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

Percentage Accurate: 95.8% → 98.9%

Time: 5.1s

Alternatives: 10

Speedup: 0.8×

• 21.7% 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: 95.8% 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: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 0.0045:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05)
   (* z (* x (+ y -1.0)))
   (if (<= z 0.0045) (+ x (* x (* y z))) (* z (- (* y x) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 0.0045) {
		tmp = x + (x * (y * z));
	} else {
		tmp = z * ((y * x) - 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 <= (-1.05d0)) then
        tmp = z * (x * (y + (-1.0d0)))
    else if (z <= 0.0045d0) then
        tmp = x + (x * (y * z))
    else
        tmp = z * ((y * x) - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 0.0045) {
		tmp = x + (x * (y * z));
	} else {
		tmp = z * ((y * x) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.05:
		tmp = z * (x * (y + -1.0))
	elif z <= 0.0045:
		tmp = x + (x * (y * z))
	else:
		tmp = z * ((y * x) - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.05)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	elseif (z <= 0.0045)
		tmp = Float64(x + Float64(x * Float64(y * z)));
	else
		tmp = Float64(z * Float64(Float64(y * x) - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.05)
		tmp = z * (x * (y + -1.0));
	elseif (z <= 0.0045)
		tmp = x + (x * (y * z));
	else
		tmp = z * ((y * x) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.05], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0045], N[(x + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000004

   1. Initial program 88.6%

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

   2. Taylor expanded in z around inf 97.1%

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

   if -1.05000000000000004 < z < 0.00449999999999999966

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. distribute-lft-neg-out 99.5%

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

      3. *-commutative 99.5%

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

   4. Simplified 99.5%

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

      1. sub-neg 99.5%

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

      2. distribute-rgt-neg-out 99.5%

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

      3. remove-double-neg 99.5%

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

      4. distribute-lft-in 99.5%

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

      5. *-commutative 99.5%

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

      6. *-un-lft-identity 99.5%

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

      7. *-commutative 99.5%

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

   6. Applied egg-rr 99.5%

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

   if 0.00449999999999999966 < z

   1. Initial program 94.5%

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

   2. Taylor expanded in z around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

      4. distribute-rgt-in 99.9%

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

      5. neg-mul-1 99.9%

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

      6. unsub-neg 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 0.0045:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \]

Alternative 2: 98.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.8%

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

   1. distribute-rgt-out-- 95.8%

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

   2. *-lft-identity 95.8%

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

   3. cancel-sign-sub-inv 95.8%

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

   4. +-commutative 95.8%

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

   5. distribute-lft-neg-in 95.8%

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

   6. associate-*l* 98.3%

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

   7. fma-def 98.3%

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

   8. neg-sub0 98.3%

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

   9. associate--r- 98.3%

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

   10. metadata-eval 98.3%

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

   11. +-commutative 98.3%

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

   12. *-commutative 98.3%

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

3. Simplified 98.3%

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

4. Final simplification 98.3%

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

Alternative 3: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{if}\;t_0 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 1.0 (* z (+ y -1.0))))))
   (if (<= t_0 2e+304) t_0 (* z (* x (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 + (z * (y + -1.0)));
	double tmp;
	if (t_0 <= 2e+304) {
		tmp = t_0;
	} else {
		tmp = z * (x * (y + -1.0));
	}
	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) :: tmp
    t_0 = x * (1.0d0 + (z * (y + (-1.0d0))))
    if (t_0 <= 2d+304) then
        tmp = t_0
    else
        tmp = z * (x * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 + (z * (y + -1.0)));
	double tmp;
	if (t_0 <= 2e+304) {
		tmp = t_0;
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 + (z * (y + -1.0)))
	tmp = 0
	if t_0 <= 2e+304:
		tmp = t_0
	else:
		tmp = z * (x * (y + -1.0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))))
	tmp = 0.0
	if (t_0 <= 2e+304)
		tmp = t_0;
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 + (z * (y + -1.0)));
	tmp = 0.0;
	if (t_0 <= 2e+304)
		tmp = t_0;
	else
		tmp = z * (x * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 2e+304], t$95$0, N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z))) < 1.9999999999999999e304

