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

Percentage Accurate: 95.9% → 97.6%

Time: 6.5s

Alternatives: 11

Speedup: 0.6×

• 21.4% 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: 95.9% 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: 97.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq 10^{+189}:\\ \;\;\;\;x \cdot \left(1 - t_0\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y + -1, z \cdot x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)))
   (if (<= t_0 1e+189) (* x (- 1.0 t_0)) (fma (+ y -1.0) (* z x) x))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= 1e+189) {
		tmp = x * (1.0 - t_0);
	} else {
		tmp = fma((y + -1.0), (z * x), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (t_0 <= 1e+189)
		tmp = Float64(x * Float64(1.0 - t_0));
	else
		tmp = fma(Float64(y + -1.0), Float64(z * x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, 1e+189], N[(x * N[(1.0 - t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(z * x), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 1 y) z) < 1e189

   1. Initial program 98.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   if 1e189 < (*.f64 (-.f64 1 y) z)

   1. Initial program 88.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 88.8%

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

      2. *-lft-identity 88.8%

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

      3. cancel-sign-sub-inv 88.8%

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

      4. +-commutative 88.8%

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

      5. distribute-lft-neg-in 88.8%

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

      6. associate-*l* 99.9%

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

      7. fma-def 99.9%

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

      8. neg-sub0 99.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \left(1 - y\right)}, z \cdot x, x\right) \]

      9. associate--r- 99.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - 1\right) + y}, z \cdot x, x\right) \]

      10. metadata-eval 99.9%

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

      11. +-commutative 99.9%

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

      12. *-commutative 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 10^{+189}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y + -1, z \cdot x, x\right)\\ \end{array} \]

Alternative 2: 97.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq 4 \cdot 10^{+306}:\\ \;\;\;\;x \cdot \left(1 - t_0\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)))
   (if (<= t_0 4e+306) (* x (- 1.0 t_0)) (* y (* z x)))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= 4e+306) {
		tmp = x * (1.0 - t_0);
	} else {
		tmp = y * (z * x);
	}
	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) :: tmp
    t_0 = (1.0d0 - y) * z
    if (t_0 <= 4d+306) then
        tmp = x * (1.0d0 - t_0)
    else
        tmp = y * (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= 4e+306) {
		tmp = x * (1.0 - t_0);
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - y) * z
	tmp = 0
	if t_0 <= 4e+306:
		tmp = x * (1.0 - t_0)
	else:
		tmp = y * (z * x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (t_0 <= 4e+306)
		tmp = Float64(x * Float64(1.0 - t_0));
	else
		tmp = Float64(y * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * z;
	tmp = 0.0;
	if (t_0 <= 4e+306)
		tmp = x * (1.0 - t_0);
	else
		tmp = y * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, 4e+306], N[(x * N[(1.0 - t$95$0), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 1 y) z) < 4.00000000000000007e306

   1. Initial program 98.7%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   if 4.00000000000000007e306 < (*.f64 (-.f64 1 y) z)

   1. Initial program 70.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 100.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 4 \cdot 10^{+306}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 3: 97.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 4 \cdot 10^{+306}:\\ \;\;\;\;x \cdot \left(\left(1 + y \cdot z\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) 4e+306) (* x (- (+ 1.0 (* y z)) z)) (* y (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= 4e+306) {
		tmp = x * ((1.0 + (y * z)) - z);
	} else {
		tmp = y * (z * x);
	}
	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) :: tmp
    if (((1.0d0 - y) * z) <= 4d+306) then
        tmp = x * ((1.0d0 + (y * z)) - z)
    else
        tmp = y * (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= 4e+306) {
		tmp = x * ((1.0 + (y * z)) - z);
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= 4e+306:
		tmp = x * ((1.0 + (y * z)) - z)
	else:
		tmp = y * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= 4e+306)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(y * z)) - z));
	else
		tmp = Float64(y * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= 4e+306)
		tmp = x * ((1.0 + (y * z)) - z);
	else
		tmp = y * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], 4e+306], N[(x * N[(N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 1 y) z) < 4.00000000000000007e306

