)
       (* x (- (* y z) (* t a)))
       (if (<= b -1.3e+113)
         t_1
         (if (<= b -2.7e+42)
           (* a (- (* c j) (* x t)))
           (if (<= b -3.4e-59)
             (* i (- (* t b) (* y j)))
             (if (<= b 1.8e+105)
               (+ (* j (- (* a c) (* y i))) (* x (* y z)))
               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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.7e+223) {
		tmp = t_1;
	} else if (b <= -7.5e+196) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= -1.3e+113) {
		tmp = t_1;
	} else if (b <= -2.7e+42) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= -3.4e-59) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= 1.8e+105) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} 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 = b * ((t * i) - (z * c))
    if (b <= (-3.7d+223)) then
        tmp = t_1
    else if (b <= (-7.5d+196)) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= (-1.3d+113)) then
        tmp = t_1
    else if (b <= (-2.7d+42)) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= (-3.4d-59)) then
        tmp = i * ((t * b) - (y * j))
    else if (b <= 1.8d+105) then
        tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
    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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.7e+223) {
		tmp = t_1;
	} else if (b <= -7.5e+196) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= -1.3e+113) {
		tmp = t_1;
	} else if (b <= -2.7e+42) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= -3.4e-59) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= 1.8e+105) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3.7e+223:
		tmp = t_1
	elif b <= -7.5e+196:
		tmp = x * ((y * z) - (t * a))
	elif b <= -1.3e+113:
		tmp = t_1
	elif b <= -2.7e+42:
		tmp = a * ((c * j) - (x * t))
	elif b <= -3.4e-59:
		tmp = i * ((t * b) - (y * j))
	elif b <= 1.8e+105:
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (b <= -3.7e+223)
		tmp = t_1;
	elseif (b <= -7.5e+196)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= -1.3e+113)
		tmp = t_1;
	elseif (b <= -2.7e+42)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= -3.4e-59)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (b <= 1.8e+105)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	else
		tmp = t_1;
	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));
	tmp = 0.0;
	if (b <= -3.7e+223)
		tmp = t_1;
	elseif (b <= -7.5e+196)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= -1.3e+113)
		tmp = t_1;
	elseif (b <= -2.7e+42)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= -3.4e-59)
		tmp = i * ((t * b) - (y * j));
	elseif (b <= 1.8e+105)
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.7e+223], t$95$1, If[LessEqual[b, -7.5e+196], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.3e+113], t$95$1, If[LessEqual[b, -2.7e+42], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.4e-59], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e+105], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.7000000000000002e223 or -7.5000000000000005e196 < b < -1.3e113 or 1.7999999999999999e105 < b

   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 b around inf 76.2%

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

   if -3.7000000000000002e223 < b < -7.5000000000000005e196

   1. Initial program 87.3%

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

   3. Taylor expanded in b around 0 87.3%

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

   4. Taylor expanded in j around 0 99.8%

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

   if -1.3e113 < b < -2.7000000000000001e42

   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 a around inf 64.1%

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

      1. +-commutative 64.1%

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

      2. mul-1-neg 64.1%

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

      3. unsub-neg 64.1%

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

   5. Simplified 64.1%

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

   if -2.7000000000000001e42 < b < -3.40000000000000018e-59

   1. Initial program 90.3%

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

   3. Taylor expanded in i around inf 71.8%

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

      1. distribute-lft-out-- 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in i around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. *-commutative 71.8%

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

      3. sub-neg 71.8%

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

      4. +-commutative 71.8%

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

      5. +-commutative 71.8%

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

      6. sub-neg 71.8%

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

      7. distribute-rgt-neg-in 71.8%

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

      8. neg-sub0 71.8%

         \[\leadsto i \cdot \color{blue}{\left(0 - \left(j \cdot y - t \cdot b\right)\right)} \]

      9. sub-neg 71.8%

         \[\leadsto i \cdot \left(0 - \color{blue}{\left(j \cdot y + \left(-t \cdot b\right)\right)}\right) \]

      10. +-commutative 71.8%

          \[\leadsto i \cdot \left(0 - \color{blue}{\left(\left(-t \cdot b\right) + j \cdot y\right)}\right) \]

      11. associate--r+ 71.8%

          \[\leadsto i \cdot \color{blue}{\left(\left(0 - \left(-t \cdot b\right)\right) - j \cdot y\right)} \]

      12. neg-sub0 71.8%

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

      13. remove-double-neg 71.8%

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

   8. Simplified 71.8%

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

   if -3.40000000000000018e-59 < b < 1.7999999999999999e105

   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 b around 0 74.0%

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

   4. Taylor expanded in t around 0 63.8%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+223}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{+42}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-59}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+105}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+75}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-64}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-140}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-242}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+181}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* z (- (* x y) (* b c)))))
   (if (<= z -1.75e+75)
     t_3
     (if (<= z -2.35e-64)
       (* c (- (* a j) (* z b)))
       (if (<= z -2.1e-111)
         t_1
         (if (<= z -2.6e-140)
           t_2
           (if (<= z 1.1e-242)
             t_1
             (if (<= z 3.6e+44) t_2 (if (<= z 2.1e+181) t_1 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 = i * ((t * b) - (y * j));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.75e+75) {
		tmp = t_3;
	} else if (z <= -2.35e-64) {
		tmp = c * ((a * j) - (z * b));
	} else if (z <= -2.1e-111) {
		tmp = t_1;
	} else if (z <= -2.6e-140) {
		tmp = t_2;
	} else if (z <= 1.1e-242) {
		tmp = t_1;
	} else if (z <= 3.6e+44) {
		tmp = t_2;
	} else if (z <= 2.1e+181) {
		tmp = t_1;
	} 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 = i * ((t * b) - (y * j))
    t_2 = a * ((c * j) - (x * t))
    t_3 = z * ((x * y) - (b * c))
    if (z <= (-1.75d+75)) then
        tmp = t_3
    else if (z <= (-2.35d-64)) then
        tmp = c * ((a * j) - (z * b))
    else if (z <= (-2.1d-111)) then
        tmp = t_1
    else if (z <= (-2.6d-140)) then
        tmp = t_2
    else if (z <= 1.1d-242) then
        tmp = t_1
    else if (z <= 3.6d+44) then
        tmp = t_2
    else if (z <= 2.1d+181) then
        tmp = t_1
    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 = i * ((t * b) - (y * j));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.75e+75) {
		tmp = t_3;
	} else if (z <= -2.35e-64) {
		tmp = c * ((a * j) - (z * b));
	} else if (z <= -2.1e-111) {
		tmp = t_1;
	} else if (z <= -2.6e-140) {
		tmp = t_2;
	} else if (z <= 1.1e-242) {
		tmp = t_1;
	} else if (z <= 3.6e+44) {
		tmp = t_2;
	} else if (z <= 2.1e+181) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = a * ((c * j) - (x * t))
	t_3 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -1.75e+75:
		tmp = t_3
	elif z <= -2.35e-64:
		tmp = c * ((a * j) - (z * b))
	elif z <= -2.1e-111:
		tmp = t_1
	elif z <= -2.6e-140:
		tmp = t_2
	elif z <= 1.1e-242:
		tmp = t_1
	elif z <= 3.6e+44:
		tmp = t_2
	elif z <= 2.1e+181:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -1.75e+75)
		tmp = t_3;
	elseif (z <= -2.35e-64)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (z <= -2.1e-111)
		tmp = t_1;
	elseif (z <= -2.6e-140)
		tmp = t_2;
	elseif (z <= 1.1e-242)
		tmp = t_1;
	elseif (z <= 3.6e+44)
		tmp = t_2;
	elseif (z <= 2.1e+181)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = a * ((c * j) - (x * t));
	t_3 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -1.75e+75)
		tmp = t_3;
	elseif (z <= -2.35e-64)
		tmp = c * ((a * j) - (z * b));
	elseif (z <= -2.1e-111)
		tmp = t_1;
	elseif (z <= -2.6e-140)
		tmp = t_2;
	elseif (z <= 1.1e-242)
		tmp = t_1;
	elseif (z <= 3.6e+44)
		tmp = t_2;
	elseif (z <= 2.1e+181)
		tmp = t_1;
	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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+75], t$95$3, If[LessEqual[z, -2.35e-64], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e-111], t$95$1, If[LessEqual[z, -2.6e-140], t$95$2, If[LessEqual[z, 1.1e-242], t$95$1, If[LessEqual[z, 3.6e+44], t$95$2, If[LessEqual[z, 2.1e+181], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.7499999999999999e75 or 2.09999999999999997e181 < z

