Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J

Percentage Accurate: 96.6% → 99.9%

Time: 9.0s

Alternatives: 11

Speedup: 0.6×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Python

def code(x, y, z):
	return x * (1.0 - ((1.0 - y) * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - ((1.0 - y) * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Python

def code(x, y, z):
	return x * (1.0 - ((1.0 - y) * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - ((1.0 - y) * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 8 \cdot 10^{-10}:\\ \;\;\;\;x\_m + z \cdot \left(x\_m \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m + x\_m \cdot \left(z \cdot \left(-1 + y\right)\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= x_m 8e-10)
    (+ x_m (* z (* x_m (+ -1.0 y))))
    (+ x_m (* x_m (* z (+ -1.0 y)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 8e-10) {
		tmp = x_m + (z * (x_m * (-1.0 + y)));
	} else {
		tmp = x_m + (x_m * (z * (-1.0 + y)));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x_m <= 8d-10) then
        tmp = x_m + (z * (x_m * ((-1.0d0) + y)))
    else
        tmp = x_m + (x_m * (z * ((-1.0d0) + y)))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 8e-10) {
		tmp = x_m + (z * (x_m * (-1.0 + y)));
	} else {
		tmp = x_m + (x_m * (z * (-1.0 + y)));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if x_m <= 8e-10:
		tmp = x_m + (z * (x_m * (-1.0 + y)))
	else:
		tmp = x_m + (x_m * (z * (-1.0 + y)))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (x_m <= 8e-10)
		tmp = Float64(x_m + Float64(z * Float64(x_m * Float64(-1.0 + y))));
	else
		tmp = Float64(x_m + Float64(x_m * Float64(z * Float64(-1.0 + y))));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (x_m <= 8e-10)
		tmp = x_m + (z * (x_m * (-1.0 + y)));
	else
		tmp = x_m + (x_m * (z * (-1.0 + y)));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[x$95$m, 8e-10], N[(x$95$m + N[(z * N[(x$95$m * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m + N[(x$95$m * N[(z * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 8.00000000000000029e-10

