Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3

Percentage Accurate: 88.1% → 97.5%

Time: 7.9s

Alternatives: 10

Speedup: 0.6×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y \cdot \left(z - x\right)}{z}\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;y + x \cdot \frac{1 - y}{z}\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+264}:\\ \;\;\;\;y + \left(\frac{x}{z} - \frac{x \cdot y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x (* y (- z x))) z)))
   (if (<= t_0 (- INFINITY))
     (+ y (* x (/ (- 1.0 y) z)))
     (if (<= t_0 5e+264)
       (+ y (- (/ x z) (/ (* x y) z)))
       (* y (- 1.0 (/ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + (y * (z - x))) / z;
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = y + (x * ((1.0 - y) / z));
	} else if (t_0 <= 5e+264) {
		tmp = y + ((x / z) - ((x * y) / z));
	} else {
		tmp = y * (1.0 - (x / z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + (y * (z - x))) / z;
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = y + (x * ((1.0 - y) / z));
	} else if (t_0 <= 5e+264) {
		tmp = y + ((x / z) - ((x * y) / z));
	} else {
		tmp = y * (1.0 - (x / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + (y * (z - x))) / z
	tmp = 0
	if t_0 <= -math.inf:
		tmp = y + (x * ((1.0 - y) / z))
	elif t_0 <= 5e+264:
		tmp = y + ((x / z) - ((x * y) / z))
	else:
		tmp = y * (1.0 - (x / z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + Float64(y * Float64(z - x))) / z)
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(y + Float64(x * Float64(Float64(1.0 - y) / z)));
	elseif (t_0 <= 5e+264)
		tmp = Float64(y + Float64(Float64(x / z) - Float64(Float64(x * y) / z)));
	else
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + (y * (z - x))) / z;
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = y + (x * ((1.0 - y) / z));
	elseif (t_0 <= 5e+264)
		tmp = y + ((x / z) - ((x * y) / z));
	else
		tmp = y * (1.0 - (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(y + N[(x * N[(N[(1.0 - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+264], N[(y + N[(N[(x / z), $MachinePrecision] - N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 74.3%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 64.7%

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

   4. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. neg-mul-1 100.0%

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

      3. sub-neg 100.0%

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

      4. div-sub 100.0%

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

   6. Simplified 100.0%

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

   if -inf.0 < (/.f64 (+.f64 x (*.f64 y (-.f64 z x))) z) < 5.00000000000000033e264

   1. Initial program 99.8%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.9%

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

   if 5.00000000000000033e264 < (/.f64 (+.f64 x (*.f64 y (-.f64 z x))) z)

   1. Initial program 53.0%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 48.7%

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

      1. associate-/l* 99.9%

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

      2. div-sub 100.0%

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

      3. *-inverses 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y \cdot \left(z - x\right)}{z} \leq -\infty:\\ \;\;\;\;y + x \cdot \frac{1 - y}{z}\\ \mathbf{elif}\;\frac{x + y \cdot \left(z - x\right)}{z} \leq 5 \cdot 10^{+264}:\\ \;\;\;\;y + \left(\frac{x}{z} - \frac{x \cdot y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -56000000000000 \lor \neg \left(y \leq 9.4 \cdot 10^{+23}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -56000000000000.0) (not (<= y 9.4e+23)))
   (* y (- 1.0 (/ x z)))
   (/ (+ x (* y (- z x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -56000000000000.0) || !(y <= 9.4e+23)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-56000000000000.0d0)) .or. (.not. (y <= 9.4d+23))) then
        tmp = y * (1.0d0 - (x / z))
    else
        tmp = (x + (y * (z - x))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -56000000000000.0) || !(y <= 9.4e+23)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -56000000000000.0) or not (y <= 9.4e+23):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = (x + (y * (z - x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -56000000000000.0) || !(y <= 9.4e+23))
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z - x))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -56000000000000.0) || ~((y <= 9.4e+23)))
		tmp = y * (1.0 - (x / z));
	else
		tmp = (x + (y * (z - x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -56000000000000.0], N[Not[LessEqual[y, 9.4e+23]], $MachinePrecision]], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6e13 or 9.3999999999999994e23 < y

