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

Percentage Accurate: 96.3% → 99.4%

Time: 7.8s

Alternatives: 11

Speedup: 1.0×

• 21.2% 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: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 + \left(y + -1\right) \cdot z\right)\\ \mathbf{if}\;t_0 \leq -\infty \lor \neg \left(t_0 \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;z \cdot \left(\left(y + -1\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \left(y \cdot z - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 1.0 (* (+ y -1.0) z)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 2e+296)))
     (* z (* (+ y -1.0) x))
     (* x (+ 1.0 (- (* y z) z))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 + ((y + -1.0) * z));
	double tmp;
	if ((t_0 <= -((double) INFINITY)) || !(t_0 <= 2e+296)) {
		tmp = z * ((y + -1.0) * x);
	} else {
		tmp = x * (1.0 + ((y * z) - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 + ((y + -1.0) * z));
	double tmp;
	if ((t_0 <= -Double.POSITIVE_INFINITY) || !(t_0 <= 2e+296)) {
		tmp = z * ((y + -1.0) * x);
	} else {
		tmp = x * (1.0 + ((y * z) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 + ((y + -1.0) * z))
	tmp = 0
	if (t_0 <= -math.inf) or not (t_0 <= 2e+296):
		tmp = z * ((y + -1.0) * x)
	else:
		tmp = x * (1.0 + ((y * z) - z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 + Float64(Float64(y + -1.0) * z)))
	tmp = 0.0
	if ((t_0 <= Float64(-Inf)) || !(t_0 <= 2e+296))
		tmp = Float64(z * Float64(Float64(y + -1.0) * x));
	else
		tmp = Float64(x * Float64(1.0 + Float64(Float64(y * z) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 + ((y + -1.0) * z));
	tmp = 0.0;
	if ((t_0 <= -Inf) || ~((t_0 <= 2e+296)))
		tmp = z * ((y + -1.0) * x);
	else
		tmp = x * (1.0 + ((y * z) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 + N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, (-Infinity)], N[Not[LessEqual[t$95$0, 2e+296]], $MachinePrecision]], N[(z * N[(N[(y + -1.0), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(N[(y * z), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z))) < -inf.0 or 1.99999999999999996e296 < (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z)))

   1. Initial program 77.9%

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

   2. Taylor expanded in z around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-*l* 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   if -inf.0 < (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z))) < 1.99999999999999996e296

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. unsub-neg 99.8%

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

      3. *-commutative 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 + \left(y + -1\right) \cdot z\right) \leq -\infty \lor \neg \left(x \cdot \left(1 + \left(y + -1\right) \cdot z\right) \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;z \cdot \left(\left(y + -1\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \left(y \cdot z - z\right)\right)\\ \end{array} \]

Alternative 2: 99.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+249}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t_0 \leq 10^{+257}:\\ \;\;\;\;x \cdot \left(1 + \left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y + -1\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (<= t_0 -5e+249)
     (* (+ y -1.0) (* x z))
     (if (<= t_0 1e+257)
       (* x (+ 1.0 (* (+ y -1.0) z)))
       (* z (* (+ y -1.0) x))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -5e+249) {
		tmp = (y + -1.0) * (x * z);
	} else if (t_0 <= 1e+257) {
		tmp = x * (1.0 + ((y + -1.0) * z));
	} else {
		tmp = z * ((y + -1.0) * 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 = z * (1.0d0 - y)
    if (t_0 <= (-5d+249)) then
        tmp = (y + (-1.0d0)) * (x * z)
    else if (t_0 <= 1d+257) then
        tmp = x * (1.0d0 + ((y + (-1.0d0)) * z))
    else
        tmp = z * ((y + (-1.0d0)) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -5e+249) {
		tmp = (y + -1.0) * (x * z);
	} else if (t_0 <= 1e+257) {
		tmp = x * (1.0 + ((y + -1.0) * z));
	} else {
		tmp = z * ((y + -1.0) * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 - y)
	tmp = 0
	if t_0 <= -5e+249:
		tmp = (y + -1.0) * (x * z)
	elif t_0 <= 1e+257:
		tmp = x * (1.0 + ((y + -1.0) * z))
	else:
		tmp = z * ((y + -1.0) * x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (t_0 <= -5e+249)
		tmp = Float64(Float64(y + -1.0) * Float64(x * z));
	elseif (t_0 <= 1e+257)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(y + -1.0) * z)));
	else
		tmp = Float64(z * Float64(Float64(y + -1.0) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (1.0 - y);
	tmp = 0.0;
	if (t_0 <= -5e+249)
		tmp = (y + -1.0) * (x * z);
	elseif (t_0 <= 1e+257)
		tmp = x * (1.0 + ((y + -1.0) * z));
	else
		tmp = z * ((y + -1.0) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+249], N[(N[(y + -1.0), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+257], N[(x * N[(1.0 + N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y + -1.0), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -4.9999999999999996e249

