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

Percentage Accurate: 73.5% → 81.2%

Time: 43.3s

Alternatives: 25

Speedup: 0.5×

• 58.6% 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: 73.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.2% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ t_1 (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c)))))))
   (if (<= t_2 INFINITY) t_2 t_1)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 + ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c))));
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 + ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c))));
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t_1 + ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c))))
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t_1 + Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t_1 + ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c))));
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + 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$2, Infinity], t$95$2, t$95$1]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.7%

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

   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 j around inf 50.4%

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

      1. *-commutative 50.4%

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

   5. Simplified 50.4%

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

4. Final simplification 84.6%

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

Alternative 2: 50.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := t\_2 - b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;c \leq -9.5 \cdot 10^{+195}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{+74}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1500000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{-49}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-151}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{-223}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (- t_2 (* b (* z c)))))
   (if (<= c -9.5e+195)
     t_2
     (if (<= c -4.4e+74)
       t_3
       (if (<= c -1.2e+69)
         t_1
         (if (<= c -1500000000000.0)
           (* x (- (* y z) (* t a)))
           (if (<= c -9.2e-49)
             t_3
             (if (<= c -6.5e-59)
               t_1
               (if (<= c -2.6e-151)
                 (* i (- (* t b) (* y j)))
                 (if (<= c -5.8e-223)
                   (* y (- (* x z) (* i j)))
                   (if (<= c 3.2e+24) (* t (- (* b i) (* x a))) t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_2 - (b * (z * c));
	double tmp;
	if (c <= -9.5e+195) {
		tmp = t_2;
	} else if (c <= -4.4e+74) {
		tmp = t_3;
	} else if (c <= -1.2e+69) {
		tmp = t_1;
	} else if (c <= -1500000000000.0) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -9.2e-49) {
		tmp = t_3;
	} else if (c <= -6.5e-59) {
		tmp = t_1;
	} else if (c <= -2.6e-151) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= -5.8e-223) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 3.2e+24) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = j * ((a * c) - (y * i))
    t_3 = t_2 - (b * (z * c))
    if (c <= (-9.5d+195)) then
        tmp = t_2
    else if (c <= (-4.4d+74)) then
        tmp = t_3
    else if (c <= (-1.2d+69)) then
        tmp = t_1
    else if (c <= (-1500000000000.0d0)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= (-9.2d-49)) then
        tmp = t_3
    else if (c <= (-6.5d-59)) then
        tmp = t_1
    else if (c <= (-2.6d-151)) then
        tmp = i * ((t * b) - (y * j))
    else if (c <= (-5.8d-223)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 3.2d+24) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_2 - (b * (z * c));
	double tmp;
	if (c <= -9.5e+195) {
		tmp = t_2;
	} else if (c <= -4.4e+74) {
		tmp = t_3;
	} else if (c <= -1.2e+69) {
		tmp = t_1;
	} else if (c <= -1500000000000.0) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -9.2e-49) {
		tmp = t_3;
	} else if (c <= -6.5e-59) {
		tmp = t_1;
	} else if (c <= -2.6e-151) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= -5.8e-223) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 3.2e+24) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = j * ((a * c) - (y * i))
	t_3 = t_2 - (b * (z * c))
	tmp = 0
	if c <= -9.5e+195:
		tmp = t_2
	elif c <= -4.4e+74:
		tmp = t_3
	elif c <= -1.2e+69:
		tmp = t_1
	elif c <= -1500000000000.0:
		tmp = x * ((y * z) - (t * a))
	elif c <= -9.2e-49:
		tmp = t_3
	elif c <= -6.5e-59:
		tmp = t_1
	elif c <= -2.6e-151:
		tmp = i * ((t * b) - (y * j))
	elif c <= -5.8e-223:
		tmp = y * ((x * z) - (i * j))
	elif c <= 3.2e+24:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(t_2 - Float64(b * Float64(z * c)))
	tmp = 0.0
	if (c <= -9.5e+195)
		tmp = t_2;
	elseif (c <= -4.4e+74)
		tmp = t_3;
	elseif (c <= -1.2e+69)
		tmp = t_1;
	elseif (c <= -1500000000000.0)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= -9.2e-49)
		tmp = t_3;
	elseif (c <= -6.5e-59)
		tmp = t_1;
	elseif (c <= -2.6e-151)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (c <= -5.8e-223)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 3.2e+24)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = j * ((a * c) - (y * i));
	t_3 = t_2 - (b * (z * c));
	tmp = 0.0;
	if (c <= -9.5e+195)
		tmp = t_2;
	elseif (c <= -4.4e+74)
		tmp = t_3;
	elseif (c <= -1.2e+69)
		tmp = t_1;
	elseif (c <= -1500000000000.0)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= -9.2e-49)
		tmp = t_3;
	elseif (c <= -6.5e-59)
		tmp = t_1;
	elseif (c <= -2.6e-151)
		tmp = i * ((t * b) - (y * j));
	elseif (c <= -5.8e-223)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 3.2e+24)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9.5e+195], t$95$2, If[LessEqual[c, -4.4e+74], t$95$3, If[LessEqual[c, -1.2e+69], t$95$1, If[LessEqual[c, -1500000000000.0], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -9.2e-49], t$95$3, If[LessEqual[c, -6.5e-59], t$95$1, If[LessEqual[c, -2.6e-151], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.8e-223], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.2e+24], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -9.5000000000000004e195

   1. Initial program 30.0%

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

   3. Taylor expanded in j around inf 77.9%

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

      1. *-commutative 77.9%

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

   5. Simplified 77.9%

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

   if -9.5000000000000004e195 < c < -4.4000000000000002e74 or -1.5e12 < c < -9.1999999999999996e-49 or 3.1999999999999997e24 < c

   1. Initial program 81.8%

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

   3. Taylor expanded in x around 0 77.7%

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

      1. *-commutative 77.7%

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

      2. *-commutative 77.7%

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

      3. *-commutative 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in t around 0 72.5%

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

      1. *-commutative 72.5%

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

   8. Simplified 72.5%

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

   if -4.4000000000000002e74 < c < -1.2000000000000001e69 or -9.1999999999999996e-49 < c < -6.50000000000000017e-59

   1. Initial program 59.7%

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

   3. Taylor expanded in z around inf 99.4%

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

      1. *-commutative 99.4%

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

   5. Simplified 99.4%

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

   if -1.2000000000000001e69 < c < -1.5e12

   1. Initial program 84.4%

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

   3. Taylor expanded in a around -inf 76.7%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in x around inf 84.6%

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

      1. *-commutative 84.6%

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

   8. Simplified 84.6%

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

   if -6.50000000000000017e-59 < c < -2.6e-151

   1. Initial program 75.8%

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

   3. Taylor expanded in a around -inf 75.4%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in i around inf 68.9%

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

      1. +-commutative 68.9%

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

      2. *-commutative 68.9%

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

      3. mul-1-neg 68.9%

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

      4. *-commutative 68.9%

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

      5. unsub-neg 68.9%

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

      6. *-commutative 68.9%

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

   8. Simplified 68.9%

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

   if -2.6e-151 < c < -5.8000000000000001e-223

   1. Initial program 60.0%

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

   3. Taylor expanded in y around inf 90.1%

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

      1. +-commutative 90.1%

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

      2. mul-1-neg 90.1%

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

      3. unsub-neg 90.1%

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

      4. *-commutative 90.1%

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

   5. Simplified 90.1%

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

   if -5.8000000000000001e-223 < c < 3.1999999999999997e24

   1. Initial program 82.1%

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

   3. Taylor expanded in a around -inf 80.9%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around inf 61.1%

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

      1. *-commutative 61.1%

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

      2. *-commutative 61.1%

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

   8. Simplified 61.1%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{+195}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{+74}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{+69}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -1500000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{-49}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-59}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-151}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{-223}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_4 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -5.7 \cdot 10^{+72}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq -400000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -5 \cdot 10^{-257}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{-259}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-210}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-147}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* i (- (* t b) (* y j))))
        (t_4 (* c (- (* a j) (* z b)))))
   (if (<= c -5.7e+72)
     t_4
     (if (<= c -400000000000.0)
       t_2
       (if (<= c -8.2e-59)
         (* b (- (* t i) (* z c)))
         (if (<= c -5e-257)
           t_3
           (if (<= c 4.4e-259)
             t_1
             (if (<= c 3.1e-210)
               t_3
               (if (<= c 7e-147) t_2 (if (<= c 1.6e+102) t_1 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 = t * ((b * i) - (x * a));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = i * ((t * b) - (y * j));
	double t_4 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -5.7e+72) {
		tmp = t_4;
	} else if (c <= -400000000000.0) {
		tmp = t_2;
	} else if (c <= -8.2e-59) {
		tmp = b * ((t * i) - (z * c));
	} else if (c <= -5e-257) {
		tmp = t_3;
	} else if (c <= 4.4e-259) {
		tmp = t_1;
	} else if (c <= 3.1e-210) {
		tmp = t_3;
	} else if (c <= 7e-147) {
		tmp = t_2;
	} else if (c <= 1.6e+102) {
		tmp = t_1;
	} 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 = t * ((b * i) - (x * a))
    t_2 = x * ((y * z) - (t * a))
    t_3 = i * ((t * b) - (y * j))
    t_4 = c * ((a * j) - (z * b))
    if (c <= (-5.7d+72)) then
        tmp = t_4
    else if (c <= (-400000000000.0d0)) then
        tmp = t_2
    else if (c <= (-8.2d-59)) then
        tmp = b * ((t * i) - (z * c))
    else if (c <= (-5d-257)) then
        tmp = t_3
    else if (c <= 4.4d-259) then
        tmp = t_1
    else if (c <= 3.1d-210) then
        tmp = t_3
    else if (c <= 7d-147) then
        tmp = t_2
    else if (c <= 1.6d+102) then
        tmp = t_1
    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 = t * ((b * i) - (x * a));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = i * ((t * b) - (y * j));
	double t_4 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -5.7e+72) {
		tmp = t_4;
	} else if (c <= -400000000000.0) {
		tmp = t_2;
	} else if (c <= -8.2e-59) {
		tmp = b * ((t * i) - (z * c));
	} else if (c <= -5e-257) {
		tmp = t_3;
	} else if (c <= 4.4e-259) {
		tmp = t_1;
	} else if (c <= 3.1e-210) {
		tmp = t_3;
	} else if (c <= 7e-147) {
		tmp = t_2;
	} else if (c <= 1.6e+102) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = x * ((y * z) - (t * a))
	t_3 = i * ((t * b) - (y * j))
	t_4 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -5.7e+72:
		tmp = t_4
	elif c <= -400000000000.0:
		tmp = t_2
	elif c <= -8.2e-59:
		tmp = b * ((t * i) - (z * c))
	elif c <= -5e-257:
		tmp = t_3
	elif c <= 4.4e-259:
		tmp = t_1
	elif c <= 3.1e-210:
		tmp = t_3
	elif c <= 7e-147:
		tmp = t_2
	elif c <= 1.6e+102:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_4 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -5.7e+72)
		tmp = t_4;
	elseif (c <= -400000000000.0)
		tmp = t_2;
	elseif (c <= -8.2e-59)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (c <= -5e-257)
		tmp = t_3;
	elseif (c <= 4.4e-259)
		tmp = t_1;
	elseif (c <= 3.1e-210)
		tmp = t_3;
	elseif (c <= 7e-147)
		tmp = t_2;
	elseif (c <= 1.6e+102)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	t_2 = x * ((y * z) - (t * a));
	t_3 = i * ((t * b) - (y * j));
	t_4 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -5.7e+72)
		tmp = t_4;
	elseif (c <= -400000000000.0)
		tmp = t_2;
	elseif (c <= -8.2e-59)
		tmp = b * ((t * i) - (z * c));
	elseif (c <= -5e-257)
		tmp = t_3;
	elseif (c <= 4.4e-259)
		tmp = t_1;
	elseif (c <= 3.1e-210)
		tmp = t_3;
	elseif (c <= 7e-147)
		tmp = t_2;
	elseif (c <= 1.6e+102)
		tmp = t_1;
	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[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.7e+72], t$95$4, If[LessEqual[c, -400000000000.0], t$95$2, If[LessEqual[c, -8.2e-59], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5e-257], t$95$3, If[LessEqual[c, 4.4e-259], t$95$1, If[LessEqual[c, 3.1e-210], t$95$3, If[LessEqual[c, 7e-147], t$95$2, If[LessEqual[c, 1.6e+102], t$95$1, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -5.6999999999999997e72 or 1.6e102 < c