   1. Initial program 98.6%

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

   if 1.9999999999999999e304 < (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z)))

   1. Initial program 77.2%

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

   2. Taylor expanded in z around inf 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 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right) \leq 2 \cdot 10^{+304}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 4: 64.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{-60}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+60} \lor \neg \left(z \leq 1.6 \cdot 10^{+171}\right) \land z \leq 1.12 \cdot 10^{+219}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x z))))
   (if (<= z -2.35e-60)
     t_0
     (if (<= z 9e-74)
       x
       (if (or (<= z 2.1e+60) (and (not (<= z 1.6e+171)) (<= z 1.12e+219)))
         t_0
         (* x (- z)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x * z);
	double tmp;
	if (z <= -2.35e-60) {
		tmp = t_0;
	} else if (z <= 9e-74) {
		tmp = x;
	} else if ((z <= 2.1e+60) || (!(z <= 1.6e+171) && (z <= 1.12e+219))) {
		tmp = t_0;
	} else {
		tmp = x * -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) :: t_0
    real(8) :: tmp
    t_0 = y * (x * z)
    if (z <= (-2.35d-60)) then
        tmp = t_0
    else if (z <= 9d-74) then
        tmp = x
    else if ((z <= 2.1d+60) .or. (.not. (z <= 1.6d+171)) .and. (z <= 1.12d+219)) then
        tmp = t_0
    else
        tmp = x * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x * z);
	double tmp;
	if (z <= -2.35e-60) {
		tmp = t_0;
	} else if (z <= 9e-74) {
		tmp = x;
	} else if ((z <= 2.1e+60) || (!(z <= 1.6e+171) && (z <= 1.12e+219))) {
		tmp = t_0;
	} else {
		tmp = x * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x * z)
	tmp = 0
	if z <= -2.35e-60:
		tmp = t_0
	elif z <= 9e-74:
		tmp = x
	elif (z <= 2.1e+60) or (not (z <= 1.6e+171) and (z <= 1.12e+219)):
		tmp = t_0
	else:
		tmp = x * -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (z <= -2.35e-60)
		tmp = t_0;
	elseif (z <= 9e-74)
		tmp = x;
	elseif ((z <= 2.1e+60) || (!(z <= 1.6e+171) && (z <= 1.12e+219)))
		tmp = t_0;
	else
		tmp = Float64(x * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x * z);
	tmp = 0.0;
	if (z <= -2.35e-60)
		tmp = t_0;
	elseif (z <= 9e-74)
		tmp = x;
	elseif ((z <= 2.1e+60) || (~((z <= 1.6e+171)) && (z <= 1.12e+219)))
		tmp = t_0;
	else
		tmp = x * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.35e-60], t$95$0, If[LessEqual[z, 9e-74], x, If[Or[LessEqual[z, 2.1e+60], And[N[Not[LessEqual[z, 1.6e+171]], $MachinePrecision], LessEqual[z, 1.12e+219]]], t$95$0, N[(x * (-z)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.35e-60 or 8.9999999999999998e-74 < z < 2.1000000000000001e60 or 1.60000000000000006e171 < z < 1.1199999999999999e219

   1. Initial program 91.3%

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

   2. Taylor expanded in y around inf 64.0%

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

   if -2.35e-60 < z < 8.9999999999999998e-74

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 81.8%

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

   if 2.1000000000000001e60 < z < 1.60000000000000006e171 or 1.1199999999999999e219 < z

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. distribute-rgt-in 99.9%

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

      5. neg-mul-1 99.9%

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

      6. unsub-neg 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. distribute-rgt-neg-out 67.8%

