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

Percentage Accurate: 96.3% → 99.0%

Time: 6.5s

Alternatives: 7

Speedup: 0.8×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -12000:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -12000.0)
   (* z (- (* y x) x))
   (if (<= z 1.0) (* x (+ 1.0 (* y z))) (* (* x z) (+ y -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -12000.0) {
		tmp = z * ((y * x) - x);
	} else if (z <= 1.0) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = (x * z) * (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) :: tmp
    if (z <= (-12000.0d0)) then
        tmp = z * ((y * x) - x)
    else if (z <= 1.0d0) then
        tmp = x * (1.0d0 + (y * z))
    else
        tmp = (x * z) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -12000.0) {
		tmp = z * ((y * x) - x);
	} else if (z <= 1.0) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = (x * z) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -12000.0:
		tmp = z * ((y * x) - x)
	elif z <= 1.0:
		tmp = x * (1.0 + (y * z))
	else:
		tmp = (x * z) * (y + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -12000.0)
		tmp = Float64(z * Float64(Float64(y * x) - x));
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	else
		tmp = Float64(Float64(x * z) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -12000.0)
		tmp = z * ((y * x) - x);
	elseif (z <= 1.0)
		tmp = x * (1.0 + (y * z));
	else
		tmp = (x * z) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -12000.0], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * z), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -12000

   1. Initial program 94.1%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

   if -12000 < z < 1

   1. Initial program 99.9%

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

      1. distribute-rgt-out-- 99.9%

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

      2. *-lft-identity 99.9%

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

      3. cancel-sign-sub-inv 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-in 99.9%

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

      6. associate-*l* 97.0%

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

      7. fma-def 97.0%

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

      8. neg-sub0 97.0%

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

      9. associate--r- 97.0%

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

      10. metadata-eval 97.0%

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

      11. +-commutative 97.0%

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

      12. *-commutative 97.0%

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

   3. Simplified 97.0%

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

      1. fma-udef 97.0%

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

      2. associate-*r* 91.3%

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

   5. Applied egg-rr 91.3%

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

   6. Taylor expanded in y around inf 90.2%

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

   7. Taylor expanded in x around 0 98.9%

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

   if 1 < z

   1. Initial program 92.6%

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

   2. Taylor expanded in z around inf 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

      5. *-commutative 99.7%

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

   4. Simplified 99.7%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -12000:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 2: 97.9% 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 96.6%

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

   1. distribute-rgt-out-- 96.6%

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

   2. *-lft-identity 96.6%

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

   3. cancel-sign-sub-inv 96.6%

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

   4. +-commutative 96.6%

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

   5. distribute-lft-neg-in 96.6%

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

   6. associate-*l* 98.5%

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

   7. fma-def 98.5%

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

   8. neg-sub0 98.5%

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

   9. associate--r- 98.5%

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

   10. metadata-eval 98.5%

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

   11. +-commutative 98.5%

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

   12. *-commutative 98.5%

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

3. Simplified 98.5%

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

4. Final simplification 98.5%

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

Alternative 3: 98.0% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 1.0 (* z (+ y -1.0))))))
   (if (<= t_0 (- INFINITY)) (* (* x z) (+ y -1.0)) t_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 <= -((double) INFINITY)) {
		tmp = (x * z) * (y + -1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * z) * (y + -1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 + (z * (y + -1.0)))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = (x * z) * (y + -1.0)
	else:
		tmp = t_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 <= Float64(-Inf))
		tmp = Float64(Float64(x * z) * Float64(y + -1.0));
	else
		tmp = t_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 <= -Inf)
		tmp = (x * z) * (y + -1.0);
	else
		tmp = t_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, (-Infinity)], N[(N[(x * z), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 85.7%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l* 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. *-commutative 100.0%