   1. Initial program 74.5%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 74.5%

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

      1. associate-/l* 99.9%

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

      2. div-sub 99.9%

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

      3. *-inverses 99.9%

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

   5. Simplified 99.9%

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

   if -5.6e13 < y < 9.3999999999999994e23

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -56000000000000 \lor \neg \left(y \leq 9.4 \cdot 10^{+23}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-21} \lor \neg \left(x \leq 9.8 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e-21) (not (<= x 9.8e-6)))
   (* x (/ (- 1.0 y) z))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e-21) || !(x <= 9.8e-6)) {
		tmp = x * ((1.0 - y) / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-5.8d-21)) .or. (.not. (x <= 9.8d-6))) then
        tmp = x * ((1.0d0 - y) / z)
    else
        tmp = y + (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e-21) || !(x <= 9.8e-6)) {
		tmp = x * ((1.0 - y) / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.8e-21) or not (x <= 9.8e-6):
		tmp = x * ((1.0 - y) / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e-21) || !(x <= 9.8e-6))
		tmp = Float64(x * Float64(Float64(1.0 - y) / z));
	else
		tmp = Float64(y + Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.8e-21) || ~((x <= 9.8e-6)))
		tmp = x * ((1.0 - y) / z);
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e-21], N[Not[LessEqual[x, 9.8e-6]], $MachinePrecision]], N[(x * N[(N[(1.0 - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.8e-21 or 9.79999999999999934e-6 < x

   1. Initial program 89.3%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 83.5%

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

      1. associate-/l* 87.8%

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

      2. mul-1-neg 87.8%

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

      3. unsub-neg 87.8%

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

   5. Simplified 87.8%

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

   if -5.8e-21 < x < 9.79999999999999934e-6

   1. Initial program 84.7%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.9%

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

   4. Taylor expanded in y around 0 84.1%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-21} \lor \neg \left(x \leq 9.8 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2.45 \cdot 10^{-14}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 2.45e-14)))
   (* y (- 1.0 (/ x z)))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 2.45e-14)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 2.45d-14))) then
        tmp = y * (1.0d0 - (x / z))
    else
        tmp = y + (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 2.45e-14)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 2.45e-14):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 2.45e-14))
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	else
		tmp = Float64(y + Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 2.45e-14)))
		tmp = y * (1.0 - (x / z));
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 2.45e-14]], $MachinePrecision]], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 2.44999999999999997e-14 < y

   1. Initial program 76.6%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.1%

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

      1. associate-/l* 99.4%

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

      2. div-sub 99.4%

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

      3. *-inverses 99.4%

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

   5. Simplified 99.4%

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

   if -1 < y < 2.44999999999999997e-14

   1. Initial program 99.9%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.1%

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

   4. Taylor expanded in y around 0 100.0%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2.45 \cdot 10^{-14}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 10^{-27}:\\ \;\;\;\;y + \frac{1}{\frac{z}{x \cdot \left(1 - y\right)}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{1 - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1e-27)
   (+ y (/ 1.0 (/ z (* x (- 1.0 y)))))
   (+ y (* x (/ (- 1.0 y) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1e-27) {
		tmp = y + (1.0 / (z / (x * (1.0 - y))));
	} else {
		tmp = y + (x * ((1.0 - 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 <= 1d-27) then
        tmp = y + (1.0d0 / (z / (x * (1.0d0 - y))))
    else
        tmp = y + (x * ((1.0d0 - y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1e-27) {
		tmp = y + (1.0 / (z / (x * (1.0 - y))));
	} else {
		tmp = y + (x * ((1.0 - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1e-27:
		tmp = y + (1.0 / (z / (x * (1.0 - y))))
	else:
		tmp = y + (x * ((1.0 - y) / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1e-27)
		tmp = Float64(y + Float64(1.0 / Float64(z / Float64(x * Float64(1.0 - y)))));
	else
		tmp = Float64(y + Float64(x * Float64(Float64(1.0 - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1e-27)
		tmp = y + (1.0 / (z / (x * (1.0 - y))));
	else
		tmp = y + (x * ((1.0 - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1e-27], N[(y + N[(1.0 / N[(z / N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x * N[(N[(1.0 - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1e-27