   1. Initial program 98.7%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 98.7%

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

   if 4.00000000000000007e306 < (*.f64 (-.f64 1 y) z)

   1. Initial program 70.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 100.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 4 \cdot 10^{+306}:\\ \;\;\;\;x \cdot \left(\left(1 + y \cdot z\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 4: 97.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(1 - t_0\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(\left(1 - y\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)))
   (if (<= t_0 5e+84) (* x (- 1.0 t_0)) (- x (* z (* (- 1.0 y) x))))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= 5e+84) {
		tmp = x * (1.0 - t_0);
	} else {
		tmp = x - (z * ((1.0 - y) * x));
	}
	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) :: tmp
    t_0 = (1.0d0 - y) * z
    if (t_0 <= 5d+84) then
        tmp = x * (1.0d0 - t_0)
    else
        tmp = x - (z * ((1.0d0 - y) * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= 5e+84) {
		tmp = x * (1.0 - t_0);
	} else {
		tmp = x - (z * ((1.0 - y) * x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - y) * z
	tmp = 0
	if t_0 <= 5e+84:
		tmp = x * (1.0 - t_0)
	else:
		tmp = x - (z * ((1.0 - y) * x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (t_0 <= 5e+84)
		tmp = Float64(x * Float64(1.0 - t_0));
	else
		tmp = Float64(x - Float64(z * Float64(Float64(1.0 - y) * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * z;
	tmp = 0.0;
	if (t_0 <= 5e+84)
		tmp = x * (1.0 - t_0);
	else
		tmp = x - (z * ((1.0 - y) * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, 5e+84], N[(x * N[(1.0 - t$95$0), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 1 y) z) < 5.0000000000000001e84

   1. Initial program 98.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   if 5.0000000000000001e84 < (*.f64 (-.f64 1 y) z)

   1. Initial program 93.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 93.5%

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

      2. *-lft-identity 93.5%

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

      3. cancel-sign-sub-inv 93.5%

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

      4. +-commutative 93.5%

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

      5. distribute-lft-neg-in 93.5%

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

      6. associate-*l* 98.6%

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

      7. fma-def 98.6%

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

      8. neg-sub0 98.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \left(1 - y\right)}, z \cdot x, x\right) \]

      9. associate--r- 98.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - 1\right) + y}, z \cdot x, x\right) \]

      10. metadata-eval 98.6%

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

      11. +-commutative 98.6%

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

      12. *-commutative 98.6%

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

   3. Simplified 98.6%

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

      1. fma-udef 98.6%

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

      2. associate-*r* 99.8%

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

   5. Applied egg-rr 99.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 5 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(\left(1 - y\right) \cdot x\right)\\ \end{array} \]

Alternative 5: 63.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+124}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* x (* y z))))
   (if (<= z -7.8e+124)
     t_0
     (if (<= z -1.6e-84)
       t_1
       (if (<= z 1.22e-51) x (if (<= z 1.15e+82) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -7.8e+124) {
		tmp = t_0;
	} else if (z <= -1.6e-84) {
		tmp = t_1;
	} else if (z <= 1.22e-51) {
		tmp = x;
	} else if (z <= 1.15e+82) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	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 = z * -x
    t_1 = x * (y * z)
    if (z <= (-7.8d+124)) then
        tmp = t_0
    else if (z <= (-1.6d-84)) then
        tmp = t_1
    else if (z <= 1.22d-51) then
        tmp = x
    else if (z <= 1.15d+82) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -7.8e+124) {
		tmp = t_0;
	} else if (z <= -1.6e-84) {
		tmp = t_1;
	} else if (z <= 1.22e-51) {
		tmp = x;
	} else if (z <= 1.15e+82) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	t_1 = x * (y * z)
	tmp = 0
	if z <= -7.8e+124:
		tmp = t_0
	elif z <= -1.6e-84:
		tmp = t_1
	elif z <= 1.22e-51:
		tmp = x
	elif z <= 1.15e+82:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -7.8e+124)
		tmp = t_0;
	elseif (z <= -1.6e-84)
		tmp = t_1;
	elseif (z <= 1.22e-51)
		tmp = x;
	elseif (z <= 1.15e+82)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	t_1 = x * (y * z);
	tmp = 0.0;
	if (z <= -7.8e+124)
		tmp = t_0;
	elseif (z <= -1.6e-84)
		tmp = t_1;
	elseif (z <= 1.22e-51)
		tmp = x;
	elseif (z <= 1.15e+82)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+124], t$95$0, If[LessEqual[z, -1.6e-84], t$95$1, If[LessEqual[z, 1.22e-51], x, If[LessEqual[z, 1.15e+82], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.8000000000000001e124 or 1.14999999999999994e82 < z