   1. Initial program 62.4%

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

   3. Taylor expanded in c around inf 71.7%

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

      1. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   if -5.6999999999999997e72 < c < -4e11 or 3.09999999999999987e-210 < c < 7.00000000000000007e-147

   1. Initial program 84.3%

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

   3. Taylor expanded in a around -inf 84.1%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in x around inf 62.6%

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

      1. *-commutative 62.6%

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

   8. Simplified 62.6%

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

   if -4e11 < c < -8.1999999999999991e-59

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 54.4%

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

      1. *-commutative 54.4%

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

      2. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   if -8.1999999999999991e-59 < c < -4.99999999999999989e-257 or 4.40000000000000019e-259 < c < 3.09999999999999987e-210

   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 77.1%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in i around inf 64.7%

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

      1. +-commutative 64.7%

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

      2. *-commutative 64.7%

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

      3. mul-1-neg 64.7%

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

      4. *-commutative 64.7%

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

      5. unsub-neg 64.7%

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

      6. *-commutative 64.7%

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

   8. Simplified 64.7%

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

   if -4.99999999999999989e-257 < c < 4.40000000000000019e-259 or 7.00000000000000007e-147 < c < 1.6e102

   1. Initial program 81.5%

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

   3. Taylor expanded in a around -inf 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in t around inf 62.2%

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

      1. *-commutative 62.2%

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

      2. *-commutative 62.2%

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

   8. Simplified 62.2%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.7 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -400000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -5 \cdot 10^{-257}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{-259}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-210}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-147}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.05 \cdot 10^{+173}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -126:\\ \;\;\;\;t\_3 + t\_1\\ \mathbf{elif}\;j \leq 6.6 \cdot 10^{-186}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 7.6 \cdot 10^{-132}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+138}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (+ (* x (- (* y z) (* t a))) t_1))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -2.05e+173)
     t_3
     (if (<= j -126.0)
       (+ t_3 t_1)
       (if (<= j 6.6e-186)
         t_2
         (if (<= j 7.6e-132)
           (* z (- (* x y) (* b c)))
           (if (<= j 2.5e+138) 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 = b * ((t * i) - (z * c));
	double t_2 = (x * ((y * z) - (t * a))) + t_1;
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.05e+173) {
		tmp = t_3;
	} else if (j <= -126.0) {
		tmp = t_3 + t_1;
	} else if (j <= 6.6e-186) {
		tmp = t_2;
	} else if (j <= 7.6e-132) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 2.5e+138) {
		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 = b * ((t * i) - (z * c))
    t_2 = (x * ((y * z) - (t * a))) + t_1
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-2.05d+173)) then
        tmp = t_3
    else if (j <= (-126.0d0)) then
        tmp = t_3 + t_1
    else if (j <= 6.6d-186) then
        tmp = t_2
    else if (j <= 7.6d-132) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 2.5d+138) 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 = b * ((t * i) - (z * c));
	double t_2 = (x * ((y * z) - (t * a))) + t_1;
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.05e+173) {
		tmp = t_3;
	} else if (j <= -126.0) {
		tmp = t_3 + t_1;
	} else if (j <= 6.6e-186) {
		tmp = t_2;
	} else if (j <= 7.6e-132) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 2.5e+138) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = (x * ((y * z) - (t * a))) + t_1
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.05e+173:
		tmp = t_3
	elif j <= -126.0:
		tmp = t_3 + t_1
	elif j <= 6.6e-186:
		tmp = t_2
	elif j <= 7.6e-132:
		tmp = z * ((x * y) - (b * c))
	elif j <= 2.5e+138:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1)
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.05e+173)
		tmp = t_3;
	elseif (j <= -126.0)
		tmp = Float64(t_3 + t_1);
	elseif (j <= 6.6e-186)
		tmp = t_2;
	elseif (j <= 7.6e-132)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 2.5e+138)
		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 = b * ((t * i) - (z * c));
	t_2 = (x * ((y * z) - (t * a))) + t_1;
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.05e+173)
		tmp = t_3;
	elseif (j <= -126.0)
		tmp = t_3 + t_1;
	elseif (j <= 6.6e-186)
		tmp = t_2;
	elseif (j <= 7.6e-132)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 2.5e+138)
		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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.05e+173], t$95$3, If[LessEqual[j, -126.0], N[(t$95$3 + t$95$1), $MachinePrecision], If[LessEqual[j, 6.6e-186], t$95$2, If[LessEqual[j, 7.6e-132], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e+138], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.04999999999999988e173 or 2.50000000000000008e138 < j

   1. Initial program 65.7%

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

   3. Taylor expanded in j around inf 76.7%

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

      1. *-commutative 76.7%

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

   5. Simplified 76.7%

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

   if -2.04999999999999988e173 < j < -126

   1. Initial program 81.6%

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

   3. Taylor expanded in x around 0 75.7%

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

      1. *-commutative 75.7%

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

      2. *-commutative 75.7%

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

      3. *-commutative 75.7%

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

   5. Simplified 75.7%

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

   if -126 < j < 6.59999999999999998e-186 or 7.5999999999999994e-132 < j < 2.50000000000000008e138

   1. Initial program 81.3%

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

   3. Taylor expanded in j around 0 78.3%

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

      1. *-commutative 78.3%

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

      2. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   if 6.59999999999999998e-186 < j < 7.5999999999999994e-132

   1. Initial program 57.5%

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

   3. Taylor expanded in z around inf 78.3%

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

      1. *-commutative 78.3%

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

   5. Simplified 78.3%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.05 \cdot 10^{+173}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -126:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6.6 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7.6 \cdot 10^{-132}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+155}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-42}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-221}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 44000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= a -1.35e+155)
     t_3
     (if (<= a -2.25e-42)
       (* c (- (* a j) (* z b)))
       (if (<= a -1.65e-143)
         t_1
         (if (<= a -1.6e-221)
           t_2
           (if (<= a -3.6e-269) t_1 (if (<= a 44000.0) 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 = y * (i * -j);
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.35e+155) {
		tmp = t_3;
	} else if (a <= -2.25e-42) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= -1.65e-143) {
		tmp = t_1;
	} else if (a <= -1.6e-221) {
		tmp = t_2;
	} else if (a <= -3.6e-269) {
		tmp = t_1;
	} else if (a <= 44000.0) {
		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 = y * (i * -j)
    t_2 = b * ((t * i) - (z * c))
    t_3 = a * ((c * j) - (x * t))
    if (a <= (-1.35d+155)) then
        tmp = t_3
    else if (a <= (-2.25d-42)) then
        tmp = c * ((a * j) - (z * b))
    else if (a <= (-1.65d-143)) then
        tmp = t_1
    else if (a <= (-1.6d-221)) then
        tmp = t_2
    else if (a <= (-3.6d-269)) then
        tmp = t_1
    else if (a <= 44000.0d0) 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 = y * (i * -j);
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.35e+155) {
		tmp = t_3;
	} else if (a <= -2.25e-42) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= -1.65e-143) {
		tmp = t_1;
	} else if (a <= -1.6e-221) {
		tmp = t_2;
	} else if (a <= -3.6e-269) {
		tmp = t_1;
	} else if (a <= 44000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	t_2 = b * ((t * i) - (z * c))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.35e+155:
		tmp = t_3
	elif a <= -2.25e-42:
		tmp = c * ((a * j) - (z * b))
	elif a <= -1.65e-143:
		tmp = t_1
	elif a <= -1.6e-221:
		tmp = t_2
	elif a <= -3.6e-269:
		tmp = t_1
	elif a <= 44000.0:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-j)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.35e+155)
		tmp = t_3;
	elseif (a <= -2.25e-42)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (a <= -1.65e-143)
		tmp = t_1;
	elseif (a <= -1.6e-221)
		tmp = t_2;
	elseif (a <= -3.6e-269)
		tmp = t_1;
	elseif (a <= 44000.0)
		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 = y * (i * -j);
	t_2 = b * ((t * i) - (z * c));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.35e+155)
		tmp = t_3;
	elseif (a <= -2.25e-42)
		tmp = c * ((a * j) - (z * b));
	elseif (a <= -1.65e-143)
		tmp = t_1;
	elseif (a <= -1.6e-221)
		tmp = t_2;
	elseif (a <= -3.6e-269)
		tmp = t_1;
	elseif (a <= 44000.0)
		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[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.35e+155], t$95$3, If[LessEqual[a, -2.25e-42], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.65e-143], t$95$1, If[LessEqual[a, -1.6e-221], t$95$2, If[LessEqual[a, -3.6e-269], t$95$1, If[LessEqual[a, 44000.0], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.34999999999999997e155 or 44000 < a

   1. Initial program 74.3%

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

   3. Taylor expanded in a around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. mul-1-neg 62.7%

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

      3. unsub-neg 62.7%

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

      4. *-commutative 62.7%

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

      5. *-commutative 62.7%

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

   5. Simplified 62.7%

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

   if -1.34999999999999997e155 < a < -2.25e-42

   1. Initial program 72.7%

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

   3. Taylor expanded in c around inf 48.9%

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

      1. *-commutative 48.9%

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

   5. Simplified 48.9%

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

   if -2.25e-42 < a < -1.65e-143 or -1.60000000000000008e-221 < a < -3.59999999999999998e-269

   1. Initial program 61.8%

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

   3. Taylor expanded in y around inf 70.1%

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

      1. +-commutative 70.1%

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

      2. mul-1-neg 70.1%

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

      3. unsub-neg 70.1%

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

      4. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in x around 0 55.0%

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

      1. mul-1-neg 55.0%

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

      2. distribute-rgt-neg-in 55.0%

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

   8. Simplified 55.0%

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

   if -1.65e-143 < a < -1.60000000000000008e-221 or -3.59999999999999998e-269 < a < 44000

   1. Initial program 83.1%

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

   3. Taylor expanded in b around inf 56.6%

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

      1. *-commutative 56.6%

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

      2. *-commutative 56.6%

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

   5. Simplified 56.6%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+155}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-42}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-143}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-221}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-269}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 44000:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+35}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-300}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-8}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 12500:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -8.2e+154)
     t_2
     (if (<= a -6.8e+35)
       (* c (- (* a j) (* z b)))
       (if (<= a -3.1e-300)
         (* i (- (* t b) (* y j)))
         (if (<= a 4.2e-72)
           t_1
           (if (<= a 5e-8)
             (* j (- (* a c) (* y i)))
             (if (<= a 12500.0) 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 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -8.2e+154) {
		tmp = t_2;
	} else if (a <= -6.8e+35) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= -3.1e-300) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 4.2e-72) {
		tmp = t_1;
	} else if (a <= 5e-8) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 12500.0) {
		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 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-8.2d+154)) then
        tmp = t_2
    else if (a <= (-6.8d+35)) then
        tmp = c * ((a * j) - (z * b))
    else if (a <= (-3.1d-300)) then
        tmp = i * ((t * b) - (y * j))
    else if (a <= 4.2d-72) then
        tmp = t_1
    else if (a <= 5d-8) then
        tmp = j * ((a * c) - (y * i))
    else if (a <= 12500.0d0) 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 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -8.2e+154) {
		tmp = t_2;
	} else if (a <= -6.8e+35) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= -3.1e-300) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 4.2e-72) {
		tmp = t_1;
	} else if (a <= 5e-8) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 12500.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -8.2e+154:
		tmp = t_2
	elif a <= -6.8e+35:
		tmp = c * ((a * j) - (z * b))
	elif a <= -3.1e-300:
		tmp = i * ((t * b) - (y * j))
	elif a <= 4.2e-72:
		tmp = t_1
	elif a <= 5e-8:
		tmp = j * ((a * c) - (y * i))
	elif a <= 12500.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -8.2e+154)
		tmp = t_2;
	elseif (a <= -6.8e+35)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (a <= -3.1e-300)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (a <= 4.2e-72)
		tmp = t_1;
	elseif (a <= 5e-8)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (a <= 12500.0)
		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 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -8.2e+154)
		tmp = t_2;
	elseif (a <= -6.8e+35)
		tmp = c * ((a * j) - (z * b));
	elseif (a <= -3.1e-300)
		tmp = i * ((t * b) - (y * j));
	elseif (a <= 4.2e-72)
		tmp = t_1;
	elseif (a <= 5e-8)
		tmp = j * ((a * c) - (y * i));
	elseif (a <= 12500.0)
		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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.2e+154], t$95$2, If[LessEqual[a, -6.8e+35], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.1e-300], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e-72], t$95$1, If[LessEqual[a, 5e-8], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 12500.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -8.2e154 or 12500 < a