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

   4. Simplified 100.0%

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

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

   1. Initial program 98.6%

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

4. Final simplification 98.8%

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

Alternative 4: 65.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+249}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* y (* x z))))
   (if (<= z -7e+249)
     t_0
     (if (<= z -1.45e-48)
       t_1
       (if (<= z 2.9e-7) x (if (<= z 7.2e+208) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = y * (x * z);
	double tmp;
	if (z <= -7e+249) {
		tmp = t_0;
	} else if (z <= -1.45e-48) {
		tmp = t_1;
	} else if (z <= 2.9e-7) {
		tmp = x;
	} else if (z <= 7.2e+208) {
		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 = x * -z
    t_1 = y * (x * z)
    if (z <= (-7d+249)) then
        tmp = t_0
    else if (z <= (-1.45d-48)) then
        tmp = t_1
    else if (z <= 2.9d-7) then
        tmp = x
    else if (z <= 7.2d+208) 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 = x * -z;
	double t_1 = y * (x * z);
	double tmp;
	if (z <= -7e+249) {
		tmp = t_0;
	} else if (z <= -1.45e-48) {
		tmp = t_1;
	} else if (z <= 2.9e-7) {
		tmp = x;
	} else if (z <= 7.2e+208) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = y * (x * z)
	tmp = 0
	if z <= -7e+249:
		tmp = t_0
	elif z <= -1.45e-48:
		tmp = t_1
	elif z <= 2.9e-7:
		tmp = x
	elif z <= 7.2e+208:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (z <= -7e+249)
		tmp = t_0;
	elseif (z <= -1.45e-48)
		tmp = t_1;
	elseif (z <= 2.9e-7)
		tmp = x;
	elseif (z <= 7.2e+208)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	t_1 = y * (x * z);
	tmp = 0.0;
	if (z <= -7e+249)
		tmp = t_0;
	elseif (z <= -1.45e-48)
		tmp = t_1;
	elseif (z <= 2.9e-7)
		tmp = x;
	elseif (z <= 7.2e+208)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+249], t$95$0, If[LessEqual[z, -1.45e-48], t$95$1, If[LessEqual[z, 2.9e-7], x, If[LessEqual[z, 7.2e+208], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.00000000000000024e249 or 7.20000000000000005e208 < z

   1. Initial program 96.9%

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

   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%

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

      2. associate-*l* 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. *-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. distribute-rgt-neg-in 75.8%

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

   7. Simplified 75.8%

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

   if -7.00000000000000024e249 < z < -1.4500000000000001e-48 or 2.8999999999999998e-7 < z < 7.20000000000000005e208

   1. Initial program 93.2%

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

   2. Taylor expanded in y around inf 64.3%

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

   if -1.4500000000000001e-48 < z < 2.8999999999999998e-7

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 85.4%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+249}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+208}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 5: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+21}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.5e+68)
   (* z (* y x))
   (if (<= y 1.35e+21) (- x (* x z)) (* y (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.5e+68) {
		tmp = z * (y * x);
	} else if (y <= 1.35e+21) {
		tmp = x - (x * 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 <= (-1.5d+68)) then
        tmp = z * (y * x)
    else if (y <= 1.35d+21) then
        tmp = x - (x * 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 <= -1.5e+68) {
		tmp = z * (y * x);
	} else if (y <= 1.35e+21) {
		tmp = x - (x * z);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.5e+68:
		tmp = z * (y * x)
	elif y <= 1.35e+21:
		tmp = x - (x * z)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.5e+68)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 1.35e+21)
		tmp = Float64(x - Float64(x * 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 <= -1.5e+68)
		tmp = z * (y * x);
	elseif (y <= 1.35e+21)
		tmp = x - (x * z);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.5e+68], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+21], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5000000000000001e68

   1. Initial program 92.7%

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

   2. Taylor expanded in y around inf 86.4%

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

      1. associate-*r* 86.3%

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

      2. *-commutative 86.3%

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

      3. associate-*l* 88.7%

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

   4. Simplified 88.7%

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

   if -1.5000000000000001e68 < y < 1.35e21

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.0%

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

      1. *-commutative 97.0%

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

      2. distribute-rgt-out-- 97.0%

         \[\leadsto \color{blue}{1 \cdot x - z \cdot x} \]

      3. *-lft-identity 97.0%

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

   4. Simplified 97.0%

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

   if 1.35e21 < y

   1. Initial program 89.8%

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

   2. Taylor expanded in y around inf 83.5%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+21}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 6: 65.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-5} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9e-5) (not (<= z 1.0))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9e-5) || !(z <= 1.0)) {
		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 <= (-9d-5)) .or. (.not. (z <= 1.0d0))) 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 <= -9e-5) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9e-5) or not (z <= 1.0):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9e-5) || !(z <= 1.0))
		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 <= -9e-5) || ~((z <= 1.0)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9e-5], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.00000000000000057e-5 or 1 < z

   1. Initial program 93.5%

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

   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%

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

      2. associate-*l* 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. *-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around 0 54.2%

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

      1. mul-1-neg 54.2%

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

      2. distribute-rgt-neg-in 54.2%

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

   7. Simplified 54.2%

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

   if -9.00000000000000057e-5 < 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 81.2%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-5} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 39.7% 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 96.6%

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

2. Taylor expanded in z around 0 41.5%

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

3. Final simplification 41.5%

   \[\leadsto x \]

Developer target: 99.8% 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 2023224 
(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))))