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

Percentage Accurate: 96.0% → 97.8%

Time: 6.4s

Alternatives: 9

Speedup: 0.8×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.0% 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: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+75}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2e+75) (* (* z x) (+ y -1.0)) (* x (+ 1.0 (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e+75) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x * (1.0 + (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 <= (-2d+75)) then
        tmp = (z * x) * (y + (-1.0d0))
    else
        tmp = x * (1.0d0 + (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 <= -2e+75) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2e+75:
		tmp = (z * x) * (y + -1.0)
	else:
		tmp = x * (1.0 + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2e+75)
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	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 (z <= -2e+75)
		tmp = (z * x) * (y + -1.0);
	else
		tmp = x * (1.0 + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2e+75], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $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 z < -1.99999999999999985e75

   1. Initial program 87.1%

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

   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%

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

   if -1.99999999999999985e75 < z

   1. Initial program 99.5%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+75}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 2: 65.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot x\right)\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{-13}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+17} \lor \neg \left(z \leq 1.25 \cdot 10^{+42}\right) \land \left(z \leq 1.32 \cdot 10^{+91} \lor \neg \left(z \leq 2.65 \cdot 10^{+209}\right) \land z \leq 3.4 \cdot 10^{+256}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z x))))
   (if (<= z -1.02e-13)
     t_0
     (if (<= z 1.15e-19)
       x
       (if (or (<= z 9.8e+17)
               (and (not (<= z 1.25e+42))
                    (or (<= z 1.32e+91)
                        (and (not (<= z 2.65e+209)) (<= z 3.4e+256)))))
         t_0
         (* z (- x)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z * x);
	double tmp;
	if (z <= -1.02e-13) {
		tmp = t_0;
	} else if (z <= 1.15e-19) {
		tmp = x;
	} else if ((z <= 9.8e+17) || (!(z <= 1.25e+42) && ((z <= 1.32e+91) || (!(z <= 2.65e+209) && (z <= 3.4e+256))))) {
		tmp = t_0;
	} else {
		tmp = z * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (z * x)
    if (z <= (-1.02d-13)) then
        tmp = t_0
    else if (z <= 1.15d-19) then
        tmp = x
    else if ((z <= 9.8d+17) .or. (.not. (z <= 1.25d+42)) .and. (z <= 1.32d+91) .or. (.not. (z <= 2.65d+209)) .and. (z <= 3.4d+256)) then
        tmp = t_0
    else
        tmp = z * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (z * x);
	double tmp;
	if (z <= -1.02e-13) {
		tmp = t_0;
	} else if (z <= 1.15e-19) {
		tmp = x;
	} else if ((z <= 9.8e+17) || (!(z <= 1.25e+42) && ((z <= 1.32e+91) || (!(z <= 2.65e+209) && (z <= 3.4e+256))))) {
		tmp = t_0;
	} else {
		tmp = z * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z * x)
	tmp = 0
	if z <= -1.02e-13:
		tmp = t_0
	elif z <= 1.15e-19:
		tmp = x
	elif (z <= 9.8e+17) or (not (z <= 1.25e+42) and ((z <= 1.32e+91) or (not (z <= 2.65e+209) and (z <= 3.4e+256)))):
		tmp = t_0
	else:
		tmp = z * -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z * x))
	tmp = 0.0
	if (z <= -1.02e-13)
		tmp = t_0;
	elseif (z <= 1.15e-19)
		tmp = x;
	elseif ((z <= 9.8e+17) || (!(z <= 1.25e+42) && ((z <= 1.32e+91) || (!(z <= 2.65e+209) && (z <= 3.4e+256)))))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z * x);
	tmp = 0.0;
	if (z <= -1.02e-13)
		tmp = t_0;
	elseif (z <= 1.15e-19)
		tmp = x;
	elseif ((z <= 9.8e+17) || (~((z <= 1.25e+42)) && ((z <= 1.32e+91) || (~((z <= 2.65e+209)) && (z <= 3.4e+256)))))
		tmp = t_0;
	else
		tmp = z * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e-13], t$95$0, If[LessEqual[z, 1.15e-19], x, If[Or[LessEqual[z, 9.8e+17], And[N[Not[LessEqual[z, 1.25e+42]], $MachinePrecision], Or[LessEqual[z, 1.32e+91], And[N[Not[LessEqual[z, 2.65e+209]], $MachinePrecision], LessEqual[z, 3.4e+256]]]]], t$95$0, N[(z * (-x)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0199999999999999e-13 or 1.1499999999999999e-19 < z < 9.8e17 or 1.25000000000000002e42 < z < 1.32000000000000003e91 or 2.64999999999999997e209 < z < 3.39999999999999984e256