   1. Initial program 74.3%

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

   3. Taylor expanded in a around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. mul-1-neg 62.7%

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

      3. unsub-neg 62.7%

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

      4. *-commutative 62.7%

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

      5. *-commutative 62.7%

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

   5. Simplified 62.7%

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

   if -8.2e154 < a < -6.8000000000000002e35

   1. Initial program 73.0%

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

   3. Taylor expanded in c around inf 58.6%

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

      1. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   if -6.8000000000000002e35 < a < -3.1000000000000002e-300

   1. Initial program 67.7%

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

   3. Taylor expanded in a around -inf 61.7%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in i around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. *-commutative 55.0%

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

      3. mul-1-neg 55.0%

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

      4. *-commutative 55.0%

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

      5. unsub-neg 55.0%

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

      6. *-commutative 55.0%

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

   8. Simplified 55.0%

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

   if -3.1000000000000002e-300 < a < 4.2e-72 or 4.9999999999999998e-8 < a < 12500

   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 b around inf 66.1%

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

      1. *-commutative 66.1%

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

      2. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   if 4.2e-72 < a < 4.9999999999999998e-8

   1. Initial program 79.9%

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

   3. Taylor expanded in j around inf 54.5%

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

      1. *-commutative 54.5%

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

   5. Simplified 54.5%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+154}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+35}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-300}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-72}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-8}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 12500:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.6 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -92000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{-154}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -7.3 \cdot 10^{-224}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -1.6e+73)
     t_1
     (if (<= c -92000000000.0)
       (* x (- (* y z) (* t a)))
       (if (<= c -1.75e-59)
         (* b (- (* t i) (* z c)))
         (if (<= c -1.02e-154)
           (* i (- (* t b) (* y j)))
           (if (<= c -7.3e-224)
             (* y (- (* x z) (* i j)))
             (if (<= c 3.2e+102) (* t (- (* b i) (* x a))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.6e+73) {
		tmp = t_1;
	} else if (c <= -92000000000.0) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -1.75e-59) {
		tmp = b * ((t * i) - (z * c));
	} else if (c <= -1.02e-154) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= -7.3e-224) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 3.2e+102) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    if (c <= (-1.6d+73)) then
        tmp = t_1
    else if (c <= (-92000000000.0d0)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= (-1.75d-59)) then
        tmp = b * ((t * i) - (z * c))
    else if (c <= (-1.02d-154)) then
        tmp = i * ((t * b) - (y * j))
    else if (c <= (-7.3d-224)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 3.2d+102) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.6e+73) {
		tmp = t_1;
	} else if (c <= -92000000000.0) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -1.75e-59) {
		tmp = b * ((t * i) - (z * c));
	} else if (c <= -1.02e-154) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= -7.3e-224) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 3.2e+102) {
		tmp = t * ((b * i) - (x * a));
	} 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 <= -1.6e+73:
		tmp = t_1
	elif c <= -92000000000.0:
		tmp = x * ((y * z) - (t * a))
	elif c <= -1.75e-59:
		tmp = b * ((t * i) - (z * c))
	elif c <= -1.02e-154:
		tmp = i * ((t * b) - (y * j))
	elif c <= -7.3e-224:
		tmp = y * ((x * z) - (i * j))
	elif c <= 3.2e+102:
		tmp = t * ((b * i) - (x * a))
	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 <= -1.6e+73)
		tmp = t_1;
	elseif (c <= -92000000000.0)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= -1.75e-59)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (c <= -1.02e-154)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (c <= -7.3e-224)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 3.2e+102)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.6e+73)
		tmp = t_1;
	elseif (c <= -92000000000.0)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= -1.75e-59)
		tmp = b * ((t * i) - (z * c));
	elseif (c <= -1.02e-154)
		tmp = i * ((t * b) - (y * j));
	elseif (c <= -7.3e-224)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 3.2e+102)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.6e+73], t$95$1, If[LessEqual[c, -92000000000.0], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.75e-59], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.02e-154], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -7.3e-224], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.2e+102], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.59999999999999991e73 or 3.1999999999999999e102 < c

   1. Initial program 62.4%

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

   3. Taylor expanded in c around inf 71.7%

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

      1. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   if -1.59999999999999991e73 < c < -9.2e10

   1. Initial program 79.7%

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

   3. Taylor expanded in a around -inf 73.0%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in x around inf 80.2%

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

      1. *-commutative 80.2%

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

   8. Simplified 80.2%

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

   if -9.2e10 < c < -1.75e-59

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 54.4%

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

      1. *-commutative 54.4%

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

      2. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   if -1.75e-59 < c < -1.01999999999999992e-154

   1. Initial program 75.8%

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

   3. Taylor expanded in a around -inf 75.4%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in i around inf 68.9%

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

      1. +-commutative 68.9%

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

      2. *-commutative 68.9%

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

      3. mul-1-neg 68.9%

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

      4. *-commutative 68.9%

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

      5. unsub-neg 68.9%

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

      6. *-commutative 68.9%

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

   8. Simplified 68.9%

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

   if -1.01999999999999992e-154 < c < -7.3e-224

   1. Initial program 60.0%

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

   3. Taylor expanded in y around inf 90.1%

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

      1. +-commutative 90.1%

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

      2. mul-1-neg 90.1%

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

      3. unsub-neg 90.1%

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

      4. *-commutative 90.1%

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

   5. Simplified 90.1%

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

   if -7.3e-224 < c < 3.1999999999999999e102

   1. Initial program 83.4%

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

   3. Taylor expanded in a around -inf 81.5%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in t around inf 57.8%

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

      1. *-commutative 57.8%

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

      2. *-commutative 57.8%

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

   8. Simplified 57.8%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.6 \cdot 10^{+73}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -92000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{-154}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -7.3 \cdot 10^{-224}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 28.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(-z \cdot b\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+82}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-296}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* z b)))))
   (if (<= y -9e+170)
     (* x (* y z))
     (if (<= y -3.4e+82)
       (* j (* a c))
       (if (<= y -7.5e-161)
         t_1
         (if (<= y 1.16e-296)
           (* i (* t b))
           (if (<= y 4.8e-205)
             t_1
             (if (<= y 7.2e-99) (* a (* x (- t))) (* y (* x 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 = c * -(z * b);
	double tmp;
	if (y <= -9e+170) {
		tmp = x * (y * z);
	} else if (y <= -3.4e+82) {
		tmp = j * (a * c);
	} else if (y <= -7.5e-161) {
		tmp = t_1;
	} else if (y <= 1.16e-296) {
		tmp = i * (t * b);
	} else if (y <= 4.8e-205) {
		tmp = t_1;
	} else if (y <= 7.2e-99) {
		tmp = a * (x * -t);
	} else {
		tmp = y * (x * 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 = c * -(z * b)
    if (y <= (-9d+170)) then
        tmp = x * (y * z)
    else if (y <= (-3.4d+82)) then
        tmp = j * (a * c)
    else if (y <= (-7.5d-161)) then
        tmp = t_1
    else if (y <= 1.16d-296) then
        tmp = i * (t * b)
    else if (y <= 4.8d-205) then
        tmp = t_1
    else if (y <= 7.2d-99) then
        tmp = a * (x * -t)
    else
        tmp = y * (x * 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 = c * -(z * b);
	double tmp;
	if (y <= -9e+170) {
		tmp = x * (y * z);
	} else if (y <= -3.4e+82) {
		tmp = j * (a * c);
	} else if (y <= -7.5e-161) {
		tmp = t_1;
	} else if (y <= 1.16e-296) {
		tmp = i * (t * b);
	} else if (y <= 4.8e-205) {
		tmp = t_1;
	} else if (y <= 7.2e-99) {
		tmp = a * (x * -t);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * -(z * b)
	tmp = 0
	if y <= -9e+170:
		tmp = x * (y * z)
	elif y <= -3.4e+82:
		tmp = j * (a * c)
	elif y <= -7.5e-161:
		tmp = t_1
	elif y <= 1.16e-296:
		tmp = i * (t * b)
	elif y <= 4.8e-205:
		tmp = t_1
	elif y <= 7.2e-99:
		tmp = a * (x * -t)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(-Float64(z * b)))
	tmp = 0.0
	if (y <= -9e+170)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -3.4e+82)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= -7.5e-161)
		tmp = t_1;
	elseif (y <= 1.16e-296)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 4.8e-205)
		tmp = t_1;
	elseif (y <= 7.2e-99)
		tmp = Float64(a * Float64(x * Float64(-t)));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * -(z * b);
	tmp = 0.0;
	if (y <= -9e+170)
		tmp = x * (y * z);
	elseif (y <= -3.4e+82)
		tmp = j * (a * c);
	elseif (y <= -7.5e-161)
		tmp = t_1;
	elseif (y <= 1.16e-296)
		tmp = i * (t * b);
	elseif (y <= 4.8e-205)
		tmp = t_1;
	elseif (y <= 7.2e-99)
		tmp = a * (x * -t);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[y, -9e+170], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.4e+82], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-161], t$95$1, If[LessEqual[y, 1.16e-296], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-205], t$95$1, If[LessEqual[y, 7.2e-99], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -9.00000000000000044e170

   1. Initial program 53.2%

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

   3. Taylor expanded in y around inf 78.4%

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

      1. +-commutative 78.4%

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

      2. mul-1-neg 78.4%

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

      3. unsub-neg 78.4%

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

      4. *-commutative 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in x around inf 61.9%

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

   if -9.00000000000000044e170 < y < -3.39999999999999994e82

   1. Initial program 62.1%

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

   3. Taylor expanded in x around 0 66.5%

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

      1. *-commutative 66.5%

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

      2. *-commutative 66.5%

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

      3. *-commutative 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in a around inf 30.7%

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

      1. associate-*r* 44.0%

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

      2. *-commutative 44.0%

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

   8. Simplified 44.0%

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

   if -3.39999999999999994e82 < y < -7.49999999999999991e-161 or 1.15999999999999996e-296 < y < 4.8000000000000004e-205

   1. Initial program 82.7%

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

   3. Taylor expanded in c around inf 53.5%

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

      1. *-commutative 53.5%

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

   5. Simplified 53.5%

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

   6. Taylor expanded in a around 0 36.6%

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

      1. mul-1-neg 36.6%

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

      2. *-commutative 36.6%

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

      3. distribute-rgt-neg-in 36.6%

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

   8. Simplified 36.6%

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

   if -7.49999999999999991e-161 < y < 1.15999999999999996e-296

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 69.4%

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

      1. *-commutative 69.4%

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

      2. *-commutative 69.4%

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

      3. *-commutative 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in t around inf 41.0%

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

      1. *-commutative 41.0%

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

      2. associate-*r* 43.5%

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

      3. *-commutative 43.5%

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

   8. Simplified 43.5%

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

   if 4.8000000000000004e-205 < y < 7.2000000000000001e-99

   1. Initial program 88.8%

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

   3. Taylor expanded in a around inf 66.5%

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

      1. +-commutative 66.5%

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

      2. mul-1-neg 66.5%

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

      3. unsub-neg 66.5%

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

      4. *-commutative 66.5%

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

      5. *-commutative 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in j around 0 44.1%