   1. Initial program 91.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 63.7%

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

      1. sub-neg 63.7%

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

      2. +-commutative 63.7%

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

      3. distribute-rgt1-in 63.7%

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

      4. cancel-sign-sub-inv 63.7%

         \[\leadsto \color{blue}{x - z \cdot x} \]

   4. Simplified 63.7%

      \[\leadsto \color{blue}{x - z \cdot x} \]

   5. Taylor expanded in z around inf 63.7%

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

      1. mul-1-neg 63.7%

         \[\leadsto \color{blue}{-z \cdot x} \]

      2. distribute-rgt-neg-in 63.7%

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

   7. Simplified 63.7%

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

   if -7.8000000000000001e124 < z < -1.6e-84 or 1.21999999999999998e-51 < z < 1.14999999999999994e82

   1. Initial program 99.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 61.9%

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

      1. *-commutative 61.9%

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

   4. Simplified 61.9%

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

   if -1.6e-84 < z < 1.21999999999999998e-51

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 81.1%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+124}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 6: 64.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.6e-76)
   (* y (* z x))
   (if (<= z 1.22e-51) x (if (<= z 2.9e+81) (* x (* y z)) (* z (- x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.6e-76) {
		tmp = y * (z * x);
	} else if (z <= 1.22e-51) {
		tmp = x;
	} else if (z <= 2.9e+81) {
		tmp = x * (y * z);
	} else {
		tmp = z * -x;
	}
	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) :: tmp
    if (z <= (-2.6d-76)) then
        tmp = y * (z * x)
    else if (z <= 1.22d-51) then
        tmp = x
    else if (z <= 2.9d+81) then
        tmp = x * (y * z)
    else
        tmp = z * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.6e-76) {
		tmp = y * (z * x);
	} else if (z <= 1.22e-51) {
		tmp = x;
	} else if (z <= 2.9e+81) {
		tmp = x * (y * z);
	} else {
		tmp = z * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.6e-76:
		tmp = y * (z * x)
	elif z <= 1.22e-51:
		tmp = x
	elif z <= 2.9e+81:
		tmp = x * (y * z)
	else:
		tmp = z * -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.6e-76)
		tmp = Float64(y * Float64(z * x));
	elseif (z <= 1.22e-51)
		tmp = x;
	elseif (z <= 2.9e+81)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(z * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.6e-76)
		tmp = y * (z * x);
	elseif (z <= 1.22e-51)
		tmp = x;
	elseif (z <= 2.9e+81)
		tmp = x * (y * z);
	else
		tmp = z * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.6e-76], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e-51], x, If[LessEqual[z, 2.9e+81], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(z * (-x)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6e-76

   1. Initial program 95.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 56.9%

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

   if -2.6e-76 < z < 1.21999999999999998e-51

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 80.3%

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

   if 1.21999999999999998e-51 < z < 2.9e81

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 66.3%

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

      1. *-commutative 66.3%

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

   4. Simplified 66.3%

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

   if 2.9e81 < z

   1. Initial program 92.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 69.5%

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

      1. sub-neg 69.5%

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

      2. +-commutative 69.5%

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

      3. distribute-rgt1-in 69.5%

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

      4. cancel-sign-sub-inv 69.5%

         \[\leadsto \color{blue}{x - z \cdot x} \]