   1. Initial program 93.2%

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

   2. Taylor expanded in y around inf 69.0%

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

   if -1.0199999999999999e-13 < z < 1.1499999999999999e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 81.5%

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

   if 9.8e17 < z < 1.25000000000000002e42 or 1.32000000000000003e91 < z < 2.64999999999999997e209 or 3.39999999999999984e256 < z

   1. Initial program 96.8%

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

   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%

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

      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%

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

   5. Taylor expanded in y around 0 81.3%

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

      1. mul-1-neg 81.3%

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

      2. distribute-rgt-neg-in 81.3%

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

   7. Simplified 81.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+17} \lor \neg \left(z \leq 1.25 \cdot 10^{+42}\right) \land \left(z \leq 1.32 \cdot 10^{+91} \lor \neg \left(z \leq 2.65 \cdot 10^{+209}\right) \land z \leq 3.4 \cdot 10^{+256}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 65.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y \cdot x\right)\\ t_1 := z \cdot \left(-x\right)\\ t_2 := y \cdot \left(z \cdot x\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+94}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+210} \lor \neg \left(z \leq 3.7 \cdot 10^{+256}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* y x))) (t_1 (* z (- x))) (t_2 (* y (* z x))))
   (if (<= z -8.5e-14)
     t_2
     (if (<= z 1.2e-19)
       x
       (if (<= z 1.2e+23)
         t_0
         (if (<= z 5.6e+40)
           t_1
           (if (<= z 1.35e+94)
             t_0
             (if (or (<= z 1.85e+210) (not (<= z 3.7e+256))) t_1 t_2))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y * x);
	double t_1 = z * -x;
	double t_2 = y * (z * x);
	double tmp;
	if (z <= -8.5e-14) {
		tmp = t_2;
	} else if (z <= 1.2e-19) {
		tmp = x;
	} else if (z <= 1.2e+23) {
		tmp = t_0;
	} else if (z <= 5.6e+40) {
		tmp = t_1;
	} else if (z <= 1.35e+94) {
		tmp = t_0;
	} else if ((z <= 1.85e+210) || !(z <= 3.7e+256)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_0 = z * (y * x)
    t_1 = z * -x
    t_2 = y * (z * x)
    if (z <= (-8.5d-14)) then
        tmp = t_2
    else if (z <= 1.2d-19) then
        tmp = x
    else if (z <= 1.2d+23) then
        tmp = t_0
    else if (z <= 5.6d+40) then
        tmp = t_1
    else if (z <= 1.35d+94) then
        tmp = t_0
    else if ((z <= 1.85d+210) .or. (.not. (z <= 3.7d+256))) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y * x);
	double t_1 = z * -x;
	double t_2 = y * (z * x);
	double tmp;
	if (z <= -8.5e-14) {
		tmp = t_2;
	} else if (z <= 1.2e-19) {
		tmp = x;
	} else if (z <= 1.2e+23) {
		tmp = t_0;
	} else if (z <= 5.6e+40) {
		tmp = t_1;
	} else if (z <= 1.35e+94) {
		tmp = t_0;
	} else if ((z <= 1.85e+210) || !(z <= 3.7e+256)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y * x)
	t_1 = z * -x
	t_2 = y * (z * x)
	tmp = 0
	if z <= -8.5e-14:
		tmp = t_2
	elif z <= 1.2e-19:
		tmp = x
	elif z <= 1.2e+23:
		tmp = t_0
	elif z <= 5.6e+40:
		tmp = t_1
	elif z <= 1.35e+94:
		tmp = t_0
	elif (z <= 1.85e+210) or not (z <= 3.7e+256):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y * x))
	t_1 = Float64(z * Float64(-x))
	t_2 = Float64(y * Float64(z * x))
	tmp = 0.0
	if (z <= -8.5e-14)
		tmp = t_2;
	elseif (z <= 1.2e-19)
		tmp = x;
	elseif (z <= 1.2e+23)
		tmp = t_0;
	elseif (z <= 5.6e+40)
		tmp = t_1;
	elseif (z <= 1.35e+94)
		tmp = t_0;
	elseif ((z <= 1.85e+210) || !(z <= 3.7e+256))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y * x);
	t_1 = z * -x;
	t_2 = y * (z * x);
	tmp = 0.0;
	if (z <= -8.5e-14)
		tmp = t_2;
	elseif (z <= 1.2e-19)
		tmp = x;
	elseif (z <= 1.2e+23)
		tmp = t_0;
	elseif (z <= 5.6e+40)
		tmp = t_1;
	elseif (z <= 1.35e+94)
		tmp = t_0;
	elseif ((z <= 1.85e+210) || ~((z <= 3.7e+256)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * (-x)), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e-14], t$95$2, If[LessEqual[z, 1.2e-19], x, If[LessEqual[z, 1.2e+23], t$95$0, If[LessEqual[z, 5.6e+40], t$95$1, If[LessEqual[z, 1.35e+94], t$95$0, If[Or[LessEqual[z, 1.85e+210], N[Not[LessEqual[z, 3.7e+256]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.50000000000000038e-14 or 1.84999999999999999e210 < z < 3.70000000000000031e256