   1. Initial program 92.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 92.6%

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

   4. Taylor expanded in y around 0 91.0%

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

      1. neg-mul-1 91.0%

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

      2. distribute-lft-neg-in 91.0%

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

      3. mul-1-neg 91.0%

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

      4. associate-*r* 94.9%

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

      5. distribute-rgt-out 96.4%

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

      6. *-commutative 96.4%

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

      7. distribute-lft-in 96.4%

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

   6. Simplified 96.4%

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

   if 8.00000000000000029e-10 < x

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 100.0%

      \[\leadsto \color{blue}{x + x \cdot \left(z \cdot \left(y - 1\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8 \cdot 10^{-10}:\\ \;\;\;\;x + z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(-1 + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 62.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := x\_m \cdot \left(z \cdot y\right)\\ t_1 := x\_m \cdot \left(-z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-120}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+136} \lor \neg \left(z \leq 3.5 \cdot 10^{+259}\right) \land z \leq 3.2 \cdot 10^{+296}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (* x_m (* z y))) (t_1 (* x_m (- z))))
   (*
    x_s
    (if (<= z -1.65e+16)
      t_1
      (if (<= z -1.15e-62)
        t_0
        (if (<= z 1.25e-120)
          x_m
          (if (or (<= z 1.25e+136) (and (not (<= z 3.5e+259)) (<= z 3.2e+296)))
            t_0
            t_1)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double t_0 = x_m * (z * y);
	double t_1 = x_m * -z;
	double tmp;
	if (z <= -1.65e+16) {
		tmp = t_1;
	} else if (z <= -1.15e-62) {
		tmp = t_0;
	} else if (z <= 1.25e-120) {
		tmp = x_m;
	} else if ((z <= 1.25e+136) || (!(z <= 3.5e+259) && (z <= 3.2e+296))) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x_m * (z * y)
    t_1 = x_m * -z
    if (z <= (-1.65d+16)) then
        tmp = t_1
    else if (z <= (-1.15d-62)) then
        tmp = t_0
    else if (z <= 1.25d-120) then
        tmp = x_m
    else if ((z <= 1.25d+136) .or. (.not. (z <= 3.5d+259)) .and. (z <= 3.2d+296)) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double t_0 = x_m * (z * y);
	double t_1 = x_m * -z;
	double tmp;
	if (z <= -1.65e+16) {
		tmp = t_1;
	} else if (z <= -1.15e-62) {
		tmp = t_0;
	} else if (z <= 1.25e-120) {
		tmp = x_m;
	} else if ((z <= 1.25e+136) || (!(z <= 3.5e+259) && (z <= 3.2e+296))) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	t_0 = x_m * (z * y)
	t_1 = x_m * -z
	tmp = 0
	if z <= -1.65e+16:
		tmp = t_1
	elif z <= -1.15e-62:
		tmp = t_0
	elif z <= 1.25e-120:
		tmp = x_m
	elif (z <= 1.25e+136) or (not (z <= 3.5e+259) and (z <= 3.2e+296)):
		tmp = t_0
	else:
		tmp = t_1
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	t_0 = Float64(x_m * Float64(z * y))
	t_1 = Float64(x_m * Float64(-z))
	tmp = 0.0
	if (z <= -1.65e+16)
		tmp = t_1;
	elseif (z <= -1.15e-62)
		tmp = t_0;
	elseif (z <= 1.25e-120)
		tmp = x_m;
	elseif ((z <= 1.25e+136) || (!(z <= 3.5e+259) && (z <= 3.2e+296)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	t_0 = x_m * (z * y);
	t_1 = x_m * -z;
	tmp = 0.0;
	if (z <= -1.65e+16)
		tmp = t_1;
	elseif (z <= -1.15e-62)
		tmp = t_0;
	elseif (z <= 1.25e-120)
		tmp = x_m;
	elseif ((z <= 1.25e+136) || (~((z <= 3.5e+259)) && (z <= 3.2e+296)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := Block[{t$95$0 = N[(x$95$m * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x$95$m * (-z)), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -1.65e+16], t$95$1, If[LessEqual[z, -1.15e-62], t$95$0, If[LessEqual[z, 1.25e-120], x$95$m, If[Or[LessEqual[z, 1.25e+136], And[N[Not[LessEqual[z, 3.5e+259]], $MachinePrecision], LessEqual[z, 3.2e+296]]], t$95$0, t$95$1]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65e16 or 1.25e136 < z < 3.4999999999999998e259 or 3.1999999999999999e296 < z

   1. Initial program 87.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 87.8%

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

      1. *-commutative 87.8%

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

      2. associate-*l* 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 62.6%

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

      1. associate-*r* 62.6%

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

      2. mul-1-neg 62.6%

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

   8. Simplified 62.6%

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

   if -1.65e16 < z < -1.15e-62 or 1.25000000000000002e-120 < z < 1.25e136 or 3.4999999999999998e259 < z < 3.1999999999999999e296

   1. Initial program 93.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 65.2%

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

      1. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   if -1.15e-62 < z < 1.25000000000000002e-120

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 83.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+136} \lor \neg \left(z \leq 3.5 \cdot 10^{+259}\right) \land z \leq 3.2 \cdot 10^{+296}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-62} \lor \neg \left(z \leq 5.5 \cdot 10^{-100}\right):\\ \;\;\;\;z \cdot \left(x\_m \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= z -2e-62) (not (<= z 5.5e-100))) (* z (* x_m (+ -1.0 y))) x_m)))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -2e-62) || !(z <= 5.5e-100)) {
		tmp = z * (x_m * (-1.0 + y));
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2d-62)) .or. (.not. (z <= 5.5d-100))) then
        tmp = z * (x_m * ((-1.0d0) + y))
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -2e-62) || !(z <= 5.5e-100)) {
		tmp = z * (x_m * (-1.0 + y));
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (z <= -2e-62) or not (z <= 5.5e-100):
		tmp = z * (x_m * (-1.0 + y))
	else:
		tmp = x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((z <= -2e-62) || !(z <= 5.5e-100))
		tmp = Float64(z * Float64(x_m * Float64(-1.0 + y)));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((z <= -2e-62) || ~((z <= 5.5e-100)))
		tmp = z * (x_m * (-1.0 + y));
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[z, -2e-62], N[Not[LessEqual[z, 5.5e-100]], $MachinePrecision]], N[(z * N[(x$95$m * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e-62 or 5.50000000000000011e-100 < z