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

      1. mul-1-neg 44.1%

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

      2. *-commutative 44.1%

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

      3. distribute-rgt-neg-in 44.1%

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

   8. Simplified 44.1%

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

   if 7.2000000000000001e-99 < y

   1. Initial program 71.6%

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

   3. Taylor expanded in y around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. mul-1-neg 55.0%

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

      3. unsub-neg 55.0%

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

      4. *-commutative 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in x around inf 30.3%

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

      1. *-commutative 30.3%

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

      2. associate-*l* 31.8%

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

      3. *-commutative 31.8%

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

   8. Simplified 31.8%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+82}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-161}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-296}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-205}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 28.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(-z \cdot b\right)\\ \mathbf{if}\;y \leq -8 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+80}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-295}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* z b)))))
   (if (<= y -8e+171)
     (* x (* y z))
     (if (<= y -1.45e+80)
       (* j (* a c))
       (if (<= y -2.1e-164)
         t_1
         (if (<= y 7.2e-295)
           (* i (* t b))
           (if (<= y 3.3e-215)
             t_1
             (if (<= y 2.5e-98) (* x (* t (- a))) (* y (* x 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 = c * -(z * b);
	double tmp;
	if (y <= -8e+171) {
		tmp = x * (y * z);
	} else if (y <= -1.45e+80) {
		tmp = j * (a * c);
	} else if (y <= -2.1e-164) {
		tmp = t_1;
	} else if (y <= 7.2e-295) {
		tmp = i * (t * b);
	} else if (y <= 3.3e-215) {
		tmp = t_1;
	} else if (y <= 2.5e-98) {
		tmp = x * (t * -a);
	} else {
		tmp = y * (x * 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 = c * -(z * b)
    if (y <= (-8d+171)) then
        tmp = x * (y * z)
    else if (y <= (-1.45d+80)) then
        tmp = j * (a * c)
    else if (y <= (-2.1d-164)) then
        tmp = t_1
    else if (y <= 7.2d-295) then
        tmp = i * (t * b)
    else if (y <= 3.3d-215) then
        tmp = t_1
    else if (y <= 2.5d-98) then
        tmp = x * (t * -a)
    else
        tmp = y * (x * 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 = c * -(z * b);
	double tmp;
	if (y <= -8e+171) {
		tmp = x * (y * z);
	} else if (y <= -1.45e+80) {
		tmp = j * (a * c);
	} else if (y <= -2.1e-164) {
		tmp = t_1;
	} else if (y <= 7.2e-295) {
		tmp = i * (t * b);
	} else if (y <= 3.3e-215) {
		tmp = t_1;
	} else if (y <= 2.5e-98) {
		tmp = x * (t * -a);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * -(z * b)
	tmp = 0
	if y <= -8e+171:
		tmp = x * (y * z)
	elif y <= -1.45e+80:
		tmp = j * (a * c)
	elif y <= -2.1e-164:
		tmp = t_1
	elif y <= 7.2e-295:
		tmp = i * (t * b)
	elif y <= 3.3e-215:
		tmp = t_1
	elif y <= 2.5e-98:
		tmp = x * (t * -a)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(-Float64(z * b)))
	tmp = 0.0
	if (y <= -8e+171)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -1.45e+80)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= -2.1e-164)
		tmp = t_1;
	elseif (y <= 7.2e-295)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 3.3e-215)
		tmp = t_1;
	elseif (y <= 2.5e-98)
		tmp = Float64(x * Float64(t * Float64(-a)));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * -(z * b);
	tmp = 0.0;
	if (y <= -8e+171)
		tmp = x * (y * z);
	elseif (y <= -1.45e+80)
		tmp = j * (a * c);
	elseif (y <= -2.1e-164)
		tmp = t_1;
	elseif (y <= 7.2e-295)
		tmp = i * (t * b);
	elseif (y <= 3.3e-215)
		tmp = t_1;
	elseif (y <= 2.5e-98)
		tmp = x * (t * -a);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[y, -8e+171], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e+80], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-164], t$95$1, If[LessEqual[y, 7.2e-295], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e-215], t$95$1, If[LessEqual[y, 2.5e-98], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -7.99999999999999963e171

   1. Initial program 53.2%

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

   3. Taylor expanded in y around inf 78.4%

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

      1. +-commutative 78.4%

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

      2. mul-1-neg 78.4%

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

      3. unsub-neg 78.4%

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

      4. *-commutative 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in x around inf 61.9%

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

   if -7.99999999999999963e171 < y < -1.44999999999999993e80

   1. Initial program 62.1%

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

   3. Taylor expanded in x around 0 66.5%

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

      1. *-commutative 66.5%

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

      2. *-commutative 66.5%

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

      3. *-commutative 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in a around inf 30.7%

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

      1. associate-*r* 44.0%

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

      2. *-commutative 44.0%

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

   8. Simplified 44.0%

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

   if -1.44999999999999993e80 < y < -2.0999999999999999e-164 or 7.2000000000000003e-295 < y < 3.2999999999999998e-215

   1. Initial program 82.9%

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

   3. Taylor expanded in c around inf 51.4%

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

      1. *-commutative 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in a around 0 37.7%

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

      1. mul-1-neg 37.7%

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

      2. *-commutative 37.7%

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

      3. distribute-rgt-neg-in 37.7%

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

   8. Simplified 37.7%

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

   if -2.0999999999999999e-164 < y < 7.2000000000000003e-295

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 69.4%

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

      1. *-commutative 69.4%

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

      2. *-commutative 69.4%

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

      3. *-commutative 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in t around inf 41.0%

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

      1. *-commutative 41.0%

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

      2. associate-*r* 43.5%

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

      3. *-commutative 43.5%

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

   8. Simplified 43.5%

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

   if 3.2999999999999998e-215 < y < 2.50000000000000009e-98

   1. Initial program 87.4%

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

   3. Taylor expanded in a around -inf 78.1%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in x around inf 44.0%

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

      1. *-commutative 44.0%

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

   8. Simplified 44.0%

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

   9. Taylor expanded in y around 0 43.6%

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

       1. associate-*r* 43.6%

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

       2. neg-mul-1 43.6%

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

   11. Simplified 43.6%

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

   if 2.50000000000000009e-98 < y

   1. Initial program 71.6%

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

   3. Taylor expanded in y around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. mul-1-neg 55.0%

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

      3. unsub-neg 55.0%

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

      4. *-commutative 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in x around inf 30.3%

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

      1. *-commutative 30.3%

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

      2. associate-*l* 31.8%

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

      3. *-commutative 31.8%

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

   8. Simplified 31.8%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+80}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-164}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-295}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-215}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 28.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(-z \cdot b\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{+81}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-295}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-214}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-100}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* z b)))))
   (if (<= y -9.2e+170)
     (* x (* y z))
     (if (<= y -4.7e+81)
       (* j (* a c))
       (if (<= y -1.4e-165)
         t_1
         (if (<= y 1.05e-295)
           (* i (* t b))
           (if (<= y 1.7e-214)
             t_1
             (if (<= y 1.1e-100) (* x (* t (- a))) (* y (* i (- 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 = c * -(z * b);
	double tmp;
	if (y <= -9.2e+170) {
		tmp = x * (y * z);
	} else if (y <= -4.7e+81) {
		tmp = j * (a * c);
	} else if (y <= -1.4e-165) {
		tmp = t_1;
	} else if (y <= 1.05e-295) {
		tmp = i * (t * b);
	} else if (y <= 1.7e-214) {
		tmp = t_1;
	} else if (y <= 1.1e-100) {
		tmp = x * (t * -a);
	} else {
		tmp = y * (i * -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) :: tmp
    t_1 = c * -(z * b)
    if (y <= (-9.2d+170)) then
        tmp = x * (y * z)
    else if (y <= (-4.7d+81)) then
        tmp = j * (a * c)
    else if (y <= (-1.4d-165)) then
        tmp = t_1
    else if (y <= 1.05d-295) then
        tmp = i * (t * b)
    else if (y <= 1.7d-214) then
        tmp = t_1
    else if (y <= 1.1d-100) then
        tmp = x * (t * -a)
    else
        tmp = y * (i * -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 = c * -(z * b);
	double tmp;
	if (y <= -9.2e+170) {
		tmp = x * (y * z);
	} else if (y <= -4.7e+81) {
		tmp = j * (a * c);
	} else if (y <= -1.4e-165) {
		tmp = t_1;
	} else if (y <= 1.05e-295) {
		tmp = i * (t * b);
	} else if (y <= 1.7e-214) {
		tmp = t_1;
	} else if (y <= 1.1e-100) {
		tmp = x * (t * -a);
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * -(z * b)
	tmp = 0
	if y <= -9.2e+170:
		tmp = x * (y * z)
	elif y <= -4.7e+81:
		tmp = j * (a * c)
	elif y <= -1.4e-165:
		tmp = t_1
	elif y <= 1.05e-295:
		tmp = i * (t * b)
	elif y <= 1.7e-214:
		tmp = t_1
	elif y <= 1.1e-100:
		tmp = x * (t * -a)
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(-Float64(z * b)))
	tmp = 0.0
	if (y <= -9.2e+170)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -4.7e+81)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= -1.4e-165)
		tmp = t_1;
	elseif (y <= 1.05e-295)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 1.7e-214)
		tmp = t_1;
	elseif (y <= 1.1e-100)
		tmp = Float64(x * Float64(t * Float64(-a)));
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * -(z * b);
	tmp = 0.0;
	if (y <= -9.2e+170)
		tmp = x * (y * z);
	elseif (y <= -4.7e+81)
		tmp = j * (a * c);
	elseif (y <= -1.4e-165)
		tmp = t_1;
	elseif (y <= 1.05e-295)
		tmp = i * (t * b);
	elseif (y <= 1.7e-214)
		tmp = t_1;
	elseif (y <= 1.1e-100)
		tmp = x * (t * -a);
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[y, -9.2e+170], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.7e+81], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.4e-165], t$95$1, If[LessEqual[y, 1.05e-295], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-214], t$95$1, If[LessEqual[y, 1.1e-100], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -9.2000000000000003e170

   1. Initial program 53.2%

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

   3. Taylor expanded in y around inf 78.4%

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

      1. +-commutative 78.4%

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

      2. mul-1-neg 78.4%

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

      3. unsub-neg 78.4%

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

      4. *-commutative 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in x around inf 61.9%

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

   if -9.2000000000000003e170 < y < -4.7000000000000002e81

   1. Initial program 62.1%

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

   3. Taylor expanded in x around 0 66.5%

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

      1. *-commutative 66.5%

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

      2. *-commutative 66.5%

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

      3. *-commutative 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in a around inf 30.7%

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

      1. associate-*r* 44.0%

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

      2. *-commutative 44.0%

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

   8. Simplified 44.0%

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

   if -4.7000000000000002e81 < y < -1.4e-165 or 1.04999999999999997e-295 < y < 1.7e-214

   1. Initial program 82.9%

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

   3. Taylor expanded in c around inf 51.4%

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

      1. *-commutative 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in a around 0 37.7%

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

      1. mul-1-neg 37.7%

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

      2. *-commutative 37.7%

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

      3. distribute-rgt-neg-in 37.7%

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

   8. Simplified 37.7%

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

   if -1.4e-165 < y < 1.04999999999999997e-295

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 69.4%

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

      1. *-commutative 69.4%

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

      2. *-commutative 69.4%

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

      3. *-commutative 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in t around inf 41.0%

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

      1. *-commutative 41.0%

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

      2. associate-*r* 43.5%

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

      3. *-commutative 43.5%

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

   8. Simplified 43.5%

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

   if 1.7e-214 < y < 1.09999999999999995e-100

   1. Initial program 87.4%

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

   3. Taylor expanded in a around -inf 78.1%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in x around inf 44.0%

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

      1. *-commutative 44.0%

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

   8. Simplified 44.0%

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

   9. Taylor expanded in y around 0 43.6%

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

       1. associate-*r* 43.6%

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

       2. neg-mul-1 43.6%

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

   11. Simplified 43.6%

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

   if 1.09999999999999995e-100 < y

   1. Initial program 71.6%

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

   3. Taylor expanded in y around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. mul-1-neg 55.0%

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

      3. unsub-neg 55.0%

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

      4. *-commutative 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in x around 0 35.6%