   1. Initial program 91.6%

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

   2. Taylor expanded in y around inf 64.1%

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

   if -8.50000000000000038e-14 < z < 1.20000000000000011e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 81.5%

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

   if 1.20000000000000011e-19 < z < 1.2e23 or 5.6000000000000003e40 < z < 1.3500000000000001e94

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 90.6%

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

      1. associate-*r* 90.7%

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

      2. *-commutative 90.7%

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

      3. associate-*l* 90.8%

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

   4. Simplified 90.8%

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

   if 1.2e23 < z < 5.6000000000000003e40 or 1.3500000000000001e94 < z < 1.84999999999999999e210 or 3.70000000000000031e256 < z

   1. Initial program 96.8%

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

   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%

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

      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%

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

   5. Taylor expanded in y around 0 81.3%

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

      1. mul-1-neg 81.3%

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

      2. distribute-rgt-neg-in 81.3%

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

   7. Simplified 81.3%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+23}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+94}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+210} \lor \neg \left(z \leq 3.7 \cdot 10^{+256}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 4: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-5} \lor \neg \left(z \leq 1.6 \cdot 10^{-19}\right):\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.8e-5) (not (<= z 1.6e-19)))
   (* z (- (* y x) x))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.8e-5) || !(z <= 1.6e-19)) {
		tmp = z * ((y * x) - 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 ((z <= (-2.8d-5)) .or. (.not. (z <= 1.6d-19))) then
        tmp = z * ((y * x) - 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 ((z <= -2.8e-5) || !(z <= 1.6e-19)) {
		tmp = z * ((y * x) - x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.8e-5) or not (z <= 1.6e-19):
		tmp = z * ((y * x) - x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.8e-5) || !(z <= 1.6e-19))
		tmp = Float64(z * Float64(Float64(y * x) - 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 ((z <= -2.8e-5) || ~((z <= 1.6e-19)))
		tmp = z * ((y * x) - x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.8e-5], N[Not[LessEqual[z, 1.6e-19]], $MachinePrecision]], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.79999999999999996e-5 or 1.59999999999999991e-19 < z