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

   7. Simplified 67.8%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+60} \lor \neg \left(z \leq 1.6 \cdot 10^{+171}\right) \land z \leq 1.12 \cdot 10^{+219}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 5: 63.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{-60}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+60}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+171} \lor \neg \left(z \leq 6 \cdot 10^{+221}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x z))))
   (if (<= z -2.05e-60)
     t_0
     (if (<= z 1.35e-76)
       x
       (if (<= z 3.15e+60)
         t_0
         (if (or (<= z 1.15e+171) (not (<= z 6e+221)))
           (* x (- z))
           (* z (* y x))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x * z);
	double tmp;
	if (z <= -2.05e-60) {
		tmp = t_0;
	} else if (z <= 1.35e-76) {
		tmp = x;
	} else if (z <= 3.15e+60) {
		tmp = t_0;
	} else if ((z <= 1.15e+171) || !(z <= 6e+221)) {
		tmp = x * -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) :: t_0
    real(8) :: tmp
    t_0 = y * (x * z)
    if (z <= (-2.05d-60)) then
        tmp = t_0
    else if (z <= 1.35d-76) then
        tmp = x
    else if (z <= 3.15d+60) then
        tmp = t_0
    else if ((z <= 1.15d+171) .or. (.not. (z <= 6d+221))) then
        tmp = x * -z
    else
        tmp = z * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x * z);
	double tmp;
	if (z <= -2.05e-60) {
		tmp = t_0;
	} else if (z <= 1.35e-76) {
		tmp = x;
	} else if (z <= 3.15e+60) {
		tmp = t_0;
	} else if ((z <= 1.15e+171) || !(z <= 6e+221)) {
		tmp = x * -z;
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x * z)
	tmp = 0
	if z <= -2.05e-60:
		tmp = t_0
	elif z <= 1.35e-76:
		tmp = x
	elif z <= 3.15e+60:
		tmp = t_0
	elif (z <= 1.15e+171) or not (z <= 6e+221):
		tmp = x * -z
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (z <= -2.05e-60)
		tmp = t_0;
	elseif (z <= 1.35e-76)
		tmp = x;
	elseif (z <= 3.15e+60)
		tmp = t_0;
	elseif ((z <= 1.15e+171) || !(z <= 6e+221))
		tmp = Float64(x * Float64(-z));
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x * z);
	tmp = 0.0;
	if (z <= -2.05e-60)
		tmp = t_0;
	elseif (z <= 1.35e-76)
		tmp = x;
	elseif (z <= 3.15e+60)
		tmp = t_0;
	elseif ((z <= 1.15e+171) || ~((z <= 6e+221)))
		tmp = x * -z;
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e-60], t$95$0, If[LessEqual[z, 1.35e-76], x, If[LessEqual[z, 3.15e+60], t$95$0, If[Or[LessEqual[z, 1.15e+171], N[Not[LessEqual[z, 6e+221]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.05000000000000006e-60 or 1.35e-76 < z < 3.1500000000000002e60

   1. Initial program 93.2%

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

   2. Taylor expanded in y around inf 61.6%

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

   if -2.05000000000000006e-60 < z < 1.35e-76

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 81.8%

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

   if 3.1500000000000002e60 < z < 1.15000000000000009e171 or 6.0000000000000003e221 < z

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. distribute-rgt-in 99.9%

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

      5. neg-mul-1 99.9%

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

      6. unsub-neg 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. distribute-rgt-neg-out 67.8%

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

   7. Simplified 67.8%

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

   if 1.15000000000000009e171 < z < 6.0000000000000003e221

   1. Initial program 73.9%

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

   2. Taylor expanded in y around inf 85.4%

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

      1. associate-*r* 59.6%

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

      2. *-commutative 59.6%

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

      3. associate-*l* 85.5%

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

   4. Simplified 85.5%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+171} \lor \neg \left(z \leq 6 \cdot 10^{+221}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 6: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -105000 \lor \neg \left(y \leq 1.02 \cdot 10^{+33}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -105000.0) (not (<= y 1.02e+33)))
   (* y (* x z))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -105000.0) || !(y <= 1.02e+33)) {
		tmp = y * (x * 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 <= (-105000.0d0)) .or. (.not. (y <= 1.02d+33))) then
        tmp = y * (x * 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 <= -105000.0) || !(y <= 1.02e+33)) {
		tmp = y * (x * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -105000.0) or not (y <= 1.02e+33):
		tmp = y * (x * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -105000.0) || !(y <= 1.02e+33))
		tmp = Float64(y * Float64(x * 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 <= -105000.0) || ~((y <= 1.02e+33)))
		tmp = y * (x * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -105000.0], N[Not[LessEqual[y, 1.02e+33]], $MachinePrecision]], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -105000 or 1.02000000000000001e33 < y