   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 z around inf 75.4%

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

      1. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   if -1.7499999999999999e75 < z < -2.3499999999999999e-64

   1. Initial program 91.6%

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

   3. Taylor expanded in c around inf 57.3%

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

      1. *-commutative 57.3%

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

   5. Simplified 57.3%

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

   if -2.3499999999999999e-64 < z < -2.0999999999999999e-111 or -2.5999999999999998e-140 < z < 1.10000000000000001e-242 or 3.6e44 < z < 2.09999999999999997e181

   1. Initial program 78.6%

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

   3. Taylor expanded in i around inf 61.1%

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

      1. distribute-lft-out-- 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in i around 0 61.1%

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

      1. mul-1-neg 61.1%

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

      2. *-commutative 61.1%

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

      3. sub-neg 61.1%

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

      4. +-commutative 61.1%

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

      5. +-commutative 61.1%

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

      6. sub-neg 61.1%

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

      7. distribute-rgt-neg-in 61.1%

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

      8. neg-sub0 61.1%

         \[\leadsto i \cdot \color{blue}{\left(0 - \left(j \cdot y - t \cdot b\right)\right)} \]

      9. sub-neg 61.1%

         \[\leadsto i \cdot \left(0 - \color{blue}{\left(j \cdot y + \left(-t \cdot b\right)\right)}\right) \]

      10. +-commutative 61.1%

          \[\leadsto i \cdot \left(0 - \color{blue}{\left(\left(-t \cdot b\right) + j \cdot y\right)}\right) \]

      11. associate--r+ 61.1%

          \[\leadsto i \cdot \color{blue}{\left(\left(0 - \left(-t \cdot b\right)\right) - j \cdot y\right)} \]

      12. neg-sub0 61.1%

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

      13. remove-double-neg 61.1%

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

   8. Simplified 61.1%

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

   if -2.0999999999999999e-111 < z < -2.5999999999999998e-140 or 1.10000000000000001e-242 < z < 3.6e44

   1. Initial program 73.5%

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

   3. Taylor expanded in a around inf 60.7%

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

      1. +-commutative 60.7%

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

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

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

   5. Simplified 60.7%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+75}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-64}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-111}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-140}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-242}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+181}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.4 \cdot 10^{-50}:\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 7.9 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(c \cdot j - x \cdot t\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{+174}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - \left(i \cdot \left(y \cdot j\right) + a \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{+209}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -2.4e-50)
     (+ t_1 (* x (* y z)))
     (if (<= j 7.9e-86)
       (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
       (if (<= j 5.6e+42)
         (* y (+ (* x z) (- (/ (* a (- (* c j) (* x t))) y) (* i j))))
         (if (<= j 6.2e+174)
           (- (* b (* t i)) (+ (* i (* y j)) (* a (* x t))))
           (if (<= j 8.8e+209)
             (* a (* c j))
             (- t_1 (* x (- (* t a) (* y 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.4e-50) {
		tmp = t_1 + (x * (y * z));
	} else if (j <= 7.9e-86) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else if (j <= 5.6e+42) {
		tmp = y * ((x * z) + (((a * ((c * j) - (x * t))) / y) - (i * j)));
	} else if (j <= 6.2e+174) {
		tmp = (b * (t * i)) - ((i * (y * j)) + (a * (x * t)));
	} else if (j <= 8.8e+209) {
		tmp = a * (c * j);
	} else {
		tmp = t_1 - (x * ((t * a) - (y * 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 = j * ((a * c) - (y * i))
    if (j <= (-2.4d-50)) then
        tmp = t_1 + (x * (y * z))
    else if (j <= 7.9d-86) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    else if (j <= 5.6d+42) then
        tmp = y * ((x * z) + (((a * ((c * j) - (x * t))) / y) - (i * j)))
    else if (j <= 6.2d+174) then
        tmp = (b * (t * i)) - ((i * (y * j)) + (a * (x * t)))
    else if (j <= 8.8d+209) then
        tmp = a * (c * j)
    else
        tmp = t_1 - (x * ((t * a) - (y * 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.4e-50) {
		tmp = t_1 + (x * (y * z));
	} else if (j <= 7.9e-86) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else if (j <= 5.6e+42) {
		tmp = y * ((x * z) + (((a * ((c * j) - (x * t))) / y) - (i * j)));
	} else if (j <= 6.2e+174) {
		tmp = (b * (t * i)) - ((i * (y * j)) + (a * (x * t)));
	} else if (j <= 8.8e+209) {
		tmp = a * (c * j);
	} else {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.4e-50:
		tmp = t_1 + (x * (y * z))
	elif j <= 7.9e-86:
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	elif j <= 5.6e+42:
		tmp = y * ((x * z) + (((a * ((c * j) - (x * t))) / y) - (i * j)))
	elif j <= 6.2e+174:
		tmp = (b * (t * i)) - ((i * (y * j)) + (a * (x * t)))
	elif j <= 8.8e+209:
		tmp = a * (c * j)
	else:
		tmp = t_1 - (x * ((t * a) - (y * z)))
	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)))
	tmp = 0.0
	if (j <= -2.4e-50)
		tmp = Float64(t_1 + Float64(x * Float64(y * z)));
	elseif (j <= 7.9e-86)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (j <= 5.6e+42)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) / y) - Float64(i * j))));
	elseif (j <= 6.2e+174)
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(Float64(i * Float64(y * j)) + Float64(a * Float64(x * t))));
	elseif (j <= 8.8e+209)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	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));
	tmp = 0.0;
	if (j <= -2.4e-50)
		tmp = t_1 + (x * (y * z));
	elseif (j <= 7.9e-86)
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	elseif (j <= 5.6e+42)
		tmp = y * ((x * z) + (((a * ((c * j) - (x * t))) / y) - (i * j)));
	elseif (j <= 6.2e+174)
		tmp = (b * (t * i)) - ((i * (y * j)) + (a * (x * t)));
	elseif (j <= 8.8e+209)
		tmp = a * (c * j);
	else
		tmp = t_1 - (x * ((t * a) - (y * z)));
	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]}, If[LessEqual[j, -2.4e-50], N[(t$95$1 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.9e-86], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.6e+42], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.2e+174], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision] + N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.8e+209], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.40000000000000002e-50