   1. Initial program 82.5%

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

   2. Taylor expanded in z around inf 82.5%

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

      1. associate-*r* 99.8%

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

      2. *-commutative 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%

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

   4. Simplified 99.8%

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

   if -4.9999999999999996e249 < (*.f64 (-.f64 1 y) z) < 1.00000000000000003e257

   1. Initial program 99.8%

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

   if 1.00000000000000003e257 < (*.f64 (-.f64 1 y) z)

   1. Initial program 65.1%

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

   2. Taylor expanded in z around inf 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-*l* 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -5 \cdot 10^{+249}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 10^{+257}:\\ \;\;\;\;x \cdot \left(1 + \left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y + -1\right) \cdot x\right)\\ \end{array} \]

Alternative 3: 61.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.65 \cdot 10^{+218}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+21} \lor \neg \left(z \leq 2.9 \cdot 10^{+239}\right) \land z \leq 1.26 \cdot 10^{+266}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* x (* y z))))
   (if (<= z -2.65e+218)
     t_0
     (if (<= z -1.4e+84)
       t_1
       (if (<= z -1.0)
         t_0
         (if (<= z 1.7e-132)
           x
           (if (or (<= z 1.7e+21) (and (not (<= z 2.9e+239)) (<= z 1.26e+266)))
             t_1
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -2.65e+218) {
		tmp = t_0;
	} else if (z <= -1.4e+84) {
		tmp = t_1;
	} else if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 1.7e-132) {
		tmp = x;
	} else if ((z <= 1.7e+21) || (!(z <= 2.9e+239) && (z <= 1.26e+266))) {
		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 = x * (y * z)
    if (z <= (-2.65d+218)) then
        tmp = t_0
    else if (z <= (-1.4d+84)) then
        tmp = t_1
    else if (z <= (-1.0d0)) then
        tmp = t_0
    else if (z <= 1.7d-132) then
        tmp = x
    else if ((z <= 1.7d+21) .or. (.not. (z <= 2.9d+239)) .and. (z <= 1.26d+266)) 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 = x * (y * z);
	double tmp;
	if (z <= -2.65e+218) {
		tmp = t_0;
	} else if (z <= -1.4e+84) {
		tmp = t_1;
	} else if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 1.7e-132) {
		tmp = x;
	} else if ((z <= 1.7e+21) || (!(z <= 2.9e+239) && (z <= 1.26e+266))) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = x * (y * z)
	tmp = 0
	if z <= -2.65e+218:
		tmp = t_0
	elif z <= -1.4e+84:
		tmp = t_1
	elif z <= -1.0:
		tmp = t_0
	elif z <= 1.7e-132:
		tmp = x
	elif (z <= 1.7e+21) or (not (z <= 2.9e+239) and (z <= 1.26e+266)):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -2.65e+218)
		tmp = t_0;
	elseif (z <= -1.4e+84)
		tmp = t_1;
	elseif (z <= -1.0)
		tmp = t_0;
	elseif (z <= 1.7e-132)
		tmp = x;
	elseif ((z <= 1.7e+21) || (!(z <= 2.9e+239) && (z <= 1.26e+266)))
		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 = x * (y * z);
	tmp = 0.0;
	if (z <= -2.65e+218)
		tmp = t_0;
	elseif (z <= -1.4e+84)
		tmp = t_1;
	elseif (z <= -1.0)
		tmp = t_0;
	elseif (z <= 1.7e-132)
		tmp = x;
	elseif ((z <= 1.7e+21) || (~((z <= 2.9e+239)) && (z <= 1.26e+266)))
		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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.65e+218], t$95$0, If[LessEqual[z, -1.4e+84], t$95$1, If[LessEqual[z, -1.0], t$95$0, If[LessEqual[z, 1.7e-132], x, If[Or[LessEqual[z, 1.7e+21], And[N[Not[LessEqual[z, 2.9e+239]], $MachinePrecision], LessEqual[z, 1.26e+266]]], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6500000000000001e218 or -1.39999999999999991e84 < z < -1 or 1.7e21 < z < 2.9000000000000002e239 or 1.26e266 < z