   1. Initial program 90.6%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.3%

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

   4. Taylor expanded in x around 0 93.5%

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

      1. +-commutative 93.5%

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

      2. neg-mul-1 93.5%

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

      3. sub-neg 93.5%

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

      4. div-sub 93.5%

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

   6. Simplified 93.5%

      \[\leadsto y + \color{blue}{x \cdot \frac{1 - y}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 98.0%

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

      2. clear-num 97.9%

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

      3. sub-neg 97.9%

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

      4. distribute-rgt-in 97.9%

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

      5. *-un-lft-identity 97.9%

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

      6. distribute-lft-neg-in 97.9%

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

      7. distribute-rgt-neg-out 97.9%

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

      8. +-commutative 97.9%

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

      9. *-commutative 97.9%

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

      10. fma-define 97.9%

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

      11. add-sqr-sqrt 54.6%

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

      12. sqrt-unprod 69.2%

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

      13. sqr-neg 69.2%

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

      14. sqrt-unprod 27.9%

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

      15. add-sqr-sqrt 63.2%

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

   8. Applied egg-rr 63.2%

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

      1. /-rgt-identity 63.2%

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

      2. clear-num 63.2%

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

      3. associate-/r/ 63.1%

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

      4. fma-undefine 63.1%

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

      5. distribute-lft-in 61.1%

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

      6. add-sqr-sqrt 39.6%

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

      7. sqrt-unprod 66.7%

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

      8. sqr-neg 66.7%

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

      9. mul-1-neg 66.7%

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

      10. mul-1-neg 66.7%

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

      11. sqrt-unprod 51.9%

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

      12. add-sqr-sqrt 89.0%

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

      13. *-commutative 89.0%

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

      14. div-inv 89.2%

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

      15. +-commutative 89.2%

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

      16. *-un-lft-identity 89.2%

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

      17. *-commutative 89.2%

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

      18. mul-1-neg 89.2%

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

      19. associate-*r* 90.5%

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

   10. Applied egg-rr 98.0%

       \[\leadsto y + \frac{1}{\color{blue}{z \cdot \frac{\frac{1}{1 - y}}{x}}} \]
   11. Step-by-step derivation

       1. associate-/l/ 97.9%

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

       2. associate-*r/ 97.9%

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

       3. *-rgt-identity 97.9%

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

   12. Simplified 97.9%

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

   if 1e-27 < z

   1. Initial program 76.0%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.4%

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

   4. Taylor expanded in x around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. neg-mul-1 99.8%

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

      3. sub-neg 99.8%

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

      4. div-sub 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 10^{-27}:\\ \;\;\;\;y + \frac{1}{\frac{z}{x \cdot \left(1 - y\right)}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{1 - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{1 - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+65) (* y (- 1.0 (/ x z))) (+ y (* x (/ (- 1.0 y) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+65) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x * ((1.0 - 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 (y <= (-2d+65)) then
        tmp = y * (1.0d0 - (x / z))
    else
        tmp = y + (x * ((1.0d0 - y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+65) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x * ((1.0 - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+65:
		tmp = y * (1.0 - (x / z))
	else:
		tmp = y + (x * ((1.0 - y) / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+65)
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	else
		tmp = Float64(y + Float64(x * Float64(Float64(1.0 - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2e+65)
		tmp = y * (1.0 - (x / z));
	else
		tmp = y + (x * ((1.0 - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+65], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x * N[(N[(1.0 - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2e65