   1. Initial program 70.8%

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

   3. Taylor expanded in b around 0 68.3%

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

   4. Taylor expanded in t around 0 68.3%

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

   if -2.40000000000000002e-50 < j < 7.8999999999999998e-86

   1. Initial program 78.7%

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

   3. Taylor expanded in j around 0 80.8%

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

   if 7.8999999999999998e-86 < j < 5.5999999999999999e42

   1. Initial program 69.9%

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

   3. Taylor expanded in b around 0 62.2%

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

   4. Taylor expanded in y around -inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. *-commutative 66.7%

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

      3. distribute-rgt-neg-in 66.7%

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

   6. Simplified 74.4%

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

   if 5.5999999999999999e42 < j < 6.2e174

   1. Initial program 73.6%

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

   3. Taylor expanded in c around 0 69.9%

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

   4. Taylor expanded in z around 0 85.0%

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

      1. neg-mul-1 85.0%

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

      2. unsub-neg 85.0%

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

      3. mul-1-neg 85.0%

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

      4. distribute-rgt-neg-in 85.0%

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

      5. distribute-rgt-neg-in 85.0%

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

   6. Simplified 85.0%

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

   if 6.2e174 < j < 8.7999999999999995e209

   1. Initial program 70.2%

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

   3. Taylor expanded in a around inf 70.3%

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

      1. +-commutative 70.3%

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

      2. mul-1-neg 70.3%

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

      3. unsub-neg 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in c around inf 70.7%

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

   if 8.7999999999999995e209 < j

   1. Initial program 87.0%

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

   3. Taylor expanded in b around 0 82.9%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{-50}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 7.9 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(c \cdot j - x \cdot t\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{+174}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - \left(i \cdot \left(y \cdot j\right) + a \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{+209}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+174}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-122}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-251}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) + \left(t\_1 - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(c \cdot j - x \cdot t\right)}{y} - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= z -2.2e+174)
     (* z (- (* x y) (* b c)))
     (if (<= z -3.7e-122)
       (- (* j (- (* a c) (* y i))) (* x (- (* t a) (* y z))))
       (if (<= z -8.6e-251)
         (+ (* b (* t i)) (- t_1 (* i (* y j))))
         (if (<= z 4.7e+45)
           (* y (+ (* x z) (- (/ (* a (- (* c j) (* x t))) y) (* i j))))
           (+ t_1 (* b (- (* t i) (* z 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 <= -2.2e+174) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= -3.7e-122) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else if (z <= -8.6e-251) {
		tmp = (b * (t * i)) + (t_1 - (i * (y * j)));
	} else if (z <= 4.7e+45) {
		tmp = y * ((x * z) + (((a * ((c * j) - (x * t))) / y) - (i * j)));
	} else {
		tmp = t_1 + (b * ((t * i) - (z * 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 <= (-2.2d+174)) then
        tmp = z * ((x * y) - (b * c))
    else if (z <= (-3.7d-122)) then
        tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
    else if (z <= (-8.6d-251)) then
        tmp = (b * (t * i)) + (t_1 - (i * (y * j)))
    else if (z <= 4.7d+45) then
        tmp = y * ((x * z) + (((a * ((c * j) - (x * t))) / y) - (i * j)))
    else
        tmp = t_1 + (b * ((t * i) - (z * 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 <= -2.2e+174) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= -3.7e-122) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else if (z <= -8.6e-251) {
		tmp = (b * (t * i)) + (t_1 - (i * (y * j)));
	} else if (z <= 4.7e+45) {
		tmp = y * ((x * z) + (((a * ((c * j) - (x * t))) / y) - (i * j)));
	} else {
		tmp = t_1 + (b * ((t * i) - (z * 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 <= -2.2e+174:
		tmp = z * ((x * y) - (b * c))
	elif z <= -3.7e-122:
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
	elif z <= -8.6e-251:
		tmp = (b * (t * i)) + (t_1 - (i * (y * j)))
	elif z <= 4.7e+45:
		tmp = y * ((x * z) + (((a * ((c * j) - (x * t))) / y) - (i * j)))
	else:
		tmp = t_1 + (b * ((t * i) - (z * 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 <= -2.2e+174)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (z <= -3.7e-122)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (z <= -8.6e-251)
		tmp = Float64(Float64(b * Float64(t * i)) + Float64(t_1 - Float64(i * Float64(y * j))));
	elseif (z <= 4.7e+45)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) / y) - Float64(i * j))));
	else
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * 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 <= -2.2e+174)
		tmp = z * ((x * y) - (b * c));
	elseif (z <= -3.7e-122)
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	elseif (z <= -8.6e-251)
		tmp = (b * (t * i)) + (t_1 - (i * (y * j)));
	elseif (z <= 4.7e+45)
		tmp = y * ((x * z) + (((a * ((c * j) - (x * t))) / y) - (i * j)));
	else
		tmp = t_1 + (b * ((t * i) - (z * 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, -2.2e+174], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.7e-122], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.6e-251], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e+45], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.2000000000000002e174