   4. Simplified 69.5%

      \[\leadsto \color{blue}{x - z \cdot x} \]

   5. Taylor expanded in z around inf 69.5%

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

      1. mul-1-neg 69.5%

         \[\leadsto \color{blue}{-z \cdot x} \]

      2. distribute-rgt-neg-in 69.5%

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

   7. Simplified 69.5%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 7: 64.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+82}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.3e-78)
   (* y (* z x))
   (if (<= z 1.15e-51) x (if (<= z 1.65e+82) (* z (* y x)) (* z (- x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.3e-78) {
		tmp = y * (z * x);
	} else if (z <= 1.15e-51) {
		tmp = x;
	} else if (z <= 1.65e+82) {
		tmp = z * (y * x);
	} else {
		tmp = z * -x;
	}
	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) :: tmp
    if (z <= (-2.3d-78)) then
        tmp = y * (z * x)
    else if (z <= 1.15d-51) then
        tmp = x
    else if (z <= 1.65d+82) then
        tmp = z * (y * x)
    else
        tmp = z * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.3e-78) {
		tmp = y * (z * x);
	} else if (z <= 1.15e-51) {
		tmp = x;
	} else if (z <= 1.65e+82) {
		tmp = z * (y * x);
	} else {
		tmp = z * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.3e-78:
		tmp = y * (z * x)
	elif z <= 1.15e-51:
		tmp = x
	elif z <= 1.65e+82:
		tmp = z * (y * x)
	else:
		tmp = z * -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.3e-78)
		tmp = Float64(y * Float64(z * x));
	elseif (z <= 1.15e-51)
		tmp = x;
	elseif (z <= 1.65e+82)
		tmp = Float64(z * Float64(y * x));
	else
		tmp = Float64(z * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.3e-78)
		tmp = y * (z * x);
	elseif (z <= 1.15e-51)
		tmp = x;
	elseif (z <= 1.65e+82)
		tmp = z * (y * x);
	else
		tmp = z * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.3e-78], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-51], x, If[LessEqual[z, 1.65e+82], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(z * (-x)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3000000000000002e-78

   1. Initial program 95.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 56.9%

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

   if -2.3000000000000002e-78 < z < 1.15000000000000001e-51

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 80.3%

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

   if 1.15000000000000001e-51 < z < 1.6499999999999999e82

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 66.3%

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

      1. associate-*r* 66.3%

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

      2. *-commutative 66.3%

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

      3. associate-*l* 66.3%

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

   4. Simplified 66.3%

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

   if 1.6499999999999999e82 < z

   1. Initial program 92.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 69.5%

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

      1. sub-neg 69.5%

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

      2. +-commutative 69.5%

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

      3. distribute-rgt1-in 69.5%

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

      4. cancel-sign-sub-inv 69.5%

         \[\leadsto \color{blue}{x - z \cdot x} \]

   4. Simplified 69.5%

      \[\leadsto \color{blue}{x - z \cdot x} \]

   5. Taylor expanded in z around inf 69.5%

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

      1. mul-1-neg 69.5%

         \[\leadsto \color{blue}{-z \cdot x} \]