   1. Initial program 90.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 84.0%

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

      1. *-commutative 84.0%

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

      2. associate-*l* 93.4%

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

      3. sub-neg 93.4%

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

      4. metadata-eval 93.4%

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

   5. Simplified 93.4%

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

   if -2.0000000000000001e-62 < z < 5.50000000000000011e-100

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 82.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-62} \lor \neg \left(z \leq 5.5 \cdot 10^{-100}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x\_m \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m + z \cdot \left(x\_m \cdot y\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= z -1.0) (not (<= z 1.0)))
    (* z (* x_m (+ -1.0 y)))
    (+ x_m (* z (* x_m y))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = z * (x_m * (-1.0 + y));
	} else {
		tmp = x_m + (z * (x_m * y));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * (x_m * ((-1.0d0) + y))
    else
        tmp = x_m + (z * (x_m * y))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = z * (x_m * (-1.0 + y));
	} else {
		tmp = x_m + (z * (x_m * y));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.0):
		tmp = z * (x_m * (-1.0 + y))
	else:
		tmp = x_m + (z * (x_m * y))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.0))
		tmp = Float64(z * Float64(x_m * Float64(-1.0 + y)));
	else
		tmp = Float64(x_m + Float64(z * Float64(x_m * y)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.0)))
		tmp = z * (x_m * (-1.0 + y));
	else
		tmp = x_m + (z * (x_m * y));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * N[(x$95$m * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m + N[(z * N[(x$95$m * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 88.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 87.5%

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

      1. *-commutative 87.5%

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

      2. associate-*l* 98.9%

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

      3. sub-neg 98.9%

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

      4. metadata-eval 98.9%

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

   5. Simplified 98.9%

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

   if -1 < z < 1

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 99.9%

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

   4. Taylor expanded in y around 0 99.9%

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

      1. neg-mul-1 99.9%

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

      2. distribute-lft-neg-in 99.9%

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

      3. mul-1-neg 99.9%

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

      4. associate-*r* 91.4%

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

      5. distribute-rgt-out 91.4%

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

      6. *-commutative 91.4%

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

      7. distribute-lft-in 91.4%

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

   6. Simplified 91.4%

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

   7. Taylor expanded in y around inf 90.4%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x\_m \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m + x\_m \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= z -1.0) (not (<= z 1.0)))
    (* z (* x_m (+ -1.0 y)))
    (+ x_m (* x_m (* z y))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = z * (x_m * (-1.0 + y));
	} else {
		tmp = x_m + (x_m * (z * y));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * (x_m * ((-1.0d0) + y))
    else
        tmp = x_m + (x_m * (z * y))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = z * (x_m * (-1.0 + y));
	} else {
		tmp = x_m + (x_m * (z * y));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.0):
		tmp = z * (x_m * (-1.0 + y))
	else:
		tmp = x_m + (x_m * (z * y))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.0))
		tmp = Float64(z * Float64(x_m * Float64(-1.0 + y)));
	else
		tmp = Float64(x_m + Float64(x_m * Float64(z * y)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.0)))
		tmp = z * (x_m * (-1.0 + y));
	else
		tmp = x_m + (x_m * (z * y));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * N[(x$95$m * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m + N[(x$95$m * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 88.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 87.5%

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

      1. *-commutative 87.5%

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

      2. associate-*l* 98.9%

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

      3. sub-neg 98.9%

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

      4. metadata-eval 98.9%

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

   5. Simplified 98.9%

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

   if -1 < z < 1

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. distribute-lft-neg-out 98.9%

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

      3. *-commutative 98.9%

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

   5. Simplified 98.9%

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

      1. *-commutative 98.9%

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

      2. cancel-sign-sub 98.9%

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

      3. *-commutative 98.9%

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

      4. distribute-rgt-in 98.9%

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

      5. *-un-lft-identity 98.9%

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

   7. Applied egg-rr 98.9%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+91} \lor \neg \left(y \leq 4.3 \cdot 10^{+111}\right):\\ \;\;\;\;x\_m \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= y -1.9e+91) (not (<= y 4.3e+111)))
    (* x_m (* z y))
    (* x_m (- 1.0 z)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -1.9e+91) || !(y <= 4.3e+111)) {
		tmp = x_m * (z * y);
	} else {
		tmp = x_m * (1.0 - z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.9d+91)) .or. (.not. (y <= 4.3d+111))) then
        tmp = x_m * (z * y)
    else
        tmp = x_m * (1.0d0 - z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -1.9e+91) || !(y <= 4.3e+111)) {
		tmp = x_m * (z * y);
	} else {
		tmp = x_m * (1.0 - z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (y <= -1.9e+91) or not (y <= 4.3e+111):
		tmp = x_m * (z * y)
	else:
		tmp = x_m * (1.0 - z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((y <= -1.9e+91) || !(y <= 4.3e+111))
		tmp = Float64(x_m * Float64(z * y));
	else
		tmp = Float64(x_m * Float64(1.0 - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((y <= -1.9e+91) || ~((y <= 4.3e+111)))
		tmp = x_m * (z * y);
	else
		tmp = x_m * (1.0 - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[y, -1.9e+91], N[Not[LessEqual[y, 4.3e+111]], $MachinePrecision]], N[(x$95$m * N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.8999999999999999e91 or 4.29999999999999993e111 < y

