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

Percentage Accurate: 95.7% → 97.7%

Time: 9.0s

Alternatives: 7

Speedup: 0.5×

• 20.9% 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: 95.7% 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: 97.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= -math.inf:
		tmp = y * (z * x)
	else:
		tmp = x + (x * (z * (y + -1.0)))
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 1 y) z) < -inf.0

   1. Initial program 50.0%

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

   3. Taylor expanded in y around inf 78.8%

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

      1. +-commutative 78.8%

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

      2. associate-/l* 89.3%

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

      3. distribute-lft-out 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around inf 99.8%

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

   if -inf.0 < (*.f64 (-.f64 1 y) z)

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. distribute-rgt-neg-out 98.3%

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

      3. +-commutative 98.3%

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

      4. distribute-rgt-neg-out 98.3%

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

      5. *-commutative 98.3%

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

      6. distribute-rgt-neg-in 98.3%

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

      7. fma-define 98.3%

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

      8. neg-sub0 98.3%

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

      9. associate--r- 98.3%

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

      10. metadata-eval 98.3%

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

      11. +-commutative 98.3%

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

   3. Simplified 98.3%

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

      1. fma-undefine 98.3%

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

      2. distribute-rgt-in 98.3%

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

      3. *-un-lft-identity 98.3%

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

   6. Applied egg-rr 98.3%

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

4. Final simplification 98.4%

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

Alternative 2: 94.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -680:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+214}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* x (* y z)))))
   (if (<= y -680.0)
     t_0
     (if (<= y 1.0) (* x (- 1.0 z)) (if (<= y 1.02e+214) t_0 (* y (* z x)))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (x * (y * z));
	double tmp;
	if (y <= -680.0) {
		tmp = t_0;
	} else if (y <= 1.0) {
		tmp = x * (1.0 - z);
	} else if (y <= 1.02e+214) {
		tmp = 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 = x + (x * (y * z))
    if (y <= (-680.0d0)) then
        tmp = t_0
    else if (y <= 1.0d0) then
        tmp = x * (1.0d0 - z)
    else if (y <= 1.02d+214) then
        tmp = 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 = x + (x * (y * z));
	double tmp;
	if (y <= -680.0) {
		tmp = t_0;
	} else if (y <= 1.0) {
		tmp = x * (1.0 - z);
	} else if (y <= 1.02e+214) {
		tmp = t_0;
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (x * (y * z))
	tmp = 0
	if y <= -680.0:
		tmp = t_0
	elif y <= 1.0:
		tmp = x * (1.0 - z)
	elif y <= 1.02e+214:
		tmp = t_0
	else:
		tmp = y * (z * x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(x * Float64(y * z)))
	tmp = 0.0
	if (y <= -680.0)
		tmp = t_0;
	elseif (y <= 1.0)
		tmp = Float64(x * Float64(1.0 - z));
	elseif (y <= 1.02e+214)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (x * (y * z));
	tmp = 0.0;
	if (y <= -680.0)
		tmp = t_0;
	elseif (y <= 1.0)
		tmp = x * (1.0 - z);
	elseif (y <= 1.02e+214)
		tmp = t_0;
	else
		tmp = y * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -680.0], t$95$0, If[LessEqual[y, 1.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e+214], t$95$0, N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -680 or 1 < y < 1.02e214

   1. Initial program 92.9%

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

      1. sub-neg 92.9%

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

      2. distribute-rgt-neg-out 92.9%

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

      3. +-commutative 92.9%

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

      4. distribute-rgt-neg-out 92.9%

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

      5. *-commutative 92.9%

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

      6. distribute-rgt-neg-in 92.9%

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

      7. fma-define 92.9%

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

      8. neg-sub0 92.9%

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

      9. associate--r- 92.9%

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

      10. metadata-eval 92.9%

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

      11. +-commutative 92.9%

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

   3. Simplified 92.9%

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

      1. fma-undefine 92.9%

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

      2. distribute-rgt-in 92.9%

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

      3. *-un-lft-identity 92.9%

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

   6. Applied egg-rr 92.9%

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

   7. Taylor expanded in y around inf 92.3%

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

      1. *-commutative 92.3%

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

   9. Simplified 92.3%

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

   if -680 < y < 1

   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 98.7%

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

   if 1.02e214 < y

   1. Initial program 71.0%

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

   3. Taylor expanded in y around inf 95.4%

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

      1. +-commutative 95.4%

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

      2. associate-/l* 99.7%

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

      3. distribute-lft-out 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around inf 95.5%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -680:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+214}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= -math.inf:
		tmp = y * (z * x)
	else:
		tmp = x * (1.0 + (z * (y + -1.0)))
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 1 y) z) < -inf.0