   1. Initial program 77.4%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 77.4%

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

      1. associate-/l* 99.9%

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

      2. div-sub 100.0%

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

      3. *-inverses 100.0%

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

   5. Simplified 100.0%

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

   if -2e65 < y

   1. Initial program 89.7%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 88.8%

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

   4. Taylor expanded in x around 0 97.9%

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

      1. +-commutative 97.9%

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

      2. neg-mul-1 97.9%

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

      3. sub-neg 97.9%

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

      4. div-sub 97.9%

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

   6. Simplified 97.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{1 - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{-27} \lor \neg \left(x \leq 1.5 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.1e-27) (not (<= x 1.5e-8))) (/ x z) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.1e-27) || !(x <= 1.5e-8)) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	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 ((x <= (-6.1d-27)) .or. (.not. (x <= 1.5d-8))) then
        tmp = x / z
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.1e-27) || !(x <= 1.5e-8)) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.1e-27) or not (x <= 1.5e-8):
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.1e-27) || !(x <= 1.5e-8))
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.1e-27) || ~((x <= 1.5e-8)))
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.1e-27], N[Not[LessEqual[x, 1.5e-8]], $MachinePrecision]], N[(x / z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -6.0999999999999999e-27 or 1.49999999999999987e-8 < x

   1. Initial program 89.0%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 55.8%

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

   if -6.0999999999999999e-27 < x < 1.49999999999999987e-8

   1. Initial program 84.8%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 64.3%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{-27} \lor \neg \left(x \leq 1.5 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.45 \cdot 10^{-14}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.45e-14) (+ y (/ x z)) (- y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.45e-14) {
		tmp = y + (x / z);
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 2.45d-14) then
        tmp = y + (x / z)
    else
        tmp = y - (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.45e-14) {
		tmp = y + (x / z);
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.45e-14:
		tmp = y + (x / z)
	else:
		tmp = y - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.45e-14)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(y - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.45e-14)
		tmp = y + (x / z);
	else
		tmp = y - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.45e-14], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.44999999999999997e-14

   1. Initial program 93.0%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 96.7%

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

   4. Taylor expanded in y around 0 85.2%

      \[\leadsto y + \color{blue}{\frac{x}{z}} \]

   if 2.44999999999999997e-14 < y

   1. Initial program 73.8%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 72.6%

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

   4. Taylor expanded in y around 0 50.7%

      \[\leadsto y + \color{blue}{\frac{x}{z}} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 23.4%

         \[\leadsto y + \frac{x}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}} \]

      2. sqrt-unprod 62.5%

         \[\leadsto y + \frac{x}{\color{blue}{\sqrt{z \cdot z}}} \]

      3. sqr-neg 62.5%

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

      4. sqrt-unprod 37.2%

         \[\leadsto y + \frac{x}{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}} \]

      5. add-sqr-sqrt 72.3%

         \[\leadsto y + \frac{x}{\color{blue}{-z}} \]

      6. distribute-neg-frac2 72.3%

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

      7. sub-neg 72.3%

         \[\leadsto \color{blue}{y - \frac{x}{z}} \]

   6. Applied egg-rr 72.3%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.45 \cdot 10^{-14}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ y + \frac{x}{z} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return y + (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 = y + (x / z)
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(y + Float64(x / z))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.1%

   \[\frac{x + y \cdot \left(z - x\right)}{z} \]
2. Add Preprocessing

3. Taylor expanded in z around inf 89.3%

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

4. Taylor expanded in y around 0 74.5%

   \[\leadsto y + \color{blue}{\frac{x}{z}} \]

5. Final simplification 74.5%

   \[\leadsto y + \frac{x}{z} \]
6. Add Preprocessing

Alternative 10: 39.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 87.1%

   \[\frac{x + y \cdot \left(z - x\right)}{z} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 37.3%

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

4. Final simplification 37.3%

   \[\leadsto y \]
5. Add Preprocessing

Developer target: 94.2% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (- (+ y (/ x z)) (/ y (/ z x))))

C

double code(double x, double y, double z) {
	return (y + (x / z)) - (y / (z / 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 = (y + (x / z)) - (y / (z / x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024077 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :alt
  (- (+ y (/ x z)) (/ y (/ z x)))

  (/ (+ x (* y (- z x))) z))