   1. Initial program 90.7%

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

   2. Taylor expanded in y around inf 75.2%

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

   if -105000 < y < 1.02000000000000001e33

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 95.1%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -105000 \lor \neg \left(y \leq 1.02 \cdot 10^{+33}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 7: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e-9)
   (* z (* x (+ y -1.0)))
   (if (<= y 2.7e+34) (* x (- 1.0 z)) (* y (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e-9) {
		tmp = z * (x * (y + -1.0));
	} else if (y <= 2.7e+34) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (x * 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 <= (-1.4d-9)) then
        tmp = z * (x * (y + (-1.0d0)))
    else if (y <= 2.7d+34) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e-9) {
		tmp = z * (x * (y + -1.0));
	} else if (y <= 2.7e+34) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e-9:
		tmp = z * (x * (y + -1.0))
	elif y <= 2.7e+34:
		tmp = x * (1.0 - z)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e-9)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	elseif (y <= 2.7e+34)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.4e-9)
		tmp = z * (x * (y + -1.0));
	elseif (y <= 2.7e+34)
		tmp = x * (1.0 - z);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e-9], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+34], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.39999999999999992e-9

   1. Initial program 94.0%

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

   2. Taylor expanded in z around inf 70.0%

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

   if -1.39999999999999992e-9 < y < 2.7e34

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 95.3%

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

   if 2.7e34 < y

   1. Initial program 86.8%

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

   2. Taylor expanded in y around inf 82.7%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 8: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e-9)
   (* z (- (* y x) x))
   (if (<= y 5.6e+34) (* x (- 1.0 z)) (* y (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e-9) {
		tmp = z * ((y * x) - x);
	} else if (y <= 5.6e+34) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (x * 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 <= (-1.4d-9)) then
        tmp = z * ((y * x) - x)
    else if (y <= 5.6d+34) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e-9) {
		tmp = z * ((y * x) - x);
	} else if (y <= 5.6e+34) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e-9:
		tmp = z * ((y * x) - x)
	elif y <= 5.6e+34:
		tmp = x * (1.0 - z)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e-9)
		tmp = Float64(z * Float64(Float64(y * x) - x));
	elseif (y <= 5.6e+34)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.4e-9)
		tmp = z * ((y * x) - x);
	elseif (y <= 5.6e+34)
		tmp = x * (1.0 - z);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e-9], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+34], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.39999999999999992e-9

   1. Initial program 94.0%

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

   2. Taylor expanded in z around inf 70.0%

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

      1. *-commutative 70.0%

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

      2. sub-neg 70.0%

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

      3. metadata-eval 70.0%

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

      4. distribute-rgt-in 70.0%

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

      5. neg-mul-1 70.0%

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

      6. unsub-neg 70.0%

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

   4. Simplified 70.0%

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

   if -1.39999999999999992e-9 < y < 5.60000000000000016e34

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 95.3%

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

   if 5.60000000000000016e34 < y

   1. Initial program 86.8%

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

   2. Taylor expanded in y around inf 82.7%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 9: 64.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.0045\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.0045))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.0045)) {
		tmp = x * -z;
	} 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 <= (-1.0d0)) .or. (.not. (z <= 0.0045d0))) then
        tmp = x * -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.0045)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 0.0045):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 0.0045))
		tmp = Float64(x * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 0.0045)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 0.0045]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 0.00449999999999999966 < z

   1. Initial program 91.8%

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

   2. Taylor expanded in z around inf 98.6%

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

      1. *-commutative 98.6%

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

      2. sub-neg 98.6%

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

      3. metadata-eval 98.6%

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

      4. distribute-rgt-in 98.6%

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

      5. neg-mul-1 98.6%

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

      6. unsub-neg 98.6%

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

   4. Simplified 98.6%

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

   5. Taylor expanded in y around 0 53.0%

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

      1. mul-1-neg 53.0%

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

      2. distribute-rgt-neg-out 53.0%

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

   7. Simplified 53.0%

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

   if -1 < z < 0.00449999999999999966

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 72.6%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.0045\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 37.8% 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 95.8%

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

2. Taylor expanded in z around 0 37.3%

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

3. Final simplification 37.3%

   \[\leadsto x \]

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 2023195 
(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))))