   1. Initial program 87.6%

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

   2. Taylor expanded in y around 0 62.5%

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

      1. sub-neg 62.5%

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

      2. distribute-rgt-in 62.5%

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

      3. *-lft-identity 62.5%

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

      4. distribute-lft-neg-out 62.5%

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

      5. *-commutative 62.5%

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

      6. unsub-neg 62.5%

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

   4. Simplified 62.5%

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

   5. Taylor expanded in z around inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. distribute-rgt-neg-in 61.6%

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

   7. Simplified 61.6%

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

   if -2.6500000000000001e218 < z < -1.39999999999999991e84 or 1.69999999999999991e-132 < z < 1.7e21 or 2.9000000000000002e239 < z < 1.26e266

   1. Initial program 93.7%

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

   2. Taylor expanded in y around inf 59.1%

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

      1. *-commutative 59.1%

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

   4. Simplified 59.1%

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

   if -1 < z < 1.69999999999999991e-132

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 79.0%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+218}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+21} \lor \neg \left(z \leq 2.9 \cdot 10^{+239}\right) \land z \leq 1.26 \cdot 10^{+266}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 4: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(\left(y + -1\right) \cdot x\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{-44}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* (+ y -1.0) x))))
   (if (<= z -2.9e-44)
     t_0
     (if (<= z 1.7e-132)
       x
       (if (<= z 4.6e-70) (* x (* y z)) (if (<= z 1.6e-55) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((y + -1.0) * x);
	double tmp;
	if (z <= -2.9e-44) {
		tmp = t_0;
	} else if (z <= 1.7e-132) {
		tmp = x;
	} else if (z <= 4.6e-70) {
		tmp = x * (y * z);
	} else if (z <= 1.6e-55) {
		tmp = x;
	} 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) :: tmp
    t_0 = z * ((y + (-1.0d0)) * x)
    if (z <= (-2.9d-44)) then
        tmp = t_0
    else if (z <= 1.7d-132) then
        tmp = x
    else if (z <= 4.6d-70) then
        tmp = x * (y * z)
    else if (z <= 1.6d-55) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * ((y + -1.0) * x);
	double tmp;
	if (z <= -2.9e-44) {
		tmp = t_0;
	} else if (z <= 1.7e-132) {
		tmp = x;
	} else if (z <= 4.6e-70) {
		tmp = x * (y * z);
	} else if (z <= 1.6e-55) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((y + -1.0) * x)
	tmp = 0
	if z <= -2.9e-44:
		tmp = t_0
	elif z <= 1.7e-132:
		tmp = x
	elif z <= 4.6e-70:
		tmp = x * (y * z)
	elif z <= 1.6e-55:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(y + -1.0) * x))
	tmp = 0.0
	if (z <= -2.9e-44)
		tmp = t_0;
	elseif (z <= 1.7e-132)
		tmp = x;
	elseif (z <= 4.6e-70)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 1.6e-55)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((y + -1.0) * x);
	tmp = 0.0;
	if (z <= -2.9e-44)
		tmp = t_0;
	elseif (z <= 1.7e-132)
		tmp = x;
	elseif (z <= 4.6e-70)
		tmp = x * (y * z);
	elseif (z <= 1.6e-55)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(N[(y + -1.0), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e-44], t$95$0, If[LessEqual[z, 1.7e-132], x, If[LessEqual[z, 4.6e-70], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-55], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9000000000000001e-44 or 1.6000000000000001e-55 < z

   1. Initial program 89.7%

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

   2. Taylor expanded in z around inf 85.1%

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

      1. *-commutative 85.1%

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

      2. associate-*l* 95.3%

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

      3. sub-neg 95.3%

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

      4. metadata-eval 95.3%

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

   4. Simplified 95.3%

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

   if -2.9000000000000001e-44 < z < 1.69999999999999991e-132 or 4.60000000000000001e-70 < z < 1.6000000000000001e-55

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 82.0%

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

   if 1.69999999999999991e-132 < z < 4.60000000000000001e-70

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 79.3%

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

      1. *-commutative 79.3%

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

   4. Simplified 79.3%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \left(\left(y + -1\right) \cdot x\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y + -1\right) \cdot x\right)\\ \end{array} \]