   1. Initial program 93.9%

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

   2. Taylor expanded in z around inf 98.7%

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

      1. *-commutative 98.7%

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

      2. sub-neg 98.7%

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

      3. metadata-eval 98.7%

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

      4. distribute-rgt-in 98.7%

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

      5. neg-mul-1 98.7%

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

      6. unsub-neg 98.7%

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

   4. Simplified 98.7%

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

   if -2.79999999999999996e-5 < z < 1.59999999999999991e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.1%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-5} \lor \neg \left(z \leq 1.6 \cdot 10^{-19}\right):\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 5: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-5}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.7e-5)
   (* (* z x) (+ y -1.0))
   (if (<= z 1.45e-19) (* x (- 1.0 z)) (* z (- (* y x) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.7e-5) {
		tmp = (z * x) * (y + -1.0);
	} else if (z <= 1.45e-19) {
		tmp = x * (1.0 - 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 <= (-1.7d-5)) then
        tmp = (z * x) * (y + (-1.0d0))
    else if (z <= 1.45d-19) then
        tmp = x * (1.0d0 - 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 <= -1.7e-5) {
		tmp = (z * x) * (y + -1.0);
	} else if (z <= 1.45e-19) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * ((y * x) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.7e-5:
		tmp = (z * x) * (y + -1.0)
	elif z <= 1.45e-19:
		tmp = x * (1.0 - z)
	else:
		tmp = z * ((y * x) - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.7e-5)
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	elseif (z <= 1.45e-19)
		tmp = Float64(x * Float64(1.0 - 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 <= -1.7e-5)
		tmp = (z * x) * (y + -1.0);
	elseif (z <= 1.45e-19)
		tmp = x * (1.0 - z);
	else
		tmp = z * ((y * x) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.7e-5], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-19], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e-5

   1. Initial program 90.5%

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

   2. Taylor expanded in z around inf 98.5%

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

      1. *-commutative 98.5%

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

      2. associate-*l* 98.5%

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

      3. sub-neg 98.5%

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

      4. metadata-eval 98.5%

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

      5. *-commutative 98.5%

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

   4. Simplified 98.5%

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

   if -1.7e-5 < z < 1.45e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.1%

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

   if 1.45e-19 < z

   1. Initial program 98.3%

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

   2. Taylor expanded in z around inf 99.0%

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

      1. *-commutative 99.0%

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

      2. sub-neg 99.0%

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

      3. metadata-eval 99.0%

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

      4. distribute-rgt-in 99.0%

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

      5. neg-mul-1 99.0%

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

      6. unsub-neg 99.0%

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

   4. Simplified 99.0%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-5}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \]

Alternative 6: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.95:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{-19}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.95)
   (* (* z x) (+ y -1.0))
   (if (<= z 1.76e-19) (+ x (* x (* z y))) (* z (- (* y x) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.95) {
		tmp = (z * x) * (y + -1.0);
	} else if (z <= 1.76e-19) {
		tmp = x + (x * (z * y));
	} 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 <= (-0.95d0)) then
        tmp = (z * x) * (y + (-1.0d0))
    else if (z <= 1.76d-19) then
        tmp = x + (x * (z * y))
    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 <= -0.95) {
		tmp = (z * x) * (y + -1.0);
	} else if (z <= 1.76e-19) {
		tmp = x + (x * (z * y));
	} else {
		tmp = z * ((y * x) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.95:
		tmp = (z * x) * (y + -1.0)
	elif z <= 1.76e-19:
		tmp = x + (x * (z * y))
	else:
		tmp = z * ((y * x) - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.95)
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	elseif (z <= 1.76e-19)
		tmp = Float64(x + Float64(x * Float64(z * y)));
	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 <= -0.95)
		tmp = (z * x) * (y + -1.0);
	elseif (z <= 1.76e-19)
		tmp = x + (x * (z * y));
	else
		tmp = z * ((y * x) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.95], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.76e-19], N[(x + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.94999999999999996