      2. distribute-rgt-neg-in 69.5%

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

   7. Simplified 69.5%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+82}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 8: 95.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \lor \neg \left(y \leq 1.35 \cdot 10^{-7}\right):\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.15) (not (<= y 1.35e-7)))
   (+ x (* x (* y z)))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15) || !(y <= 1.35e-7)) {
		tmp = x + (x * (y * z));
	} else {
		tmp = x * (1.0 - z);
	}
	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) :: tmp
    if ((y <= (-1.15d0)) .or. (.not. (y <= 1.35d-7))) then
        tmp = x + (x * (y * z))
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15) || !(y <= 1.35e-7)) {
		tmp = x + (x * (y * z));
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.15) or not (y <= 1.35e-7):
		tmp = x + (x * (y * z))
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.15) || !(y <= 1.35e-7))
		tmp = Float64(x + Float64(x * Float64(y * z)));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.15) || ~((y <= 1.35e-7)))
		tmp = x + (x * (y * z));
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.15], N[Not[LessEqual[y, 1.35e-7]], $MachinePrecision]], N[(x + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1499999999999999 or 1.35000000000000004e-7 < y

   1. Initial program 94.1%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 92.7%

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

      1. mul-1-neg 92.7%

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

      2. distribute-lft-neg-out 92.7%

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

      3. *-commutative 92.7%

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

   4. Simplified 92.7%

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

      1. *-commutative 92.7%

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

      2. cancel-sign-sub 92.7%

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

      3. distribute-lft-in 92.7%

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

      4. *-commutative 92.7%

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

      5. *-un-lft-identity 92.7%

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

   6. Applied egg-rr 92.7%

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

   if -1.1499999999999999 < y < 1.35000000000000004e-7

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 99.4%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \lor \neg \left(y \leq 1.35 \cdot 10^{-7}\right):\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 9: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3e+47)
   (* y (* z x))
   (if (<= y 5.8e+47) (* x (- 1.0 z)) (* z (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3e+47) {
		tmp = y * (z * x);
	} else if (y <= 5.8e+47) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (y * x);
	}
	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) :: tmp
    if (y <= (-3d+47)) then
        tmp = y * (z * x)
    else if (y <= 5.8d+47) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3e+47) {
		tmp = y * (z * x);
	} else if (y <= 5.8e+47) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3e+47:
		tmp = y * (z * x)
	elif y <= 5.8e+47:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3e+47)
		tmp = Float64(y * Float64(z * x));
	elseif (y <= 5.8e+47)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3e+47)
		tmp = y * (z * x);
	elseif (y <= 5.8e+47)
		tmp = x * (1.0 - z);
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3e+47], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+47], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0000000000000001e47

   1. Initial program 94.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 82.3%

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

   if -3.0000000000000001e47 < y < 5.79999999999999961e47

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 94.9%

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

   if 5.79999999999999961e47 < y

   1. Initial program 91.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 73.5%

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

      1. associate-*r* 71.1%

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

      2. *-commutative 71.1%

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

      3. associate-*l* 74.3%

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

   4. Simplified 74.3%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 10: 65.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -14500000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -14500000.0) (not (<= z 1.0))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -14500000.0) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	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) :: tmp
    if ((z <= (-14500000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -14500000.0) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -14500000.0) or not (z <= 1.0):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -14500000.0) || !(z <= 1.0))
		tmp = Float64(z * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -14500000.0) || ~((z <= 1.0)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -14500000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e7 or 1 < z

   1. Initial program 93.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 57.8%

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

      1. sub-neg 57.8%

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

      2. +-commutative 57.8%

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

      3. distribute-rgt1-in 57.8%

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

      4. cancel-sign-sub-inv 57.8%

         \[\leadsto \color{blue}{x - z \cdot x} \]

   4. Simplified 57.8%

      \[\leadsto \color{blue}{x - z \cdot x} \]

   5. Taylor expanded in z around inf 56.8%

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

      1. mul-1-neg 56.8%

         \[\leadsto \color{blue}{-z \cdot x} \]

      2. distribute-rgt-neg-in 56.8%

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

   7. Simplified 56.8%

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

   if -1.45e7 < z < 1

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 67.9%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -14500000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 38.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

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

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
end function

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 97.0%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

2. Taylor expanded in z around 0 35.9%

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

3. Final simplification 35.9%

   \[\leadsto x \]

Developer target: 99.7% accurate, 0.3× 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 2023208 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (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))))