   1. Initial program 59.9%

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

   3. Taylor expanded in z around inf 85.1%

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

      1. *-commutative 85.1%

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

   5. Simplified 85.1%

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

   if -2.2000000000000002e174 < z < -3.6999999999999997e-122

   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 b around 0 72.1%

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

   if -3.6999999999999997e-122 < z < -8.6000000000000004e-251

   1. Initial program 84.6%

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

   3. Taylor expanded in c around 0 76.8%

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

   if -8.6000000000000004e-251 < z < 4.70000000000000002e45

   1. Initial program 76.1%

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

   3. Taylor expanded in b around 0 68.5%

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

   4. Taylor expanded in y around -inf 73.2%

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

      1. mul-1-neg 73.2%

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

      2. *-commutative 73.2%

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

      3. distribute-rgt-neg-in 73.2%

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

   6. Simplified 75.5%

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

   if 4.70000000000000002e45 < z

   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 j around 0 74.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+174}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-122}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-251}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(c \cdot j - x \cdot t\right)}{y} - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ t_3 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -5.1 \cdot 10^{-61}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -4.25 \cdot 10^{-306}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 9.4 \cdot 10^{+50} \lor \neg \left(c \leq 1.15 \cdot 10^{+246}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))) (t_2 (* y (* x z))) (t_3 (* a (* c j))))
   (if (<= c -5.1e-61)
     t_3
     (if (<= c -6.5e-265)
       t_1
       (if (<= c -4.25e-306)
         t_2
         (if (<= c 4.3e-160)
           t_1
           (if (<= c 3e-59)
             (* b (* t i))
             (if (or (<= c 9.4e+50) (not (<= c 1.15e+246))) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (y * -j);
	double t_2 = y * (x * z);
	double t_3 = a * (c * j);
	double tmp;
	if (c <= -5.1e-61) {
		tmp = t_3;
	} else if (c <= -6.5e-265) {
		tmp = t_1;
	} else if (c <= -4.25e-306) {
		tmp = t_2;
	} else if (c <= 4.3e-160) {
		tmp = t_1;
	} else if (c <= 3e-59) {
		tmp = b * (t * i);
	} else if ((c <= 9.4e+50) || !(c <= 1.15e+246)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * (y * -j)
    t_2 = y * (x * z)
    t_3 = a * (c * j)
    if (c <= (-5.1d-61)) then
        tmp = t_3
    else if (c <= (-6.5d-265)) then
        tmp = t_1
    else if (c <= (-4.25d-306)) then
        tmp = t_2
    else if (c <= 4.3d-160) then
        tmp = t_1
    else if (c <= 3d-59) then
        tmp = b * (t * i)
    else if ((c <= 9.4d+50) .or. (.not. (c <= 1.15d+246))) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (y * -j);
	double t_2 = y * (x * z);
	double t_3 = a * (c * j);
	double tmp;
	if (c <= -5.1e-61) {
		tmp = t_3;
	} else if (c <= -6.5e-265) {
		tmp = t_1;
	} else if (c <= -4.25e-306) {
		tmp = t_2;
	} else if (c <= 4.3e-160) {
		tmp = t_1;
	} else if (c <= 3e-59) {
		tmp = b * (t * i);
	} else if ((c <= 9.4e+50) || !(c <= 1.15e+246)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	t_2 = y * (x * z)
	t_3 = a * (c * j)
	tmp = 0
	if c <= -5.1e-61:
		tmp = t_3
	elif c <= -6.5e-265:
		tmp = t_1
	elif c <= -4.25e-306:
		tmp = t_2
	elif c <= 4.3e-160:
		tmp = t_1
	elif c <= 3e-59:
		tmp = b * (t * i)
	elif (c <= 9.4e+50) or not (c <= 1.15e+246):
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	t_2 = Float64(y * Float64(x * z))
	t_3 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (c <= -5.1e-61)
		tmp = t_3;
	elseif (c <= -6.5e-265)
		tmp = t_1;
	elseif (c <= -4.25e-306)
		tmp = t_2;
	elseif (c <= 4.3e-160)
		tmp = t_1;
	elseif (c <= 3e-59)
		tmp = Float64(b * Float64(t * i));
	elseif ((c <= 9.4e+50) || !(c <= 1.15e+246))
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (y * -j);
	t_2 = y * (x * z);
	t_3 = a * (c * j);
	tmp = 0.0;
	if (c <= -5.1e-61)
		tmp = t_3;
	elseif (c <= -6.5e-265)
		tmp = t_1;
	elseif (c <= -4.25e-306)
		tmp = t_2;
	elseif (c <= 4.3e-160)
		tmp = t_1;
	elseif (c <= 3e-59)
		tmp = b * (t * i);
	elseif ((c <= 9.4e+50) || ~((c <= 1.15e+246)))
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.1e-61], t$95$3, If[LessEqual[c, -6.5e-265], t$95$1, If[LessEqual[c, -4.25e-306], t$95$2, If[LessEqual[c, 4.3e-160], t$95$1, If[LessEqual[c, 3e-59], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 9.4e+50], N[Not[LessEqual[c, 1.15e+246]], $MachinePrecision]], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -5.09999999999999968e-61 or 9.39999999999999947e50 < c < 1.15000000000000007e246

   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 51.9%

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

      1. +-commutative 51.9%

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

      2. mul-1-neg 51.9%

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

      3. unsub-neg 51.9%

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

   5. Simplified 51.9%

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

   6. Taylor expanded in c around inf 42.3%

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

   if -5.09999999999999968e-61 < c < -6.5000000000000005e-265 or -4.2500000000000001e-306 < c < 4.30000000000000014e-160

   1. Initial program 87.5%

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

   3. Taylor expanded in y around inf 44.8%

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

      1. +-commutative 44.8%

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

      2. mul-1-neg 44.8%

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

      3. unsub-neg 44.8%

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

      4. *-commutative 44.8%

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

   5. Simplified 44.8%

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

   6. Taylor expanded in z around 0 43.1%

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

      1. neg-mul-1 43.1%

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

      2. distribute-rgt-neg-in 43.1%

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

      3. distribute-lft-neg-in 43.1%

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

   8. Simplified 43.1%

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

   if -6.5000000000000005e-265 < c < -4.2500000000000001e-306 or 3.0000000000000001e-59 < c < 9.39999999999999947e50 or 1.15000000000000007e246 < c

   1. Initial program 73.6%

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

   3. Taylor expanded in y around inf 53.8%

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

      1. +-commutative 53.8%

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

      2. mul-1-neg 53.8%

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

      3. unsub-neg 53.8%

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

      4. *-commutative 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in z around inf 45.3%

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

      1. *-commutative 45.3%

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

   8. Simplified 45.3%

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

   if 4.30000000000000014e-160 < c < 3.0000000000000001e-59

   1. Initial program 89.3%

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

   3. Taylor expanded in t around inf 69.2%

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

      1. distribute-lft-out-- 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in a around 0 53.8%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.1 \cdot 10^{-61}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-265}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq -4.25 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{-160}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 9.4 \cdot 10^{+50} \lor \neg \left(c \leq 1.15 \cdot 10^{+246}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 28.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -6.1 \cdot 10^{-62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq -4.1 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+49} \lor \neg \left(c \leq 1.15 \cdot 10^{+246}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))) (t_2 (* a (* c j))))
   (if (<= c -6.1e-62)
     t_2
     (if (<= c -1.75e-274)
       (* b (* t i))
       (if (<= c -4.1e-306)
         t_1
         (if (<= c 2.5e-58)
           (* t (* b i))
           (if (or (<= c 2.3e+49) (not (<= c 1.15e+246))) 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 = y * (x * z);
	double t_2 = a * (c * j);
	double tmp;
	if (c <= -6.1e-62) {
		tmp = t_2;
	} else if (c <= -1.75e-274) {
		tmp = b * (t * i);
	} else if (c <= -4.1e-306) {
		tmp = t_1;
	} else if (c <= 2.5e-58) {
		tmp = t * (b * i);
	} else if ((c <= 2.3e+49) || !(c <= 1.15e+246)) {
		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 = y * (x * z)
    t_2 = a * (c * j)
    if (c <= (-6.1d-62)) then
        tmp = t_2
    else if (c <= (-1.75d-274)) then
        tmp = b * (t * i)
    else if (c <= (-4.1d-306)) then
        tmp = t_1
    else if (c <= 2.5d-58) then
        tmp = t * (b * i)
    else if ((c <= 2.3d+49) .or. (.not. (c <= 1.15d+246))) 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 = y * (x * z);
	double t_2 = a * (c * j);
	double tmp;
	if (c <= -6.1e-62) {
		tmp = t_2;
	} else if (c <= -1.75e-274) {
		tmp = b * (t * i);
	} else if (c <= -4.1e-306) {
		tmp = t_1;
	} else if (c <= 2.5e-58) {
		tmp = t * (b * i);
	} else if ((c <= 2.3e+49) || !(c <= 1.15e+246)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	t_2 = a * (c * j)
	tmp = 0
	if c <= -6.1e-62:
		tmp = t_2
	elif c <= -1.75e-274:
		tmp = b * (t * i)
	elif c <= -4.1e-306:
		tmp = t_1
	elif c <= 2.5e-58:
		tmp = t * (b * i)
	elif (c <= 2.3e+49) or not (c <= 1.15e+246):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (c <= -6.1e-62)
		tmp = t_2;
	elseif (c <= -1.75e-274)
		tmp = Float64(b * Float64(t * i));
	elseif (c <= -4.1e-306)
		tmp = t_1;
	elseif (c <= 2.5e-58)
		tmp = Float64(t * Float64(b * i));
	elseif ((c <= 2.3e+49) || !(c <= 1.15e+246))
		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 = y * (x * z);
	t_2 = a * (c * j);
	tmp = 0.0;
	if (c <= -6.1e-62)
		tmp = t_2;
	elseif (c <= -1.75e-274)
		tmp = b * (t * i);
	elseif (c <= -4.1e-306)
		tmp = t_1;
	elseif (c <= 2.5e-58)
		tmp = t * (b * i);
	elseif ((c <= 2.3e+49) || ~((c <= 1.15e+246)))
		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[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.1e-62], t$95$2, If[LessEqual[c, -1.75e-274], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.1e-306], t$95$1, If[LessEqual[c, 2.5e-58], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 2.3e+49], N[Not[LessEqual[c, 1.15e+246]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -6.1e-62 or 2.30000000000000002e49 < c < 1.15000000000000007e246