Alternative 5: 82.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -6.9 \cdot 10^{+47}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 130000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 10^{+118} \lor \neg \left(y \leq 1.7 \cdot 10^{+166}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* y z))))
   (if (<= y -6.9e+47)
     t_0
     (if (<= y 130000000000.0)
       (* x (- 1.0 z))
       (if (or (<= y 1e+118) (not (<= y 1.7e+166))) t_0 x)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double tmp;
	if (y <= -6.9e+47) {
		tmp = t_0;
	} else if (y <= 130000000000.0) {
		tmp = x * (1.0 - z);
	} else if ((y <= 1e+118) || !(y <= 1.7e+166)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * (y * z)
    if (y <= (-6.9d+47)) then
        tmp = t_0
    else if (y <= 130000000000.0d0) then
        tmp = x * (1.0d0 - z)
    else if ((y <= 1d+118) .or. (.not. (y <= 1.7d+166))) then
        tmp = t_0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double tmp;
	if (y <= -6.9e+47) {
		tmp = t_0;
	} else if (y <= 130000000000.0) {
		tmp = x * (1.0 - z);
	} else if ((y <= 1e+118) || !(y <= 1.7e+166)) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y * z)
	tmp = 0
	if y <= -6.9e+47:
		tmp = t_0
	elif y <= 130000000000.0:
		tmp = x * (1.0 - z)
	elif (y <= 1e+118) or not (y <= 1.7e+166):
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -6.9e+47)
		tmp = t_0;
	elseif (y <= 130000000000.0)
		tmp = Float64(x * Float64(1.0 - z));
	elseif ((y <= 1e+118) || !(y <= 1.7e+166))
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y * z);
	tmp = 0.0;
	if (y <= -6.9e+47)
		tmp = t_0;
	elseif (y <= 130000000000.0)
		tmp = x * (1.0 - z);
	elseif ((y <= 1e+118) || ~((y <= 1.7e+166)))
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.9e+47], t$95$0, If[LessEqual[y, 130000000000.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1e+118], N[Not[LessEqual[y, 1.7e+166]], $MachinePrecision]], t$95$0, x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.9000000000000004e47 or 1.3e11 < y < 9.99999999999999967e117 or 1.7e166 < y

   1. Initial program 86.5%

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

   2. Taylor expanded in y around inf 72.5%

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

      1. *-commutative 72.5%

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

   4. Simplified 72.5%

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

   if -6.9000000000000004e47 < y < 1.3e11

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 94.3%

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

   if 9.99999999999999967e117 < y < 1.7e166

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 80.2%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 130000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 10^{+118} \lor \neg \left(y \leq 1.7 \cdot 10^{+166}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 80.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-44} \lor \neg \left(z \leq 1.7 \cdot 10^{-132}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3e-44) (not (<= z 1.7e-132))) (* x (- (* y z) z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e-44) || !(z <= 1.7e-132)) {
		tmp = x * ((y * z) - 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-44)) .or. (.not. (z <= 1.7d-132))) then
        tmp = x * ((y * z) - 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-44) || !(z <= 1.7e-132)) {
		tmp = x * ((y * z) - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3e-44) or not (z <= 1.7e-132):
		tmp = x * ((y * z) - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3e-44) || !(z <= 1.7e-132))
		tmp = Float64(x * Float64(Float64(y * z) - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3e-44) || ~((z <= 1.7e-132)))
		tmp = x * ((y * z) - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3e-44], N[Not[LessEqual[z, 1.7e-132]], $MachinePrecision]], N[(x * N[(N[(y * z), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.0000000000000002e-44 or 1.69999999999999991e-132 < z

   1. Initial program 90.5%

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

   2. Taylor expanded in y around 0 90.5%

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

      1. mul-1-neg 90.5%

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

      2. unsub-neg 90.5%

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

      3. *-commutative 90.5%

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

   4. Simplified 90.5%

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

   5. Taylor expanded in z around inf 83.2%

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

      1. sub-neg 83.2%

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

      2. metadata-eval 83.2%

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

      3. distribute-rgt-in 83.3%

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

      4. neg-mul-1 83.3%

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

      5. fma-def 83.2%

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

      6. fma-neg 83.3%

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

   7. Simplified 83.3%

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

   if -3.0000000000000002e-44 < z < 1.69999999999999991e-132

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 81.5%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-44} \lor \neg \left(z \leq 1.7 \cdot 10^{-132}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.94 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(\left(y + -1\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.94) (not (<= z 1.0)))
   (* z (* (+ y -1.0) x))
   (+ x (* x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.94) || !(z <= 1.0)) {
		tmp = z * ((y + -1.0) * x);
	} else {
		tmp = x + (x * (y * 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 <= (-0.94d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * ((y + (-1.0d0)) * x)
    else
        tmp = x + (x * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.94) || !(z <= 1.0)) {
		tmp = z * ((y + -1.0) * x);
	} else {
		tmp = x + (x * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.94) or not (z <= 1.0):
		tmp = z * ((y + -1.0) * x)
	else:
		tmp = x + (x * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.94) || !(z <= 1.0))
		tmp = Float64(z * Float64(Float64(y + -1.0) * x));
	else
		tmp = Float64(x + Float64(x * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.94) || ~((z <= 1.0)))
		tmp = z * ((y + -1.0) * x);
	else
		tmp = x + (x * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.94], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * N[(N[(y + -1.0), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.93999999999999995 or 1 < z