   1. Initial program 50.0%

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

   3. Taylor expanded in y around inf 78.8%

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

      1. +-commutative 78.8%

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

      2. associate-/l* 89.3%

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

      3. distribute-lft-out 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around inf 99.8%

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

   if -inf.0 < (*.f64 (-.f64 1 y) z)

   1. Initial program 98.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

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

Alternative 4: 59.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-15} \lor \neg \left(z \leq 7.5 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3e-15) (not (<= z 7.5e-23))) (* x (* y z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e-15) || !(z <= 7.5e-23)) {
		tmp = x * (y * 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 <= (-3d-15)) .or. (.not. (z <= 7.5d-23))) then
        tmp = x * (y * 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 <= -3e-15) || !(z <= 7.5e-23)) {
		tmp = x * (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3e-15) or not (z <= 7.5e-23):
		tmp = x * (y * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3e-15) || !(z <= 7.5e-23))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3e-15) || ~((z <= 7.5e-23)))
		tmp = x * (y * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3e-15], N[Not[LessEqual[z, 7.5e-23]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3e-15 or 7.4999999999999998e-23 < z

   1. Initial program 90.8%

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

   3. Taylor expanded in y around inf 44.5%

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

      1. *-commutative 44.5%

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

   5. Simplified 44.5%

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

   if -3e-15 < z < 7.4999999999999998e-23

   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 79.6%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-15} \lor \neg \left(z \leq 7.5 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+95} \lor \neg \left(y \leq 1.3\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.05e+95) (not (<= y 1.3))) (* x (* y z)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.05e+95) || !(y <= 1.3)) {
		tmp = 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 <= (-2.05d+95)) .or. (.not. (y <= 1.3d0))) then
        tmp = 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 <= -2.05e+95) || !(y <= 1.3)) {
		tmp = x * (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.05e+95) or not (y <= 1.3):
		tmp = x * (y * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.05e+95) || !(y <= 1.3))
		tmp = 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 <= -2.05e+95) || ~((y <= 1.3)))
		tmp = x * (y * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.05e+95], N[Not[LessEqual[y, 1.3]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.04999999999999993e95 or 1.30000000000000004 < y

   1. Initial program 86.9%

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

   3. Taylor expanded in y around inf 68.5%

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

      1. *-commutative 68.5%

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

   5. Simplified 68.5%

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

   if -2.04999999999999993e95 < y < 1.30000000000000004

   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 95.2%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+95} \lor \neg \left(y \leq 1.3\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+100} \lor \neg \left(y \leq 1.3\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.2e+100) (not (<= y 1.3))) (* y (* z x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e+100) || !(y <= 1.3)) {
		tmp = y * (z * x);
	} 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 <= (-4.2d+100)) .or. (.not. (y <= 1.3d0))) then
        tmp = y * (z * x)
    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 <= -4.2e+100) || !(y <= 1.3)) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.2e+100) or not (y <= 1.3):
		tmp = y * (z * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.2e+100) || !(y <= 1.3))
		tmp = Float64(y * Float64(z * x));
	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 <= -4.2e+100) || ~((y <= 1.3)))
		tmp = y * (z * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.2e+100], N[Not[LessEqual[y, 1.3]], $MachinePrecision]], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1999999999999997e100 or 1.30000000000000004 < y

   1. Initial program 86.9%

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

   3. Taylor expanded in y around inf 87.4%

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

      1. +-commutative 87.4%

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

      2. associate-/l* 91.3%

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

      3. distribute-lft-out 96.1%

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

   5. Simplified 96.1%

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

   6. Taylor expanded in y around inf 79.9%

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

   if -4.1999999999999997e100 < y < 1.30000000000000004

   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 95.2%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+100} \lor \neg \left(y \leq 1.3\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.5% 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 94.7%

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

3. Taylor expanded in z around 0 36.4%

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

4. Final simplification 36.4%

   \[\leadsto x \]
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 2024080 
(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))))