   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 51.9%

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

      1. +-commutative 51.9%

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

      2. mul-1-neg 51.9%

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

      3. unsub-neg 51.9%

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

   5. Simplified 51.9%

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

   6. Taylor expanded in c around inf 42.3%

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

   if -6.1e-62 < c < -1.74999999999999991e-274

   1. Initial program 87.3%

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

   3. Taylor expanded in t around inf 40.0%

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

      1. distribute-lft-out-- 40.0%

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

   5. Simplified 40.0%

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

   6. Taylor expanded in a around 0 39.7%

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

   if -1.74999999999999991e-274 < c < -4.09999999999999985e-306 or 2.49999999999999989e-58 < c < 2.30000000000000002e49 or 1.15000000000000007e246 < c

   1. Initial program 71.4%

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

   3. Taylor expanded in y around inf 55.9%

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

      1. +-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. *-commutative 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in z around inf 46.9%

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

      1. *-commutative 46.9%

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

   8. Simplified 46.9%

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

   if -4.09999999999999985e-306 < c < 2.49999999999999989e-58

   1. Initial program 89.2%

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

   3. Taylor expanded in t around inf 61.0%

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

      1. distribute-lft-out-- 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in a around 0 36.1%

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

      1. associate-*r* 38.4%

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

      2. *-commutative 38.4%

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

   8. Simplified 38.4%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.1 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq -4.1 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+49} \lor \neg \left(c \leq 1.15 \cdot 10^{+246}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.45 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 102000000000:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+138} \lor \neg \left(c \leq 6.5 \cdot 10^{+164}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 - i \cdot \left(y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -1.45e-12)
     t_2
     (if (<= c 102000000000.0)
       (+ t_1 (* b (* t i)))
       (if (or (<= c 2.5e+138) (not (<= c 6.5e+164)))
         t_2
         (- t_1 (* i (* y j))))))))

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 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.45e-12) {
		tmp = t_2;
	} else if (c <= 102000000000.0) {
		tmp = t_1 + (b * (t * i));
	} else if ((c <= 2.5e+138) || !(c <= 6.5e+164)) {
		tmp = t_2;
	} else {
		tmp = t_1 - (i * (y * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-1.45d-12)) then
        tmp = t_2
    else if (c <= 102000000000.0d0) then
        tmp = t_1 + (b * (t * i))
    else if ((c <= 2.5d+138) .or. (.not. (c <= 6.5d+164))) then
        tmp = t_2
    else
        tmp = t_1 - (i * (y * 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 t_1 = x * ((y * z) - (t * a));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.45e-12) {
		tmp = t_2;
	} else if (c <= 102000000000.0) {
		tmp = t_1 + (b * (t * i));
	} else if ((c <= 2.5e+138) || !(c <= 6.5e+164)) {
		tmp = t_2;
	} else {
		tmp = t_1 - (i * (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -1.45e-12:
		tmp = t_2
	elif c <= 102000000000.0:
		tmp = t_1 + (b * (t * i))
	elif (c <= 2.5e+138) or not (c <= 6.5e+164):
		tmp = t_2
	else:
		tmp = t_1 - (i * (y * j))
	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(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.45e-12)
		tmp = t_2;
	elseif (c <= 102000000000.0)
		tmp = Float64(t_1 + Float64(b * Float64(t * i)));
	elseif ((c <= 2.5e+138) || !(c <= 6.5e+164))
		tmp = t_2;
	else
		tmp = Float64(t_1 - Float64(i * Float64(y * j)));
	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 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.45e-12)
		tmp = t_2;
	elseif (c <= 102000000000.0)
		tmp = t_1 + (b * (t * i));
	elseif ((c <= 2.5e+138) || ~((c <= 6.5e+164)))
		tmp = t_2;
	else
		tmp = t_1 - (i * (y * j));
	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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.45e-12], t$95$2, If[LessEqual[c, 102000000000.0], N[(t$95$1 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 2.5e+138], N[Not[LessEqual[c, 6.5e+164]], $MachinePrecision]], t$95$2, N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.4500000000000001e-12 or 1.02e11 < c < 2.50000000000000008e138 or 6.5000000000000003e164 < c

   1. Initial program 65.0%

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

   3. Taylor expanded in c around inf 65.6%

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

      1. *-commutative 65.6%

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

   5. Simplified 65.6%

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

   if -1.4500000000000001e-12 < c < 1.02e11

   1. Initial program 86.6%

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

   3. Taylor expanded in c around 0 80.4%

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

   4. Taylor expanded in i around 0 66.0%

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

   if 2.50000000000000008e138 < c < 6.5000000000000003e164

   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 b around 0 70.9%

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

   4. Taylor expanded in a around 0 85.2%

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

      1. associate-*r* 85.2%

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

      2. neg-mul-1 85.2%

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

   6. Simplified 85.2%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.45 \cdot 10^{-12}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 102000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+138} \lor \neg \left(c \leq 6.5 \cdot 10^{+164}\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.9 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-154}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 3.45 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -2.9e+17)
     t_1
     (if (<= c 1.8e-154)
       (- (* x (- (* y z) (* t a))) (* i (* y j)))
       (if (<= c 2.2e-59)
         (* t (- (* b i) (* x a)))
         (if (<= c 3.45e+25)
           (+ (* j (- (* a c) (* y i))) (* x (* y z)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -2.9e+17) {
		tmp = t_1;
	} else if (c <= 1.8e-154) {
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	} else if (c <= 2.2e-59) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 3.45e+25) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} 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 * ((a * j) - (z * b))
    if (c <= (-2.9d+17)) then
        tmp = t_1
    else if (c <= 1.8d-154) then
        tmp = (x * ((y * z) - (t * a))) - (i * (y * j))
    else if (c <= 2.2d-59) then
        tmp = t * ((b * i) - (x * a))
    else if (c <= 3.45d+25) then
        tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -2.9e+17) {
		tmp = t_1;
	} else if (c <= 1.8e-154) {
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	} else if (c <= 2.2e-59) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 3.45e+25) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -2.9e+17:
		tmp = t_1
	elif c <= 1.8e-154:
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j))
	elif c <= 2.2e-59:
		tmp = t * ((b * i) - (x * a))
	elif c <= 3.45e+25:
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.9e+17)
		tmp = t_1;
	elseif (c <= 1.8e-154)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(i * Float64(y * j)));
	elseif (c <= 2.2e-59)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (c <= 3.45e+25)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.9e+17)
		tmp = t_1;
	elseif (c <= 1.8e-154)
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	elseif (c <= 2.2e-59)
		tmp = t * ((b * i) - (x * a));
	elseif (c <= 3.45e+25)
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.9e+17], t$95$1, If[LessEqual[c, 1.8e-154], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e-59], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.45e+25], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.9e17 or 3.4499999999999999e25 < c