   1. Initial program 87.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 74.1%

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

      1. *-commutative 74.1%

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

   5. Simplified 74.1%

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

   if -1.8999999999999999e91 < y < 4.29999999999999993e111

   1. Initial program 98.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 87.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+91} \lor \neg \left(y \leq 4.3 \cdot 10^{+111}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+91} \lor \neg \left(y \leq 4.8 \cdot 10^{+36}\right):\\ \;\;\;\;z \cdot \left(x\_m \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= y -1.45e+91) (not (<= y 4.8e+36)))
    (* z (* x_m y))
    (* x_m (- 1.0 z)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -1.45e+91) || !(y <= 4.8e+36)) {
		tmp = z * (x_m * y);
	} else {
		tmp = x_m * (1.0 - z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.45d+91)) .or. (.not. (y <= 4.8d+36))) then
        tmp = z * (x_m * y)
    else
        tmp = x_m * (1.0d0 - z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y <= -1.45e+91) || !(y <= 4.8e+36)) {
		tmp = z * (x_m * y);
	} else {
		tmp = x_m * (1.0 - z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (y <= -1.45e+91) or not (y <= 4.8e+36):
		tmp = z * (x_m * y)
	else:
		tmp = x_m * (1.0 - z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((y <= -1.45e+91) || !(y <= 4.8e+36))
		tmp = Float64(z * Float64(x_m * y));
	else
		tmp = Float64(x_m * Float64(1.0 - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((y <= -1.45e+91) || ~((y <= 4.8e+36)))
		tmp = z * (x_m * y);
	else
		tmp = x_m * (1.0 - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[y, -1.45e+91], N[Not[LessEqual[y, 4.8e+36]], $MachinePrecision]], N[(z * N[(x$95$m * y), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.45000000000000007e91 or 4.79999999999999985e36 < y

   1. Initial program 87.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 68.5%

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

      1. *-commutative 68.5%

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

      2. associate-*l* 76.1%

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

      3. sub-neg 76.1%

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

      4. metadata-eval 76.1%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in y around inf 76.1%

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

   if -1.45000000000000007e91 < y < 4.79999999999999985e36

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 93.2%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+91} \lor \neg \left(y \leq 4.8 \cdot 10^{+36}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x\_m \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (or (<= z -1.0) (not (<= z 1.0))) (* x_m (- z)) x_m)))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = x_m * -z;
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x_m * -z
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = x_m * -z;
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.0):
		tmp = x_m * -z
	else:
		tmp = x_m
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.0))
		tmp = Float64(x_m * Float64(-z));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.0)))
		tmp = x_m * -z;
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x$95$m * (-z)), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 88.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 87.5%

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

      1. *-commutative 87.5%

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

      2. associate-*l* 98.9%

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

      3. sub-neg 98.9%

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

      4. metadata-eval 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in y around 0 52.6%

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

      1. associate-*r* 52.6%

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

      2. mul-1-neg 52.6%

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

   8. Simplified 52.6%

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

   if -1 < z < 1

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 72.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 2500000000000:\\ \;\;\;\;x\_m \cdot \left(1 + z \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x\_m \cdot \left(-1 + y\right)\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= z 2500000000000.0)
    (* x_m (+ 1.0 (* z (+ -1.0 y))))
    (* z (* x_m (+ -1.0 y))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= 2500000000000.0) {
		tmp = x_m * (1.0 + (z * (-1.0 + y)));
	} else {
		tmp = z * (x_m * (-1.0 + y));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 2500000000000.0d0) then
        tmp = x_m * (1.0d0 + (z * ((-1.0d0) + y)))
    else
        tmp = z * (x_m * ((-1.0d0) + y))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= 2500000000000.0) {
		tmp = x_m * (1.0 + (z * (-1.0 + y)));
	} else {
		tmp = z * (x_m * (-1.0 + y));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if z <= 2500000000000.0:
		tmp = x_m * (1.0 + (z * (-1.0 + y)))
	else:
		tmp = z * (x_m * (-1.0 + y))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (z <= 2500000000000.0)
		tmp = Float64(x_m * Float64(1.0 + Float64(z * Float64(-1.0 + y))));
	else
		tmp = Float64(z * Float64(x_m * Float64(-1.0 + y)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (z <= 2500000000000.0)
		tmp = x_m * (1.0 + (z * (-1.0 + y)));
	else
		tmp = z * (x_m * (-1.0 + y));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[z, 2500000000000.0], N[(x$95$m * N[(1.0 + N[(z * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x$95$m * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < 2.5e12