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

      1. mul-1-neg 35.6%

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

      2. distribute-rgt-neg-in 35.6%

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

   8. Simplified 35.6%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{+81}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-165}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-295}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-214}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-100}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 28.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(-z \cdot b\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{+81}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-296}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* z b)))))
   (if (<= y -9e+170)
     (* x (* y z))
     (if (<= y -3.25e+81)
       (* j (* a c))
       (if (<= y -4.5e-162)
         t_1
         (if (<= y 2.8e-296)
           (* i (* t b))
           (if (<= y 8e-215)
             t_1
             (if (<= y 2.9e-98) (* x (* t (- a))) (* j (* y (- i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * -(z * b);
	double tmp;
	if (y <= -9e+170) {
		tmp = x * (y * z);
	} else if (y <= -3.25e+81) {
		tmp = j * (a * c);
	} else if (y <= -4.5e-162) {
		tmp = t_1;
	} else if (y <= 2.8e-296) {
		tmp = i * (t * b);
	} else if (y <= 8e-215) {
		tmp = t_1;
	} else if (y <= 2.9e-98) {
		tmp = x * (t * -a);
	} else {
		tmp = j * (y * -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) :: t_1
    real(8) :: tmp
    t_1 = c * -(z * b)
    if (y <= (-9d+170)) then
        tmp = x * (y * z)
    else if (y <= (-3.25d+81)) then
        tmp = j * (a * c)
    else if (y <= (-4.5d-162)) then
        tmp = t_1
    else if (y <= 2.8d-296) then
        tmp = i * (t * b)
    else if (y <= 8d-215) then
        tmp = t_1
    else if (y <= 2.9d-98) then
        tmp = x * (t * -a)
    else
        tmp = j * (y * -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 t_1 = c * -(z * b);
	double tmp;
	if (y <= -9e+170) {
		tmp = x * (y * z);
	} else if (y <= -3.25e+81) {
		tmp = j * (a * c);
	} else if (y <= -4.5e-162) {
		tmp = t_1;
	} else if (y <= 2.8e-296) {
		tmp = i * (t * b);
	} else if (y <= 8e-215) {
		tmp = t_1;
	} else if (y <= 2.9e-98) {
		tmp = x * (t * -a);
	} else {
		tmp = j * (y * -i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * -(z * b)
	tmp = 0
	if y <= -9e+170:
		tmp = x * (y * z)
	elif y <= -3.25e+81:
		tmp = j * (a * c)
	elif y <= -4.5e-162:
		tmp = t_1
	elif y <= 2.8e-296:
		tmp = i * (t * b)
	elif y <= 8e-215:
		tmp = t_1
	elif y <= 2.9e-98:
		tmp = x * (t * -a)
	else:
		tmp = j * (y * -i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(-Float64(z * b)))
	tmp = 0.0
	if (y <= -9e+170)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -3.25e+81)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= -4.5e-162)
		tmp = t_1;
	elseif (y <= 2.8e-296)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 8e-215)
		tmp = t_1;
	elseif (y <= 2.9e-98)
		tmp = Float64(x * Float64(t * Float64(-a)));
	else
		tmp = Float64(j * Float64(y * Float64(-i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * -(z * b);
	tmp = 0.0;
	if (y <= -9e+170)
		tmp = x * (y * z);
	elseif (y <= -3.25e+81)
		tmp = j * (a * c);
	elseif (y <= -4.5e-162)
		tmp = t_1;
	elseif (y <= 2.8e-296)
		tmp = i * (t * b);
	elseif (y <= 8e-215)
		tmp = t_1;
	elseif (y <= 2.9e-98)
		tmp = x * (t * -a);
	else
		tmp = j * (y * -i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[y, -9e+170], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.25e+81], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.5e-162], t$95$1, If[LessEqual[y, 2.8e-296], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-215], t$95$1, If[LessEqual[y, 2.9e-98], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -9.00000000000000044e170

   1. Initial program 53.2%

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

   3. Taylor expanded in y around inf 78.4%

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

      1. +-commutative 78.4%

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

      2. mul-1-neg 78.4%

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

      3. unsub-neg 78.4%

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

      4. *-commutative 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in x around inf 61.9%

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

   if -9.00000000000000044e170 < y < -3.2499999999999998e81

   1. Initial program 62.1%

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

   3. Taylor expanded in x around 0 66.5%

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

      1. *-commutative 66.5%

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

      2. *-commutative 66.5%

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

      3. *-commutative 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in a around inf 30.7%

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

      1. associate-*r* 44.0%

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

      2. *-commutative 44.0%

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

   8. Simplified 44.0%

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

   if -3.2499999999999998e81 < y < -4.50000000000000023e-162 or 2.7999999999999999e-296 < y < 8.00000000000000033e-215

   1. Initial program 82.9%

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

   3. Taylor expanded in c around inf 51.4%

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

      1. *-commutative 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in a around 0 37.7%

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

      1. mul-1-neg 37.7%

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

      2. *-commutative 37.7%

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

      3. distribute-rgt-neg-in 37.7%

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

   8. Simplified 37.7%

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

   if -4.50000000000000023e-162 < y < 2.7999999999999999e-296

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 69.4%

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

      1. *-commutative 69.4%

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

      2. *-commutative 69.4%

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

      3. *-commutative 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in t around inf 41.0%

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

      1. *-commutative 41.0%

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

      2. associate-*r* 43.5%

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

      3. *-commutative 43.5%

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

   8. Simplified 43.5%

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

   if 8.00000000000000033e-215 < y < 2.9e-98

   1. Initial program 87.4%

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

   3. Taylor expanded in a around -inf 78.1%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in x around inf 44.0%

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

      1. *-commutative 44.0%

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

   8. Simplified 44.0%

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

   9. Taylor expanded in y around 0 43.6%

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

       1. associate-*r* 43.6%

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

       2. neg-mul-1 43.6%

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

   11. Simplified 43.6%

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

   if 2.9e-98 < y

   1. Initial program 71.6%

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

   3. Taylor expanded in x around 0 56.8%

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

      1. *-commutative 56.8%

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

      2. *-commutative 56.8%

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

      3. *-commutative 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in y around inf 34.3%

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

      1. associate-*r* 34.3%

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

      2. neg-mul-1 34.3%

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

      3. *-commutative 34.3%

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

      4. associate-*r* 35.7%

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

      5. distribute-lft-neg-in 35.7%

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

      6. distribute-rgt-neg-in 35.7%

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

   8. Simplified 35.7%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{+81}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-162}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-296}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-215}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -5.8 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -540000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -8.5 \cdot 10^{-262}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -5.8e+72)
     t_1
     (if (<= c -540000000000.0)
       (* x (* y z))
       (if (<= c -1.65e-59)
         (* b (- (* t i) (* z c)))
         (if (<= c -8.5e-262)
           (* i (- (* t b) (* y j)))
           (if (<= c 8.5e+102) (* t (- (* b i) (* x a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -5.8e+72) {
		tmp = t_1;
	} else if (c <= -540000000000.0) {
		tmp = x * (y * z);
	} else if (c <= -1.65e-59) {
		tmp = b * ((t * i) - (z * c));
	} else if (c <= -8.5e-262) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 8.5e+102) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    if (c <= (-5.8d+72)) then
        tmp = t_1
    else if (c <= (-540000000000.0d0)) then
        tmp = x * (y * z)
    else if (c <= (-1.65d-59)) then
        tmp = b * ((t * i) - (z * c))
    else if (c <= (-8.5d-262)) then
        tmp = i * ((t * b) - (y * j))
    else if (c <= 8.5d+102) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -5.8e+72) {
		tmp = t_1;
	} else if (c <= -540000000000.0) {
		tmp = x * (y * z);
	} else if (c <= -1.65e-59) {
		tmp = b * ((t * i) - (z * c));
	} else if (c <= -8.5e-262) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 8.5e+102) {
		tmp = t * ((b * i) - (x * a));
	} 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 <= -5.8e+72:
		tmp = t_1
	elif c <= -540000000000.0:
		tmp = x * (y * z)
	elif c <= -1.65e-59:
		tmp = b * ((t * i) - (z * c))
	elif c <= -8.5e-262:
		tmp = i * ((t * b) - (y * j))
	elif c <= 8.5e+102:
		tmp = t * ((b * i) - (x * a))
	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 <= -5.8e+72)
		tmp = t_1;
	elseif (c <= -540000000000.0)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= -1.65e-59)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (c <= -8.5e-262)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (c <= 8.5e+102)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -5.8e+72)
		tmp = t_1;
	elseif (c <= -540000000000.0)
		tmp = x * (y * z);
	elseif (c <= -1.65e-59)
		tmp = b * ((t * i) - (z * c));
	elseif (c <= -8.5e-262)
		tmp = i * ((t * b) - (y * j));
	elseif (c <= 8.5e+102)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.8e+72], t$95$1, If[LessEqual[c, -540000000000.0], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.65e-59], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.5e-262], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.5e+102], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -5.80000000000000034e72 or 8.4999999999999996e102 < c

   1. Initial program 62.4%

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

   3. Taylor expanded in c around inf 71.7%

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

      1. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   if -5.80000000000000034e72 < c < -5.4e11

   1. Initial program 79.7%

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

   3. Taylor expanded in y around inf 54.9%

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

      1. +-commutative 54.9%

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

      2. mul-1-neg 54.9%

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

      3. unsub-neg 54.9%

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

      4. *-commutative 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in x around inf 66.9%

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

   if -5.4e11 < c < -1.64999999999999991e-59

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 54.4%

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

      1. *-commutative 54.4%

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

      2. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   if -1.64999999999999991e-59 < c < -8.5e-262

   1. Initial program 71.6%

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

   3. Taylor expanded in a around -inf 73.7%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in i around inf 57.7%

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

      1. +-commutative 57.7%

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

      2. *-commutative 57.7%

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

      3. mul-1-neg 57.7%

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

      4. *-commutative 57.7%

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

      5. unsub-neg 57.7%

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

      6. *-commutative 57.7%

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

   8. Simplified 57.7%

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

   if -8.5e-262 < c < 8.4999999999999996e102

   1. Initial program 83.6%

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

   3. Taylor expanded in a around -inf 81.5%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in t around inf 58.6%

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

      1. *-commutative 58.6%

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

      2. *-commutative 58.6%

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

   8. Simplified 58.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.8 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -540000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -8.5 \cdot 10^{-262}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{+186}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-149}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-225}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -6.5e+186)
   (* j (- (* a c) (* y i)))
   (if (<= c -1e-58)
     (* z (- (* x y) (* b c)))
     (if (<= c -2.7e-149)
       (* i (- (* t b) (* y j)))
       (if (<= c -3.1e-225)
         (* y (- (* x z) (* i j)))
         (if (<= c 1.5e+103)
           (* t (- (* b i) (* x a)))
           (* c (- (* a j) (* z b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -6.5e+186) {
		tmp = j * ((a * c) - (y * i));
	} else if (c <= -1e-58) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -2.7e-149) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= -3.1e-225) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1.5e+103) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-6.5d+186)) then
        tmp = j * ((a * c) - (y * i))
    else if (c <= (-1d-58)) then
        tmp = z * ((x * y) - (b * c))
    else if (c <= (-2.7d-149)) then
        tmp = i * ((t * b) - (y * j))
    else if (c <= (-3.1d-225)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 1.5d+103) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = c * ((a * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -6.5e+186) {
		tmp = j * ((a * c) - (y * i));
	} else if (c <= -1e-58) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -2.7e-149) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= -3.1e-225) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1.5e+103) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -6.5e+186:
		tmp = j * ((a * c) - (y * i))
	elif c <= -1e-58:
		tmp = z * ((x * y) - (b * c))
	elif c <= -2.7e-149:
		tmp = i * ((t * b) - (y * j))
	elif c <= -3.1e-225:
		tmp = y * ((x * z) - (i * j))
	elif c <= 1.5e+103:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = c * ((a * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -6.5e+186)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (c <= -1e-58)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (c <= -2.7e-149)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (c <= -3.1e-225)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 1.5e+103)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -6.5e+186)
		tmp = j * ((a * c) - (y * i));
	elseif (c <= -1e-58)
		tmp = z * ((x * y) - (b * c));
	elseif (c <= -2.7e-149)
		tmp = i * ((t * b) - (y * j));
	elseif (c <= -3.1e-225)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 1.5e+103)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -6.5e+186], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1e-58], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.7e-149], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.1e-225], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.5e+103], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -6.4999999999999997e186