   1. Initial program 65.1%

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

   3. Taylor expanded in c around inf 63.5%

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

      1. *-commutative 63.5%

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

   5. Simplified 63.5%

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

   if -2.9e17 < c < 1.8000000000000001e-154

   1. Initial program 87.6%

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

   3. Taylor expanded in b around 0 69.1%

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

   4. Taylor expanded in a around 0 66.1%

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

      1. associate-*r* 66.1%

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

      2. neg-mul-1 66.1%

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

   6. Simplified 66.1%

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

   if 1.8000000000000001e-154 < c < 2.1999999999999999e-59

   1. Initial program 88.1%

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

   3. Taylor expanded in t around inf 71.4%

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

      1. distribute-lft-out-- 71.4%

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

   5. Simplified 71.4%

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

   if 2.1999999999999999e-59 < c < 3.4499999999999999e25

   1. Initial program 76.6%

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

   3. Taylor expanded in b around 0 66.1%

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

   4. Taylor expanded in t around 0 66.1%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{+17}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-154}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 3.45 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -0.042:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-263}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* i (- (* t b) (* y j))))
        (t_3 (* c (- (* a j) (* z b)))))
   (if (<= c -0.042)
     t_3
     (if (<= c -5.2e-263)
       t_2
       (if (<= c 1.9e-282)
         t_1
         (if (<= c 3.6e-38) t_2 (if (<= c 7.5e+29) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -0.042) {
		tmp = t_3;
	} else if (c <= -5.2e-263) {
		tmp = t_2;
	} else if (c <= 1.9e-282) {
		tmp = t_1;
	} else if (c <= 3.6e-38) {
		tmp = t_2;
	} else if (c <= 7.5e+29) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = i * ((t * b) - (y * j))
    t_3 = c * ((a * j) - (z * b))
    if (c <= (-0.042d0)) then
        tmp = t_3
    else if (c <= (-5.2d-263)) then
        tmp = t_2
    else if (c <= 1.9d-282) then
        tmp = t_1
    else if (c <= 3.6d-38) then
        tmp = t_2
    else if (c <= 7.5d+29) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -0.042) {
		tmp = t_3;
	} else if (c <= -5.2e-263) {
		tmp = t_2;
	} else if (c <= 1.9e-282) {
		tmp = t_1;
	} else if (c <= 3.6e-38) {
		tmp = t_2;
	} else if (c <= 7.5e+29) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = i * ((t * b) - (y * j))
	t_3 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -0.042:
		tmp = t_3
	elif c <= -5.2e-263:
		tmp = t_2
	elif c <= 1.9e-282:
		tmp = t_1
	elif c <= 3.6e-38:
		tmp = t_2
	elif c <= 7.5e+29:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -0.042)
		tmp = t_3;
	elseif (c <= -5.2e-263)
		tmp = t_2;
	elseif (c <= 1.9e-282)
		tmp = t_1;
	elseif (c <= 3.6e-38)
		tmp = t_2;
	elseif (c <= 7.5e+29)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = i * ((t * b) - (y * j));
	t_3 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -0.042)
		tmp = t_3;
	elseif (c <= -5.2e-263)
		tmp = t_2;
	elseif (c <= 1.9e-282)
		tmp = t_1;
	elseif (c <= 3.6e-38)
		tmp = t_2;
	elseif (c <= 7.5e+29)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -0.042], t$95$3, If[LessEqual[c, -5.2e-263], t$95$2, If[LessEqual[c, 1.9e-282], t$95$1, If[LessEqual[c, 3.6e-38], t$95$2, If[LessEqual[c, 7.5e+29], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -0.0420000000000000026 or 7.49999999999999945e29 < c

   1. Initial program 65.4%

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

   3. Taylor expanded in c around inf 63.7%

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

      1. *-commutative 63.7%

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

   5. Simplified 63.7%

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

   if -0.0420000000000000026 < c < -5.2000000000000001e-263 or 1.89999999999999996e-282 < c < 3.6000000000000001e-38

   1. Initial program 86.7%

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

   3. Taylor expanded in i around inf 61.6%

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

      1. distribute-lft-out-- 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in i around 0 61.6%

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

      1. mul-1-neg 61.6%

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

      2. *-commutative 61.6%

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

      3. sub-neg 61.6%

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

      4. +-commutative 61.6%

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

      5. +-commutative 61.6%

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

      6. sub-neg 61.6%

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

      7. distribute-rgt-neg-in 61.6%

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

      8. neg-sub0 61.6%

         \[\leadsto i \cdot \color{blue}{\left(0 - \left(j \cdot y - t \cdot b\right)\right)} \]

      9. sub-neg 61.6%

         \[\leadsto i \cdot \left(0 - \color{blue}{\left(j \cdot y + \left(-t \cdot b\right)\right)}\right) \]

      10. +-commutative 61.6%

          \[\leadsto i \cdot \left(0 - \color{blue}{\left(\left(-t \cdot b\right) + j \cdot y\right)}\right) \]

      11. associate--r+ 61.6%

          \[\leadsto i \cdot \color{blue}{\left(\left(0 - \left(-t \cdot b\right)\right) - j \cdot y\right)} \]

      12. neg-sub0 61.6%

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

      13. remove-double-neg 61.6%

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

   8. Simplified 61.6%

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

   if -5.2000000000000001e-263 < c < 1.89999999999999996e-282 or 3.6000000000000001e-38 < c < 7.49999999999999945e29

   1. Initial program 84.9%

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

   3. Taylor expanded in b around 0 74.9%

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

   4. Taylor expanded in j around 0 61.8%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -0.042:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-263}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-282}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-38}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.56 \cdot 10^{+116} \lor \neg \left(b \leq -6.2 \cdot 10^{+65}\right) \land \left(b \leq -2.4 \cdot 10^{-95} \lor \neg \left(b \leq 3.6 \cdot 10^{+29}\right)\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.56e+116)
         (and (not (<= b -6.2e+65)) (or (<= b -2.4e-95) (not (<= b 3.6e+29)))))
   (* b (- (* t i) (* z c)))
   (* a (- (* c j) (* x t)))))

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 <= -1.56e+116) || (!(b <= -6.2e+65) && ((b <= -2.4e-95) || !(b <= 3.6e+29)))) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	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 <= (-1.56d+116)) .or. (.not. (b <= (-6.2d+65))) .and. (b <= (-2.4d-95)) .or. (.not. (b <= 3.6d+29))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    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 <= -1.56e+116) || (!(b <= -6.2e+65) && ((b <= -2.4e-95) || !(b <= 3.6e+29)))) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.56e+116) or (not (b <= -6.2e+65) and ((b <= -2.4e-95) or not (b <= 3.6e+29))):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.56e+116) || (!(b <= -6.2e+65) && ((b <= -2.4e-95) || !(b <= 3.6e+29))))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.56e+116) || (~((b <= -6.2e+65)) && ((b <= -2.4e-95) || ~((b <= 3.6e+29)))))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.56e+116], And[N[Not[LessEqual[b, -6.2e+65]], $MachinePrecision], Or[LessEqual[b, -2.4e-95], N[Not[LessEqual[b, 3.6e+29]], $MachinePrecision]]]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.56000000000000002e116 or -6.19999999999999981e65 < b < -2.4e-95 or 3.59999999999999976e29 < b

   1. Initial program 76.8%

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

   3. Taylor expanded in b around inf 66.3%

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

   if -1.56000000000000002e116 < b < -6.19999999999999981e65 or -2.4e-95 < b < 3.59999999999999976e29