   1. Initial program 97.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   if 2.5e12 < z

   1. Initial program 85.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-*l* 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   5. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(y + -1\right) \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2500000000000:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 2500000000000:\\ \;\;\;\;x\_m + x\_m \cdot \left(z \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x\_m \cdot \left(-1 + y\right)\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= z 2500000000000.0)
    (+ x_m (* x_m (* z (+ -1.0 y))))
    (* z (* x_m (+ -1.0 y))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= 2500000000000.0) {
		tmp = x_m + (x_m * (z * (-1.0 + y)));
	} else {
		tmp = z * (x_m * (-1.0 + y));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 2500000000000.0d0) then
        tmp = x_m + (x_m * (z * ((-1.0d0) + y)))
    else
        tmp = z * (x_m * ((-1.0d0) + y))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (z <= 2500000000000.0) {
		tmp = x_m + (x_m * (z * (-1.0 + y)));
	} else {
		tmp = z * (x_m * (-1.0 + y));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if z <= 2500000000000.0:
		tmp = x_m + (x_m * (z * (-1.0 + y)))
	else:
		tmp = z * (x_m * (-1.0 + y))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (z <= 2500000000000.0)
		tmp = Float64(x_m + Float64(x_m * Float64(z * Float64(-1.0 + y))));
	else
		tmp = Float64(z * Float64(x_m * Float64(-1.0 + y)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (z <= 2500000000000.0)
		tmp = x_m + (x_m * (z * (-1.0 + y)));
	else
		tmp = z * (x_m * (-1.0 + y));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[z, 2500000000000.0], N[(x$95$m + N[(x$95$m * N[(z * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x$95$m * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < 2.5e12

   1. Initial program 97.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 97.8%

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

   if 2.5e12 < z

   1. Initial program 85.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-*l* 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   5. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(y + -1\right) \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2500000000000:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.6% accurate, 9.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot x\_m \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s x_m))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	return x_s * x_m;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x_s * x_m
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	return x_s * x_m;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	return x_s * x_m

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	return Float64(x_s * x_m)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z)
	tmp = x_s * x_m;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * x$95$m), $MachinePrecision]

Derivation

1. Initial program 94.4%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0 39.0%

   \[\leadsto \color{blue}{x} \]

4. Final simplification 39.0%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ t_1 := x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{if}\;t\_0 < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* (- 1.0 y) z))))
        (t_1 (+ x (* (- 1.0 y) (* (- z) x)))))
   (if (< t_0 -1.618195973607049e+50)
     t_1
     (if (< t_0 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (1.0d0 - ((1.0d0 - y) * z))
    t_1 = x + ((1.0d0 - y) * (-z * x))
    if (t_0 < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (t_0 < 3.892237649663903d+134) then
        tmp = ((x * y) * z) - ((x * z) - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - ((1.0 - y) * z))
	t_1 = x + ((1.0 - y) * (-z * x))
	tmp = 0
	if t_0 < -1.618195973607049e+50:
		tmp = t_1
	elif t_0 < 3.892237649663903e+134:
		tmp = ((x * y) * z) - ((x * z) - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
	t_1 = Float64(x + Float64(Float64(1.0 - y) * Float64(Float64(-z) * x)))
	tmp = 0.0
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = Float64(Float64(Float64(x * y) * z) - Float64(Float64(x * z) - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - ((1.0 - y) * z));
	t_1 = x + ((1.0 - y) * (-z * x));
	tmp = 0.0;
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = ((x * y) * z) - ((x * z) - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(N[(1.0 - y), $MachinePrecision] * N[((-z) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$0, -1.618195973607049e+50], t$95$1, If[Less[t$95$0, 3.892237649663903e+134], N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] - N[(N[(x * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024048 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :alt
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

  (* x (- 1.0 (* (- 1.0 y) z))))