   1. Initial program 36.4%

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

   3. Taylor expanded in j around inf 79.9%

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

      1. *-commutative 79.9%

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

   5. Simplified 79.9%

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

   if -6.4999999999999997e186 < c < -1e-58

   1. Initial program 79.5%

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

   3. Taylor expanded in z around inf 59.7%

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

      1. *-commutative 59.7%

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

   5. Simplified 59.7%

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

   if -1e-58 < c < -2.70000000000000014e-149

   1. Initial program 75.8%

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

   3. Taylor expanded in a around -inf 75.4%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in i around inf 68.9%

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

      1. +-commutative 68.9%

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

      2. *-commutative 68.9%

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

      3. mul-1-neg 68.9%

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

      4. *-commutative 68.9%

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

      5. unsub-neg 68.9%

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

      6. *-commutative 68.9%

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

   8. Simplified 68.9%

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

   if -2.70000000000000014e-149 < c < -3.09999999999999996e-225

   1. Initial program 60.0%

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

   3. Taylor expanded in y around inf 90.1%

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

      1. +-commutative 90.1%

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

      2. mul-1-neg 90.1%

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

      3. unsub-neg 90.1%

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

      4. *-commutative 90.1%

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

   5. Simplified 90.1%

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

   if -3.09999999999999996e-225 < c < 1.5e103

   1. Initial program 83.4%

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

   3. Taylor expanded in a around -inf 81.5%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in t around inf 57.8%

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

      1. *-commutative 57.8%

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

      2. *-commutative 57.8%

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

   8. Simplified 57.8%

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

   if 1.5e103 < c

   1. Initial program 78.3%

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

   3. Taylor expanded in c around inf 78.9%

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

      1. *-commutative 78.9%

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

   5. Simplified 78.9%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{+186}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-149}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-225}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -6 \cdot 10^{+250}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t\_1\\ \mathbf{elif}\;b \leq -1.06 \cdot 10^{+54} \lor \neg \left(b \leq 7 \cdot 10^{-103}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -6e+250)
     (+ (* j (- (* a c) (* y i))) t_1)
     (if (or (<= b -1.06e+54) (not (<= b 7e-103)))
       (+ (* x (- (* y z) (* t a))) t_1)
       (+ (* y (- (* x z) (* i j))) (* 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 t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -6e+250) {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	} else if ((b <= -1.06e+54) || !(b <= 7e-103)) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = (y * ((x * z) - (i * j))) + (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) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-6d+250)) then
        tmp = (j * ((a * c) - (y * i))) + t_1
    else if ((b <= (-1.06d+54)) .or. (.not. (b <= 7d-103))) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else
        tmp = (y * ((x * z) - (i * j))) + (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 t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -6e+250) {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	} else if ((b <= -1.06e+54) || !(b <= 7e-103)) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)));
	}
	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 <= -6e+250:
		tmp = (j * ((a * c) - (y * i))) + t_1
	elif (b <= -1.06e+54) or not (b <= 7e-103):
		tmp = (x * ((y * z) - (t * a))) + t_1
	else:
		tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)))
	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 <= -6e+250)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_1);
	elseif ((b <= -1.06e+54) || !(b <= 7e-103))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + 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)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -6e+250)
		tmp = (j * ((a * c) - (y * i))) + t_1;
	elseif ((b <= -1.06e+54) || ~((b <= 7e-103)))
		tmp = (x * ((y * z) - (t * a))) + t_1;
	else
		tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)));
	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, -6e+250], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[Or[LessEqual[b, -1.06e+54], N[Not[LessEqual[b, 7e-103]], $MachinePrecision]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.99999999999999953e250

   1. Initial program 70.5%

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

   3. Taylor expanded in x around 0 82.2%

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

      1. *-commutative 82.2%

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

      2. *-commutative 82.2%

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

      3. *-commutative 82.2%

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

   5. Simplified 82.2%

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

   if -5.99999999999999953e250 < b < -1.06e54 or 7.00000000000000032e-103 < b

   1. Initial program 77.1%

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

   3. Taylor expanded in j around 0 75.7%

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

      1. *-commutative 75.7%

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

      2. *-commutative 75.7%

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

   5. Simplified 75.7%

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

   if -1.06e54 < b < 7.00000000000000032e-103

   1. Initial program 75.4%

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

   3. Taylor expanded in a around -inf 73.5%

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

   5. Simplified 73.5%

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

   6. Taylor expanded in b around 0 73.6%

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

      1. *-commutative 73.6%

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

      2. *-commutative 73.6%

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

   8. Simplified 73.6%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+250}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.06 \cdot 10^{+54} \lor \neg \left(b \leq 7 \cdot 10^{-103}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(x \cdot \left(-a\right)\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;i \leq -1.65 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-220}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* x (- a)))) (t_2 (* x (* y z))))
   (if (<= i -1.65e+101)
     (* i (* t b))
     (if (<= i -1.35e-85)
       t_1
       (if (<= i -1.35e-220)
         t_2
         (if (<= i 2e-93) t_1 (if (<= i 1.5e+51) t_2 (* 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 t_1 = t * (x * -a);
	double t_2 = x * (y * z);
	double tmp;
	if (i <= -1.65e+101) {
		tmp = i * (t * b);
	} else if (i <= -1.35e-85) {
		tmp = t_1;
	} else if (i <= -1.35e-220) {
		tmp = t_2;
	} else if (i <= 2e-93) {
		tmp = t_1;
	} else if (i <= 1.5e+51) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (x * -a)
    t_2 = x * (y * z)
    if (i <= (-1.65d+101)) then
        tmp = i * (t * b)
    else if (i <= (-1.35d-85)) then
        tmp = t_1
    else if (i <= (-1.35d-220)) then
        tmp = t_2
    else if (i <= 2d-93) then
        tmp = t_1
    else if (i <= 1.5d+51) then
        tmp = t_2
    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 t_1 = t * (x * -a);
	double t_2 = x * (y * z);
	double tmp;
	if (i <= -1.65e+101) {
		tmp = i * (t * b);
	} else if (i <= -1.35e-85) {
		tmp = t_1;
	} else if (i <= -1.35e-220) {
		tmp = t_2;
	} else if (i <= 2e-93) {
		tmp = t_1;
	} else if (i <= 1.5e+51) {
		tmp = t_2;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (x * -a)
	t_2 = x * (y * z)
	tmp = 0
	if i <= -1.65e+101:
		tmp = i * (t * b)
	elif i <= -1.35e-85:
		tmp = t_1
	elif i <= -1.35e-220:
		tmp = t_2
	elif i <= 2e-93:
		tmp = t_1
	elif i <= 1.5e+51:
		tmp = t_2
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(x * Float64(-a)))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (i <= -1.65e+101)
		tmp = Float64(i * Float64(t * b));
	elseif (i <= -1.35e-85)
		tmp = t_1;
	elseif (i <= -1.35e-220)
		tmp = t_2;
	elseif (i <= 2e-93)
		tmp = t_1;
	elseif (i <= 1.5e+51)
		tmp = t_2;
	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)
	t_1 = t * (x * -a);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (i <= -1.65e+101)
		tmp = i * (t * b);
	elseif (i <= -1.35e-85)
		tmp = t_1;
	elseif (i <= -1.35e-220)
		tmp = t_2;
	elseif (i <= 2e-93)
		tmp = t_1;
	elseif (i <= 1.5e+51)
		tmp = t_2;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.65e+101], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.35e-85], t$95$1, If[LessEqual[i, -1.35e-220], t$95$2, If[LessEqual[i, 2e-93], t$95$1, If[LessEqual[i, 1.5e+51], t$95$2, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.65000000000000006e101

   1. Initial program 63.2%

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

   3. Taylor expanded in x around 0 58.6%

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

      1. *-commutative 58.6%

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

      2. *-commutative 58.6%

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

      3. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in t around inf 43.8%

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

      1. *-commutative 43.8%

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

      2. associate-*r* 48.5%

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

      3. *-commutative 48.5%

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

   8. Simplified 48.5%

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

   if -1.65000000000000006e101 < i < -1.3500000000000001e-85 or -1.35e-220 < i < 1.9999999999999998e-93

   1. Initial program 80.8%

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

   3. Taylor expanded in a around inf 45.2%

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

      1. +-commutative 45.2%

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

      2. mul-1-neg 45.2%

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

      3. unsub-neg 45.2%

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

      4. *-commutative 45.2%

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

      5. *-commutative 45.2%

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

   5. Simplified 45.2%

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

   6. Taylor expanded in j around 0 33.9%

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

      1. mul-1-neg 33.9%

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

      2. *-commutative 33.9%

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

      3. distribute-rgt-neg-in 33.9%

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

   8. Simplified 33.9%

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

   9. Taylor expanded in a around 0 33.9%

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

       1. mul-1-neg 33.9%

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

       2. *-commutative 33.9%

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

       3. associate-*l* 34.9%

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

       4. *-commutative 34.9%

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

   11. Simplified 34.9%

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

   if -1.3500000000000001e-85 < i < -1.35e-220 or 1.9999999999999998e-93 < i < 1.5e51

   1. Initial program 78.9%

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

   3. Taylor expanded in y around inf 37.7%

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

      1. +-commutative 37.7%

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

      2. mul-1-neg 37.7%

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

      3. unsub-neg 37.7%

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

      4. *-commutative 37.7%

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

   5. Simplified 37.7%

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

   6. Taylor expanded in x around inf 36.8%

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

   if 1.5e51 < i

   1. Initial program 73.9%

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

   3. Taylor expanded in i around inf 67.9%

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

      1. distribute-lft-out-- 67.9%

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

      2. *-commutative 67.9%

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

      3. *-commutative 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in y around 0 38.6%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.65 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-220}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-93}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+165}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-159}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-268}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-47}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= y -5.2e+165)
     (* x (* y z))
     (if (<= y -3.9e-16)
       t_1
       (if (<= y -4.6e-159)
         (* a (* x (- t)))
         (if (<= y 2.25e-268)
           t_1
           (if (<= y 5.2e-47) (* c (* a j)) (* y (* x 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 = i * (t * b);
	double tmp;
	if (y <= -5.2e+165) {
		tmp = x * (y * z);
	} else if (y <= -3.9e-16) {
		tmp = t_1;
	} else if (y <= -4.6e-159) {
		tmp = a * (x * -t);
	} else if (y <= 2.25e-268) {
		tmp = t_1;
	} else if (y <= 5.2e-47) {
		tmp = c * (a * j);
	} else {
		tmp = y * (x * 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 = i * (t * b)
    if (y <= (-5.2d+165)) then
        tmp = x * (y * z)
    else if (y <= (-3.9d-16)) then
        tmp = t_1
    else if (y <= (-4.6d-159)) then
        tmp = a * (x * -t)
    else if (y <= 2.25d-268) then
        tmp = t_1
    else if (y <= 5.2d-47) then
        tmp = c * (a * j)
    else
        tmp = y * (x * 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 = i * (t * b);
	double tmp;
	if (y <= -5.2e+165) {
		tmp = x * (y * z);
	} else if (y <= -3.9e-16) {
		tmp = t_1;
	} else if (y <= -4.6e-159) {
		tmp = a * (x * -t);
	} else if (y <= 2.25e-268) {
		tmp = t_1;
	} else if (y <= 5.2e-47) {
		tmp = c * (a * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if y <= -5.2e+165:
		tmp = x * (y * z)
	elif y <= -3.9e-16:
		tmp = t_1
	elif y <= -4.6e-159:
		tmp = a * (x * -t)
	elif y <= 2.25e-268:
		tmp = t_1
	elif y <= 5.2e-47:
		tmp = c * (a * j)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (y <= -5.2e+165)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -3.9e-16)
		tmp = t_1;
	elseif (y <= -4.6e-159)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (y <= 2.25e-268)
		tmp = t_1;
	elseif (y <= 5.2e-47)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	tmp = 0.0;
	if (y <= -5.2e+165)
		tmp = x * (y * z);
	elseif (y <= -3.9e-16)
		tmp = t_1;
	elseif (y <= -4.6e-159)
		tmp = a * (x * -t);
	elseif (y <= 2.25e-268)
		tmp = t_1;
	elseif (y <= 5.2e-47)
		tmp = c * (a * j);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+165], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.9e-16], t$95$1, If[LessEqual[y, -4.6e-159], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e-268], t$95$1, If[LessEqual[y, 5.2e-47], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.2000000000000002e165