   1. Initial program 74.6%

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

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

   5. Simplified 49.8%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.56 \cdot 10^{+116} \lor \neg \left(b \leq -6.2 \cdot 10^{+65}\right) \land \left(b \leq -2.4 \cdot 10^{-95} \lor \neg \left(b \leq 3.6 \cdot 10^{+29}\right)\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -0.44:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{-276}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -4.25 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -0.44)
     t_2
     (if (<= c -6.6e-276)
       t_1
       (if (<= c -4.25e-306) (* y (* x z)) (if (<= c 6.5e-43) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -0.44) {
		tmp = t_2;
	} else if (c <= -6.6e-276) {
		tmp = t_1;
	} else if (c <= -4.25e-306) {
		tmp = y * (x * z);
	} else if (c <= 6.5e-43) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-0.44d0)) then
        tmp = t_2
    else if (c <= (-6.6d-276)) then
        tmp = t_1
    else if (c <= (-4.25d-306)) then
        tmp = y * (x * z)
    else if (c <= 6.5d-43) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -0.44) {
		tmp = t_2;
	} else if (c <= -6.6e-276) {
		tmp = t_1;
	} else if (c <= -4.25e-306) {
		tmp = y * (x * z);
	} else if (c <= 6.5e-43) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -0.44:
		tmp = t_2
	elif c <= -6.6e-276:
		tmp = t_1
	elif c <= -4.25e-306:
		tmp = y * (x * z)
	elif c <= 6.5e-43:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -0.44)
		tmp = t_2;
	elseif (c <= -6.6e-276)
		tmp = t_1;
	elseif (c <= -4.25e-306)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 6.5e-43)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -0.44)
		tmp = t_2;
	elseif (c <= -6.6e-276)
		tmp = t_1;
	elseif (c <= -4.25e-306)
		tmp = y * (x * z);
	elseif (c <= 6.5e-43)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -0.44], t$95$2, If[LessEqual[c, -6.6e-276], t$95$1, If[LessEqual[c, -4.25e-306], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.5e-43], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -0.440000000000000002 or 6.50000000000000001e-43 < c

   1. Initial program 67.6%

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

   3. Taylor expanded in c around inf 60.9%

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

      1. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   if -0.440000000000000002 < c < -6.59999999999999982e-276 or -4.2500000000000001e-306 < c < 6.50000000000000001e-43

   1. Initial program 86.5%

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

   3. Taylor expanded in i around inf 59.4%

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

      1. distribute-lft-out-- 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in i around 0 59.4%

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

      1. mul-1-neg 59.4%

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

      2. *-commutative 59.4%

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

      3. sub-neg 59.4%

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

      4. +-commutative 59.4%

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

      5. +-commutative 59.4%

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

      6. sub-neg 59.4%

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

      7. distribute-rgt-neg-in 59.4%

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

      8. neg-sub0 59.4%

         \[\leadsto i \cdot \color{blue}{\left(0 - \left(j \cdot y - t \cdot b\right)\right)} \]

      9. sub-neg 59.4%

         \[\leadsto i \cdot \left(0 - \color{blue}{\left(j \cdot y + \left(-t \cdot b\right)\right)}\right) \]

      10. +-commutative 59.4%

          \[\leadsto i \cdot \left(0 - \color{blue}{\left(\left(-t \cdot b\right) + j \cdot y\right)}\right) \]

      11. associate--r+ 59.4%

          \[\leadsto i \cdot \color{blue}{\left(\left(0 - \left(-t \cdot b\right)\right) - j \cdot y\right)} \]

      12. neg-sub0 59.4%

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

      13. remove-double-neg 59.4%

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

   8. Simplified 59.4%

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

   if -6.59999999999999982e-276 < c < -4.2500000000000001e-306

   1. Initial program 82.3%

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

   3. Taylor expanded in y around inf 73.4%

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

      1. +-commutative 73.4%

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

      2. mul-1-neg 73.4%

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

      3. unsub-neg 73.4%

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

      4. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in z around inf 64.6%

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

      1. *-commutative 64.6%

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

   8. Simplified 64.6%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -0.44:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{-276}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -4.25 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-43}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+224}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+178}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+143}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -3.1e+224)
   (* b (* t i))
   (if (<= b -7.5e+196)
     (* x (* y z))
     (if (<= b -9.2e+178)
       (* i (* t b))
       (if (<= b 8.6e+143) (* a (- (* c j) (* x t))) (* t (* b 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 (b <= -3.1e+224) {
		tmp = b * (t * i);
	} else if (b <= -7.5e+196) {
		tmp = x * (y * z);
	} else if (b <= -9.2e+178) {
		tmp = i * (t * b);
	} else if (b <= 8.6e+143) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t * (b * 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 (b <= (-3.1d+224)) then
        tmp = b * (t * i)
    else if (b <= (-7.5d+196)) then
        tmp = x * (y * z)
    else if (b <= (-9.2d+178)) then
        tmp = i * (t * b)
    else if (b <= 8.6d+143) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t * (b * 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 (b <= -3.1e+224) {
		tmp = b * (t * i);
	} else if (b <= -7.5e+196) {
		tmp = x * (y * z);
	} else if (b <= -9.2e+178) {
		tmp = i * (t * b);
	} else if (b <= 8.6e+143) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -3.1e+224:
		tmp = b * (t * i)
	elif b <= -7.5e+196:
		tmp = x * (y * z)
	elif b <= -9.2e+178:
		tmp = i * (t * b)
	elif b <= 8.6e+143:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -3.1e+224)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= -7.5e+196)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= -9.2e+178)
		tmp = Float64(i * Float64(t * b));
	elseif (b <= 8.6e+143)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -3.1e+224)
		tmp = b * (t * i);
	elseif (b <= -7.5e+196)
		tmp = x * (y * z);
	elseif (b <= -9.2e+178)
		tmp = i * (t * b);
	elseif (b <= 8.6e+143)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -3.1e+224], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.5e+196], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.2e+178], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.6e+143], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.0999999999999999e224

   1. Initial program 64.1%

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

   3. Taylor expanded in t around inf 55.7%

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

      1. distribute-lft-out-- 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in a around 0 60.1%

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

   if -3.0999999999999999e224 < b < -7.5000000000000005e196

   1. Initial program 87.3%

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

   3. Taylor expanded in y around inf 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

      4. *-commutative 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in z around inf 75.7%

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

      1. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   if -7.5000000000000005e196 < b < -9.2000000000000003e178

   1. Initial program 99.5%

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

   3. Taylor expanded in i around inf 100.0%

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

      1. distribute-lft-out-- 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in j around 0 99.5%

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

      1. remove-double-neg 99.5%

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

      2. mul-1-neg 99.5%

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

      3. associate-*r* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-*l* 100.0%

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

      6. neg-mul-1 100.0%

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

      7. distribute-rgt-neg-in 100.0%

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

      8. distribute-rgt-neg-in 100.0%

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

      9. remove-double-neg 100.0%

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

   8. Simplified 100.0%

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

   if -9.2000000000000003e178 < b < 8.60000000000000003e143

   1. Initial program 77.8%

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

   3. Taylor expanded in a around inf 44.2%

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

      1. +-commutative 44.2%

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

      2. mul-1-neg 44.2%

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

      3. unsub-neg 44.2%

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

   5. Simplified 44.2%

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

   if 8.60000000000000003e143 < b

   1. Initial program 64.3%

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

   3. Taylor expanded in t around inf 58.3%

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

      1. distribute-lft-out-- 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in a around 0 51.3%