   1. Initial program 88.8%

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

   2. Taylor expanded in z around inf 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-*l* 98.3%

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

      3. sub-neg 98.3%

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

      4. metadata-eval 98.3%

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

   4. Simplified 98.3%

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

   if -0.93999999999999995 < z < 1

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in y around inf 99.2%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.94 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(\left(y + -1\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 8: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \left(\left(y + -1\right) \cdot x\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3e-44)
   (* z (* (+ y -1.0) x))
   (if (<= z 1.7e-132) x (* (+ y -1.0) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e-44) {
		tmp = z * ((y + -1.0) * x);
	} else if (z <= 1.7e-132) {
		tmp = x;
	} else {
		tmp = (y + -1.0) * (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 (z <= (-3d-44)) then
        tmp = z * ((y + (-1.0d0)) * x)
    else if (z <= 1.7d-132) then
        tmp = x
    else
        tmp = (y + (-1.0d0)) * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e-44) {
		tmp = z * ((y + -1.0) * x);
	} else if (z <= 1.7e-132) {
		tmp = x;
	} else {
		tmp = (y + -1.0) * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3e-44:
		tmp = z * ((y + -1.0) * x)
	elif z <= 1.7e-132:
		tmp = x
	else:
		tmp = (y + -1.0) * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3e-44)
		tmp = Float64(z * Float64(Float64(y + -1.0) * x));
	elseif (z <= 1.7e-132)
		tmp = x;
	else
		tmp = Float64(Float64(y + -1.0) * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3e-44)
		tmp = z * ((y + -1.0) * x);
	elseif (z <= 1.7e-132)
		tmp = x;
	else
		tmp = (y + -1.0) * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3e-44], N[(z * N[(N[(y + -1.0), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-132], x, N[(N[(y + -1.0), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.0000000000000002e-44

   1. Initial program 91.1%

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

   2. Taylor expanded in z around inf 86.4%

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

      1. *-commutative 86.4%

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

      2. associate-*l* 95.2%

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

      3. sub-neg 95.2%

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

      4. metadata-eval 95.2%

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

   4. Simplified 95.2%

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

   if -3.0000000000000002e-44 < z < 1.69999999999999991e-132

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 81.5%

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

   if 1.69999999999999991e-132 < z

   1. Initial program 89.9%

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

   2. Taylor expanded in z around inf 80.4%

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

      1. associate-*r* 89.2%

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

      2. *-commutative 89.2%

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

      3. sub-neg 89.2%

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

      4. metadata-eval 89.2%

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

   4. Simplified 89.2%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \left(\left(y + -1\right) \cdot x\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 9: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + ((y + -1.0) * (x * 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 + ((y + (-1.0d0)) * (x * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.0%

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

2. Taylor expanded in z around 0 94.0%

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

   1. +-commutative 94.0%

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

   2. associate-*r* 97.6%

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

   3. *-commutative 97.6%

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

   4. fma-def 97.6%

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

   5. sub-neg 97.6%

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

   6. metadata-eval 97.6%

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

4. Applied egg-rr 97.6%

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

   1. fma-udef 97.6%

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

6. Applied egg-rr 97.6%

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

7. Final simplification 97.6%

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

Alternative 10: 64.5% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(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 <= (-1.0d0)) .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 <= -1.0) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 88.8%

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

   2. Taylor expanded in y around 0 54.4%

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

      1. sub-neg 54.4%

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

      2. distribute-rgt-in 54.3%

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

      3. *-lft-identity 54.3%

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

      4. distribute-lft-neg-out 54.3%

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

      5. *-commutative 54.3%

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

      6. unsub-neg 54.3%

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

   4. Simplified 54.3%

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

   5. Taylor expanded in z around inf 52.8%

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

      1. mul-1-neg 52.8%

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

      2. distribute-rgt-neg-in 52.8%

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

   7. Simplified 52.8%

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

   if -1 < z < 1

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 72.5%

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

4. Final simplification 62.1%

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

Alternative 11: 37.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 94.0%

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

2. Taylor expanded in z around 0 36.1%

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

3. Final simplification 36.1%

   \[\leadsto x \]

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 2023290 
(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))))