   1. Initial program 55.7%

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

   3. Taylor expanded in y around inf 74.5%

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

      1. +-commutative 74.5%

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

      2. mul-1-neg 74.5%

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

      3. unsub-neg 74.5%

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

      4. *-commutative 74.5%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in x around inf 58.8%

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

   if -5.2000000000000002e165 < y < -3.89999999999999977e-16 or -4.59999999999999957e-159 < y < 2.2500000000000001e-268

   1. Initial program 79.8%

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

   3. Taylor expanded in x around 0 70.7%

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

      1. *-commutative 70.7%

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

      2. *-commutative 70.7%

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

      3. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in t around inf 39.1%

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

      1. *-commutative 39.1%

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

      2. associate-*r* 40.2%

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

      3. *-commutative 40.2%

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

   8. Simplified 40.2%

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

   if -3.89999999999999977e-16 < y < -4.59999999999999957e-159

   1. Initial program 81.9%

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

   3. Taylor expanded in a around inf 40.9%

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

      1. +-commutative 40.9%

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

      2. mul-1-neg 40.9%

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

      3. unsub-neg 40.9%

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

      4. *-commutative 40.9%

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

      5. *-commutative 40.9%

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

   5. Simplified 40.9%

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

   6. Taylor expanded in j around 0 30.9%

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

      1. mul-1-neg 30.9%

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

      2. *-commutative 30.9%

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

      3. distribute-rgt-neg-in 30.9%

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

   8. Simplified 30.9%

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

   if 2.2500000000000001e-268 < y < 5.2e-47

   1. Initial program 86.9%

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

   3. Taylor expanded in c around inf 55.9%

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

      1. *-commutative 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in a around inf 33.7%

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

      1. *-commutative 33.7%

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

   8. Simplified 33.7%

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

   if 5.2e-47 < y

   1. Initial program 71.1%

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

   3. Taylor expanded in y around inf 59.0%

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

      1. +-commutative 59.0%

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

      2. mul-1-neg 59.0%

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

      3. unsub-neg 59.0%

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

      4. *-commutative 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in x around inf 32.5%

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

      1. *-commutative 32.5%

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

      2. associate-*l* 34.2%

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

      3. *-commutative 34.2%

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

   8. Simplified 34.2%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+165}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-16}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-159}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-268}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-47}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 63.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+192}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+187}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+260}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -1.75e+192)
     t_2
     (if (<= x 1.8e+187)
       (+ t_1 (* b (- (* t i) (* z c))))
       (if (<= x 2.05e+260) t_2 (- t_1 (* b (* 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 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.75e+192) {
		tmp = t_2;
	} else if (x <= 1.8e+187) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (x <= 2.05e+260) {
		tmp = t_2;
	} else {
		tmp = t_1 - (b * (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) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-1.75d+192)) then
        tmp = t_2
    else if (x <= 1.8d+187) then
        tmp = t_1 + (b * ((t * i) - (z * c)))
    else if (x <= 2.05d+260) then
        tmp = t_2
    else
        tmp = t_1 - (b * (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 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.75e+192) {
		tmp = t_2;
	} else if (x <= 1.8e+187) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (x <= 2.05e+260) {
		tmp = t_2;
	} else {
		tmp = t_1 - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.75e+192:
		tmp = t_2
	elif x <= 1.8e+187:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	elif x <= 2.05e+260:
		tmp = t_2
	else:
		tmp = t_1 - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.75e+192)
		tmp = t_2;
	elseif (x <= 1.8e+187)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (x <= 2.05e+260)
		tmp = t_2;
	else
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.75e+192)
		tmp = t_2;
	elseif (x <= 1.8e+187)
		tmp = t_1 + (b * ((t * i) - (z * c)));
	elseif (x <= 2.05e+260)
		tmp = t_2;
	else
		tmp = t_1 - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.75e+192], t$95$2, If[LessEqual[x, 1.8e+187], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e+260], t$95$2, N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.74999999999999991e192 or 1.80000000000000018e187 < x < 2.05000000000000013e260

   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 a around -inf 66.1%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in x around inf 81.2%

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

      1. *-commutative 81.2%

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

   8. Simplified 81.2%

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

   if -1.74999999999999991e192 < x < 1.80000000000000018e187

   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 x around 0 64.0%

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

      1. *-commutative 64.0%

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

      2. *-commutative 64.0%

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

      3. *-commutative 64.0%

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

   5. Simplified 64.0%

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

   if 2.05000000000000013e260 < x

   1. Initial program 77.6%

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

   3. Taylor expanded in x around 0 78.3%

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

      1. *-commutative 78.3%

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

      2. *-commutative 78.3%

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

      3. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in t around 0 89.2%

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

      1. *-commutative 89.2%

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

   8. Simplified 89.2%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+187}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+260}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 43.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -0.000108:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-300}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-72}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-7}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -0.000108)
     t_1
     (if (<= a -7.6e-300)
       (* y (* i (- j)))
       (if (<= a 6.5e-72)
         (* b (* t i))
         (if (<= a 1.25e-7) (* j (* y (- 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) - (x * t));
	double tmp;
	if (a <= -0.000108) {
		tmp = t_1;
	} else if (a <= -7.6e-300) {
		tmp = y * (i * -j);
	} else if (a <= 6.5e-72) {
		tmp = b * (t * i);
	} else if (a <= 1.25e-7) {
		tmp = j * (y * -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) - (x * t))
    if (a <= (-0.000108d0)) then
        tmp = t_1
    else if (a <= (-7.6d-300)) then
        tmp = y * (i * -j)
    else if (a <= 6.5d-72) then
        tmp = b * (t * i)
    else if (a <= 1.25d-7) then
        tmp = j * (y * -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) - (x * t));
	double tmp;
	if (a <= -0.000108) {
		tmp = t_1;
	} else if (a <= -7.6e-300) {
		tmp = y * (i * -j);
	} else if (a <= 6.5e-72) {
		tmp = b * (t * i);
	} else if (a <= 1.25e-7) {
		tmp = j * (y * -i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -0.000108:
		tmp = t_1
	elif a <= -7.6e-300:
		tmp = y * (i * -j)
	elif a <= 6.5e-72:
		tmp = b * (t * i)
	elif a <= 1.25e-7:
		tmp = j * (y * -i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -0.000108)
		tmp = t_1;
	elseif (a <= -7.6e-300)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (a <= 6.5e-72)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 1.25e-7)
		tmp = Float64(j * Float64(y * Float64(-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) - (x * t));
	tmp = 0.0;
	if (a <= -0.000108)
		tmp = t_1;
	elseif (a <= -7.6e-300)
		tmp = y * (i * -j);
	elseif (a <= 6.5e-72)
		tmp = b * (t * i);
	elseif (a <= 1.25e-7)
		tmp = j * (y * -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[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.000108], t$95$1, If[LessEqual[a, -7.6e-300], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-72], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e-7], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.08e-4 or 1.24999999999999994e-7 < a

   1. Initial program 73.4%

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

   3. Taylor expanded in a around inf 55.4%

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

      1. +-commutative 55.4%

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

      2. mul-1-neg 55.4%

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

      3. unsub-neg 55.4%

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

      4. *-commutative 55.4%

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

      5. *-commutative 55.4%

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

   5. Simplified 55.4%

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

   if -1.08e-4 < a < -7.60000000000000026e-300

   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 y around inf 53.6%

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

      1. +-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

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

      4. *-commutative 53.6%

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

   5. Simplified 53.6%

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

   6. Taylor expanded in x around 0 34.7%

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

      1. mul-1-neg 34.7%

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

      2. distribute-rgt-neg-in 34.7%

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

   8. Simplified 34.7%

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

   if -7.60000000000000026e-300 < a < 6.4999999999999997e-72

   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 i around inf 45.9%

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

      1. distribute-lft-out-- 45.9%

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

      2. *-commutative 45.9%

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

      3. *-commutative 45.9%

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

   5. Simplified 45.9%

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

   6. Taylor expanded in y around 0 39.0%

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

   if 6.4999999999999997e-72 < a < 1.24999999999999994e-7

   1. Initial program 81.2%

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

   3. Taylor expanded in x around 0 68.9%

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

      1. *-commutative 68.9%

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

      2. *-commutative 68.9%

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

      3. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in y around inf 43.2%

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

      1. associate-*r* 43.2%

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

      2. neg-mul-1 43.2%

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

      3. *-commutative 43.2%

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

      4. associate-*r* 48.8%

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

      5. distribute-lft-neg-in 48.8%

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

      6. distribute-rgt-neg-in 48.8%

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

   8. Simplified 48.8%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.000108:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-300}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-72}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-7}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 51.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{+108}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-269}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 14500:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -8.5e+108)
     t_2
     (if (<= a -3.1e-221)
       t_1
       (if (<= a -3.6e-269) (* y (* i (- j))) (if (<= a 14500.0) 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 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -8.5e+108) {
		tmp = t_2;
	} else if (a <= -3.1e-221) {
		tmp = t_1;
	} else if (a <= -3.6e-269) {
		tmp = y * (i * -j);
	} else if (a <= 14500.0) {
		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 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-8.5d+108)) then
        tmp = t_2
    else if (a <= (-3.1d-221)) then
        tmp = t_1
    else if (a <= (-3.6d-269)) then
        tmp = y * (i * -j)
    else if (a <= 14500.0d0) 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 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -8.5e+108) {
		tmp = t_2;
	} else if (a <= -3.1e-221) {
		tmp = t_1;
	} else if (a <= -3.6e-269) {
		tmp = y * (i * -j);
	} else if (a <= 14500.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -8.5e+108:
		tmp = t_2
	elif a <= -3.1e-221:
		tmp = t_1
	elif a <= -3.6e-269:
		tmp = y * (i * -j)
	elif a <= 14500.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -8.5e+108)
		tmp = t_2;
	elseif (a <= -3.1e-221)
		tmp = t_1;
	elseif (a <= -3.6e-269)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (a <= 14500.0)
		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 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -8.5e+108)
		tmp = t_2;
	elseif (a <= -3.1e-221)
		tmp = t_1;
	elseif (a <= -3.6e-269)
		tmp = y * (i * -j);
	elseif (a <= 14500.0)
		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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.5e+108], t$95$2, If[LessEqual[a, -3.1e-221], t$95$1, If[LessEqual[a, -3.6e-269], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 14500.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.50000000000000016e108 or 14500 < a

   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 a around inf 61.2%

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

      1. +-commutative 61.2%

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

      2. mul-1-neg 61.2%

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

      3. unsub-neg 61.2%

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

      4. *-commutative 61.2%

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

      5. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   if -8.50000000000000016e108 < a < -3.0999999999999999e-221 or -3.59999999999999998e-269 < a < 14500