   1. Initial program 90.4%

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

   2. Taylor expanded in z around inf 98.4%

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

      1. *-commutative 98.4%

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

      2. associate-*l* 98.5%

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

      3. sub-neg 98.5%

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

      4. metadata-eval 98.5%

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

      5. *-commutative 98.5%

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

   4. Simplified 98.5%

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

   if -0.94999999999999996 < z < 1.75999999999999993e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. distribute-lft-neg-out 99.4%

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

      3. *-commutative 99.4%

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

   4. Simplified 99.4%

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

      1. sub-neg 99.4%

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

      2. distribute-rgt-neg-out 99.4%

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

      3. remove-double-neg 99.4%

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

      4. distribute-lft-in 99.4%

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

      5. *-commutative 99.4%

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

      6. *-un-lft-identity 99.4%

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

   6. Applied egg-rr 99.4%

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

   if 1.75999999999999993e-19 < z

   1. Initial program 98.3%

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

   2. Taylor expanded in z around inf 99.0%

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

      1. *-commutative 99.0%

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

      2. sub-neg 99.0%

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

      3. metadata-eval 99.0%

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

      4. distribute-rgt-in 99.0%

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

      5. neg-mul-1 99.0%

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

      6. unsub-neg 99.0%

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

   4. Simplified 99.0%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.95:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{-19}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \]

Alternative 7: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+48} \lor \neg \left(y \leq 5.3\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.1e+48) (not (<= y 5.3))) (* z (* y x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.1e+48) || !(y <= 5.3)) {
		tmp = z * (y * 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 <= (-2.1d+48)) .or. (.not. (y <= 5.3d0))) then
        tmp = z * (y * 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 <= -2.1e+48) || !(y <= 5.3)) {
		tmp = z * (y * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.1e+48) or not (y <= 5.3):
		tmp = z * (y * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.1e+48) || !(y <= 5.3))
		tmp = Float64(z * Float64(y * 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 <= -2.1e+48) || ~((y <= 5.3)))
		tmp = z * (y * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.1e+48], N[Not[LessEqual[y, 5.3]], $MachinePrecision]], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0999999999999998e48 or 5.29999999999999982 < y

   1. Initial program 93.5%

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

   2. Taylor expanded in y around inf 74.8%

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

      1. associate-*r* 75.6%

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

      2. *-commutative 75.6%

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

      3. associate-*l* 80.3%

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

   4. Simplified 80.3%

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

   if -2.0999999999999998e48 < y < 5.29999999999999982

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 97.8%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+48} \lor \neg \left(y \leq 5.3\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 8: 64.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 4 \cdot 10^{-14}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 4e-14))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 4e-14)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 4d-14))) then
        tmp = z * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 4e-14)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 4e-14):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 4e-14))
		tmp = Float64(z * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 4e-14)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 4e-14]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 4e-14 < z

   1. Initial program 93.8%

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

   2. Taylor expanded in z around inf 98.7%

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

      1. *-commutative 98.7%

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

      2. associate-*l* 98.7%

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

      3. sub-neg 98.7%

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

      4. metadata-eval 98.7%

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

      5. *-commutative 98.7%

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

   4. Simplified 98.7%

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

   5. Taylor expanded in y around 0 49.2%

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

      1. mul-1-neg 49.2%

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

      2. distribute-rgt-neg-in 49.2%

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

   7. Simplified 49.2%

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

   if -1 < z < 4e-14

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 79.2%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 4 \cdot 10^{-14}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 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 96.6%

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

2. Taylor expanded in z around 0 38.0%

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

3. Final simplification 38.0%

   \[\leadsto x \]

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 2023229 
(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))))