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

      1. associate-*r* 58.3%

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

      2. *-commutative 58.3%

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

   8. Simplified 58.3%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+224}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+178}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+143}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 67.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.4 \cdot 10^{-52}:\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -2.4e-52)
     (+ t_1 (* x (* y z)))
     (if (<= j 4.8e-19)
       (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
       (- t_1 (* x (- (* t a) (* y 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.4e-52) {
		tmp = t_1 + (x * (y * z));
	} else if (j <= 4.8e-19) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1 - (x * ((t * a) - (y * 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 = j * ((a * c) - (y * i))
    if (j <= (-2.4d-52)) then
        tmp = t_1 + (x * (y * z))
    else if (j <= 4.8d-19) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    else
        tmp = t_1 - (x * ((t * a) - (y * 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.4e-52) {
		tmp = t_1 + (x * (y * z));
	} else if (j <= 4.8e-19) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.4e-52:
		tmp = t_1 + (x * (y * z))
	elif j <= 4.8e-19:
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	else:
		tmp = t_1 - (x * ((t * a) - (y * z)))
	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)))
	tmp = 0.0
	if (j <= -2.4e-52)
		tmp = Float64(t_1 + Float64(x * Float64(y * z)));
	elseif (j <= 4.8e-19)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	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));
	tmp = 0.0;
	if (j <= -2.4e-52)
		tmp = t_1 + (x * (y * z));
	elseif (j <= 4.8e-19)
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	else
		tmp = t_1 - (x * ((t * a) - (y * z)));
	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]}, If[LessEqual[j, -2.4e-52], N[(t$95$1 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.8e-19], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.4000000000000002e-52

   1. Initial program 70.8%

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

   3. Taylor expanded in b around 0 68.3%

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

   4. Taylor expanded in t around 0 68.3%

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

   if -2.4000000000000002e-52 < j < 4.80000000000000046e-19

   1. Initial program 76.7%

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

   3. Taylor expanded in j around 0 77.7%

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

   if 4.80000000000000046e-19 < j

   1. Initial program 78.5%

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

   3. Taylor expanded in b around 0 71.5%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{-52}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -1.1 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.95 \cdot 10^{-276}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 6.1 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= c -1.1e-56)
     t_1
     (if (<= c -2.95e-276)
       (* b (* t i))
       (if (<= c -5.5e-306)
         (* x (* y z))
         (if (<= c 6.1e-59) (* 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 = a * (c * j);
	double tmp;
	if (c <= -1.1e-56) {
		tmp = t_1;
	} else if (c <= -2.95e-276) {
		tmp = b * (t * i);
	} else if (c <= -5.5e-306) {
		tmp = x * (y * z);
	} else if (c <= 6.1e-59) {
		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 = a * (c * j)
    if (c <= (-1.1d-56)) then
        tmp = t_1
    else if (c <= (-2.95d-276)) then
        tmp = b * (t * i)
    else if (c <= (-5.5d-306)) then
        tmp = x * (y * z)
    else if (c <= 6.1d-59) 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 = a * (c * j);
	double tmp;
	if (c <= -1.1e-56) {
		tmp = t_1;
	} else if (c <= -2.95e-276) {
		tmp = b * (t * i);
	} else if (c <= -5.5e-306) {
		tmp = x * (y * z);
	} else if (c <= 6.1e-59) {
		tmp = t * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if c <= -1.1e-56:
		tmp = t_1
	elif c <= -2.95e-276:
		tmp = b * (t * i)
	elif c <= -5.5e-306:
		tmp = x * (y * z)
	elif c <= 6.1e-59:
		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(a * Float64(c * j))
	tmp = 0.0
	if (c <= -1.1e-56)
		tmp = t_1;
	elseif (c <= -2.95e-276)
		tmp = Float64(b * Float64(t * i));
	elseif (c <= -5.5e-306)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 6.1e-59)
		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 = a * (c * j);
	tmp = 0.0;
	if (c <= -1.1e-56)
		tmp = t_1;
	elseif (c <= -2.95e-276)
		tmp = b * (t * i);
	elseif (c <= -5.5e-306)
		tmp = x * (y * z);
	elseif (c <= 6.1e-59)
		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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.1e-56], t$95$1, If[LessEqual[c, -2.95e-276], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.5e-306], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.1e-59], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.10000000000000002e-56 or 6.0999999999999996e-59 < c

   1. Initial program 67.4%

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

   3. Taylor expanded in a around inf 47.0%

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

      1. +-commutative 47.0%

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

      2. mul-1-neg 47.0%

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

      3. unsub-neg 47.0%

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

   5. Simplified 47.0%

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

   6. Taylor expanded in c around inf 35.8%

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

   if -1.10000000000000002e-56 < c < -2.94999999999999988e-276

   1. Initial program 87.3%

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

   3. Taylor expanded in t around inf 40.0%

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

      1. distribute-lft-out-- 40.0%

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

   5. Simplified 40.0%

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

   6. Taylor expanded in a around 0 39.7%

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

   if -2.94999999999999988e-276 < c < -5.49999999999999992e-306

   1. Initial program 90.2%

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

   3. Taylor expanded in y around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. mul-1-neg 70.7%

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

      3. unsub-neg 70.7%

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

      4. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in z around inf 60.9%

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

      1. *-commutative 60.9%

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

   8. Simplified 60.9%

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

   if -5.49999999999999992e-306 < c < 6.0999999999999996e-59

   1. Initial program 87.6%

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

   3. Taylor expanded in t around inf 60.0%

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

      1. distribute-lft-out-- 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in a around 0 35.5%

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

      1. associate-*r* 37.7%

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

      2. *-commutative 37.7%

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

   8. Simplified 37.7%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.1 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -2.95 \cdot 10^{-276}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-306}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 6.1 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.2 \cdot 10^{-58} \lor \neg \left(c \leq 1.7 \cdot 10^{-59}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -8.2e-58) (not (<= c 1.7e-59))) (* 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 <= -8.2e-58) || !(c <= 1.7e-59)) {
		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 <= (-8.2d-58)) .or. (.not. (c <= 1.7d-59))) 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 <= -8.2e-58) || !(c <= 1.7e-59)) {
		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 <= -8.2e-58) or not (c <= 1.7e-59):
		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 <= -8.2e-58) || !(c <= 1.7e-59))
		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 <= -8.2e-58) || ~((c <= 1.7e-59)))
		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, -8.2e-58], N[Not[LessEqual[c, 1.7e-59]], $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 < -8.20000000000000056e-58 or 1.70000000000000009e-59 < c

   1. Initial program 67.4%

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

   3. Taylor expanded in a around inf 47.0%

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

      1. +-commutative 47.0%

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

      2. mul-1-neg 47.0%

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

      3. unsub-neg 47.0%

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

   5. Simplified 47.0%

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

   6. Taylor expanded in c around inf 35.8%

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

   if -8.20000000000000056e-58 < c < 1.70000000000000009e-59

   1. Initial program 87.7%

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

   3. Taylor expanded in t around inf 50.7%

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

      1. distribute-lft-out-- 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in a around 0 34.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.2 \cdot 10^{-58} \lor \neg \left(c \leq 1.7 \cdot 10^{-59}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 22.9% 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 75.7%

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

3. Taylor expanded in a around inf 38.8%

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

   1. +-commutative 38.8%

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

   2. mul-1-neg 38.8%

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

   3. unsub-neg 38.8%

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

5. Simplified 38.8%

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

6. Taylor expanded in c around inf 24.1%

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

Developer target: 60.4% 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 2024085 
(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)))))