   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 inf 51.2%

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

      1. *-commutative 51.2%

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

      2. *-commutative 51.2%

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

   5. Simplified 51.2%

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

   if -3.0999999999999999e-221 < a < -3.59999999999999998e-269

   1. Initial program 67.3%

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

   3. Taylor expanded in y around inf 88.7%

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

      1. +-commutative 88.7%

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

      2. mul-1-neg 88.7%

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

      3. unsub-neg 88.7%

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

      4. *-commutative 88.7%

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

   5. Simplified 88.7%

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

   6. Taylor expanded in x around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. distribute-rgt-neg-in 67.8%

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

   8. Simplified 67.8%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+108}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-221}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-269}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 14500:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 52.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{+35}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-300}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 920:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -8.2e+154)
     t_1
     (if (<= a -6.4e+35)
       (* c (- (* a j) (* z b)))
       (if (<= a -8.5e-300)
         (* i (- (* t b) (* y j)))
         (if (<= a 920.0) (* b (- (* t i) (* z c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -8.2e+154) {
		tmp = t_1;
	} else if (a <= -6.4e+35) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= -8.5e-300) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 920.0) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-8.2d+154)) then
        tmp = t_1
    else if (a <= (-6.4d+35)) then
        tmp = c * ((a * j) - (z * b))
    else if (a <= (-8.5d-300)) then
        tmp = i * ((t * b) - (y * j))
    else if (a <= 920.0d0) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -8.2e+154) {
		tmp = t_1;
	} else if (a <= -6.4e+35) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= -8.5e-300) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 920.0) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -8.2e+154:
		tmp = t_1
	elif a <= -6.4e+35:
		tmp = c * ((a * j) - (z * b))
	elif a <= -8.5e-300:
		tmp = i * ((t * b) - (y * j))
	elif a <= 920.0:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -8.2e+154)
		tmp = t_1;
	elseif (a <= -6.4e+35)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (a <= -8.5e-300)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (a <= 920.0)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -8.2e+154)
		tmp = t_1;
	elseif (a <= -6.4e+35)
		tmp = c * ((a * j) - (z * b));
	elseif (a <= -8.5e-300)
		tmp = i * ((t * b) - (y * j));
	elseif (a <= 920.0)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.2e+154], t$95$1, If[LessEqual[a, -6.4e+35], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.5e-300], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 920.0], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.2e154 or 920 < a

   1. Initial program 74.3%

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

   3. Taylor expanded in a around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. mul-1-neg 62.7%

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

      3. unsub-neg 62.7%

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

      4. *-commutative 62.7%

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

      5. *-commutative 62.7%

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

   5. Simplified 62.7%

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

   if -8.2e154 < a < -6.39999999999999965e35

   1. Initial program 73.0%

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

   3. Taylor expanded in c around inf 58.6%

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

      1. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   if -6.39999999999999965e35 < a < -8.4999999999999995e-300

   1. Initial program 67.7%

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

   3. Taylor expanded in a around -inf 61.7%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in i around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. *-commutative 55.0%

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

      3. mul-1-neg 55.0%

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

      4. *-commutative 55.0%

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

      5. unsub-neg 55.0%

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

      6. *-commutative 55.0%

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

   8. Simplified 55.0%

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

   if -8.4999999999999995e-300 < a < 920

   1. Initial program 87.2%

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

   3. Taylor expanded in b around inf 57.9%

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

      1. *-commutative 57.9%

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

      2. *-commutative 57.9%

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

   5. Simplified 57.9%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+154}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{+35}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-300}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 920:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.7 \cdot 10^{+35}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-107}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq 4.9 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -2.7e+35)
   (* i (* t b))
   (if (<= i 2e-107)
     (* c (* a j))
     (if (<= i 4.9e+51) (* x (* y z)) (* 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 (i <= -2.7e+35) {
		tmp = i * (t * b);
	} else if (i <= 2e-107) {
		tmp = c * (a * j);
	} else if (i <= 4.9e+51) {
		tmp = x * (y * z);
	} 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 (i <= (-2.7d+35)) then
        tmp = i * (t * b)
    else if (i <= 2d-107) then
        tmp = c * (a * j)
    else if (i <= 4.9d+51) then
        tmp = x * (y * z)
    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 (i <= -2.7e+35) {
		tmp = i * (t * b);
	} else if (i <= 2e-107) {
		tmp = c * (a * j);
	} else if (i <= 4.9e+51) {
		tmp = x * (y * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -2.7e+35:
		tmp = i * (t * b)
	elif i <= 2e-107:
		tmp = c * (a * j)
	elif i <= 4.9e+51:
		tmp = x * (y * z)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -2.7e+35)
		tmp = Float64(i * Float64(t * b));
	elseif (i <= 2e-107)
		tmp = Float64(c * Float64(a * j));
	elseif (i <= 4.9e+51)
		tmp = Float64(x * Float64(y * z));
	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 (i <= -2.7e+35)
		tmp = i * (t * b);
	elseif (i <= 2e-107)
		tmp = c * (a * j);
	elseif (i <= 4.9e+51)
		tmp = x * (y * z);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -2.7e+35], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2e-107], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.9e+51], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.70000000000000003e35

   1. Initial program 66.2%

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

   3. Taylor expanded in x around 0 57.6%

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

      1. *-commutative 57.6%

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

      2. *-commutative 57.6%

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

      3. *-commutative 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in t around inf 41.3%

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

      1. *-commutative 41.3%

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

      2. associate-*r* 44.7%

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

      3. *-commutative 44.7%

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

   8. Simplified 44.7%

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

   if -2.70000000000000003e35 < i < 2e-107

   1. Initial program 80.8%

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

   3. Taylor expanded in c around inf 47.6%

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

      1. *-commutative 47.6%

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

   5. Simplified 47.6%

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

   6. Taylor expanded in a around inf 26.5%

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

      1. *-commutative 26.5%

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

   8. Simplified 26.5%

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

   if 2e-107 < i < 4.89999999999999983e51

   1. Initial program 80.4%

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

   3. Taylor expanded in y around inf 42.3%

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

      1. +-commutative 42.3%

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

      2. mul-1-neg 42.3%

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

      3. unsub-neg 42.3%

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

      4. *-commutative 42.3%

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

   5. Simplified 42.3%

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

   6. Taylor expanded in x around inf 40.6%

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

   if 4.89999999999999983e51 < i

   1. Initial program 73.9%

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

   3. Taylor expanded in i around inf 67.9%

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

      1. distribute-lft-out-- 67.9%

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

      2. *-commutative 67.9%

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

      3. *-commutative 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in y around 0 38.6%

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

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.7 \cdot 10^{+35}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-107}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq 4.9 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.6 \cdot 10^{-75} \lor \neg \left(c \leq 1.35 \cdot 10^{+103}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.6e-75) (not (<= c 1.35e+103))) (* 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 <= -1.6e-75) || !(c <= 1.35e+103)) {
		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 <= (-1.6d-75)) .or. (.not. (c <= 1.35d+103))) 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 <= -1.6e-75) || !(c <= 1.35e+103)) {
		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 <= -1.6e-75) or not (c <= 1.35e+103):
		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 <= -1.6e-75) || !(c <= 1.35e+103))
		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 <= -1.6e-75) || ~((c <= 1.35e+103)))
		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, -1.6e-75], N[Not[LessEqual[c, 1.35e+103]], $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 < -1.59999999999999988e-75 or 1.34999999999999996e103 < c

   1. Initial program 69.7%

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

   3. Taylor expanded in a around inf 37.4%

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

      1. +-commutative 37.4%

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

      2. mul-1-neg 37.4%

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

      3. unsub-neg 37.4%

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

      4. *-commutative 37.4%

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

      5. *-commutative 37.4%

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

   5. Simplified 37.4%

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

   6. Taylor expanded in j around inf 33.1%

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

      1. *-commutative 33.1%

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

   8. Simplified 33.1%

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

   if -1.59999999999999988e-75 < c < 1.34999999999999996e103

   1. Initial program 81.6%

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

   3. Taylor expanded in i around inf 48.3%

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

      1. distribute-lft-out-- 48.3%

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

      2. *-commutative 48.3%

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

      3. *-commutative 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in y around 0 31.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.6 \cdot 10^{-75} \lor \neg \left(c \leq 1.35 \cdot 10^{+103}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+53} \lor \neg \left(b \leq 7.6 \cdot 10^{+96}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -4.4e+53) (not (<= b 7.6e+96))) (* b (* t i)) (* c (* a j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -4.4e+53) || !(b <= 7.6e+96)) {
		tmp = b * (t * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-4.4d+53)) .or. (.not. (b <= 7.6d+96))) then
        tmp = b * (t * i)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -4.4e+53) || !(b <= 7.6e+96)) {
		tmp = b * (t * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -4.4e+53) or not (b <= 7.6e+96):
		tmp = b * (t * i)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -4.4e+53) || !(b <= 7.6e+96))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -4.4e+53) || ~((b <= 7.6e+96)))
		tmp = b * (t * i);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -4.4e+53], N[Not[LessEqual[b, 7.6e+96]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.39999999999999997e53 or 7.6000000000000003e96 < b

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 50.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 50.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 50.0%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right)\right) \]

      3. *-commutative 50.0%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 50.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - t \cdot b\right)\right)} \]

   6. Taylor expanded in y around 0 41.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -4.39999999999999997e53 < b < 7.6000000000000003e96

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 36.2%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 36.2%

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{z \cdot b}\right) \]

   5. Simplified 36.2%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   6. Taylor expanded in a around inf 26.9%

      \[\leadsto c \cdot \color{blue}{\left(a \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 26.9%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   8. Simplified 26.9%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+53} \lor \neg \left(b \leq 7.6 \cdot 10^{+96}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 21.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+205}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -7.4e+205) (* a (* x t)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -7.4e+205) {
		tmp = a * (x * t);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-7.4d+205)) then
        tmp = a * (x * t)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -7.4e+205) {
		tmp = a * (x * t);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -7.4e+205:
		tmp = a * (x * t)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -7.4e+205)
		tmp = Float64(a * Float64(x * t));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -7.4e+205)
		tmp = a * (x * t);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -7.4e+205], N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.39999999999999961e205

   1. Initial program 85.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 36.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 36.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 36.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 36.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 36.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 36.0%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   5. Simplified 36.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   6. Taylor expanded in j around 0 35.9%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 35.9%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. *-commutative 35.9%

         \[\leadsto a \cdot \left(-\color{blue}{x \cdot t}\right) \]

      3. distribute-rgt-neg-in 35.9%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   8. Simplified 35.9%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 20.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(x \cdot \left(-t\right)\right)\right)\right)} \]

      2. expm1-udef 20.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(x \cdot \left(-t\right)\right)\right)} - 1} \]

      3. associate-*r* 24.5%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(a \cdot x\right) \cdot \left(-t\right)}\right)} - 1 \]

      4. add-sqr-sqrt 24.5%

         \[\leadsto e^{\mathsf{log1p}\left(\left(a \cdot x\right) \cdot \color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)}\right)} - 1 \]

      5. sqrt-unprod 15.6%

         \[\leadsto e^{\mathsf{log1p}\left(\left(a \cdot x\right) \cdot \color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}\right)} - 1 \]

      6. sqr-neg 15.6%

         \[\leadsto e^{\mathsf{log1p}\left(\left(a \cdot x\right) \cdot \sqrt{\color{blue}{t \cdot t}}\right)} - 1 \]

      7. sqrt-unprod 0.0%

         \[\leadsto e^{\mathsf{log1p}\left(\left(a \cdot x\right) \cdot \color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)}\right)} - 1 \]

      8. add-sqr-sqrt 10.9%

         \[\leadsto e^{\mathsf{log1p}\left(\left(a \cdot x\right) \cdot \color{blue}{t}\right)} - 1 \]

   10. Applied egg-rr 10.9%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(a \cdot x\right) \cdot t\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 10.9%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(a \cdot x\right) \cdot t\right)\right)} \]

       2. expm1-log1p 16.6%

          \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot t} \]

       3. associate-*l* 30.8%

          \[\leadsto \color{blue}{a \cdot \left(x \cdot t\right)} \]

       4. *-commutative 30.8%

          \[\leadsto a \cdot \color{blue}{\left(t \cdot x\right)} \]

   12. Simplified 30.8%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot x\right)} \]

   if -7.39999999999999961e205 < t

   1. Initial program 75.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 33.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 33.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 33.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 33.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 33.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 33.8%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   5. Simplified 33.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   6. Taylor expanded in j around inf 19.6%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 19.6%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Simplified 19.6%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 20.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+205}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 22.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.0%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf 33.9%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 33.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 33.9%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 33.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 33.9%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. *-commutative 33.9%

      \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

5. Simplified 33.9%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

6. Taylor expanded in j around inf 18.2%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
7. Step-by-step derivation

   1. *-commutative 18.2%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

8. Simplified 18.2%

   \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

9. Final simplification 18.2%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer target: 59.4% 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 2024026 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))