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

Percentage Accurate: 88.5% → 99.3%

Time: 6.9s

Alternatives: 9

Speedup: 0.6×

• 20.4% 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: 88.5% 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: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+15} \lor \neg \left(y \leq 2 \cdot 10^{+141}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x \cdot \left(1 - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.2e+15) (not (<= y 2e+141)))
   (* y (- 1.0 (/ x z)))
   (+ y (/ (* x (- 1.0 y)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e+15) || !(y <= 2e+141)) {
		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 <= (-7.2d+15)) .or. (.not. (y <= 2d+141))) 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 <= -7.2e+15) || !(y <= 2e+141)) {
		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 <= -7.2e+15) or not (y <= 2e+141):
		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 <= -7.2e+15) || !(y <= 2e+141))
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	else
		tmp = Float64(y + Float64(Float64(x * Float64(1.0 - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.2e+15) || ~((y <= 2e+141)))
		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[Or[LessEqual[y, -7.2e+15], N[Not[LessEqual[y, 2e+141]], $MachinePrecision]], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.2e15 or 2.00000000000000003e141 < y

   1. Initial program 70.9%

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

   3. Taylor expanded in y around inf 70.9%

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

      1. associate-/l* 99.8%

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

      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 -7.2e15 < y < 2.00000000000000003e141

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf 97.4%

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

      1. associate-+r+ 97.4%

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

      2. +-commutative 97.4%

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

      3. mul-1-neg 97.4%

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

      4. unsub-neg 97.4%

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

      5. div-sub 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in z around inf 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+15} \lor \neg \left(y \leq 2 \cdot 10^{+141}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x \cdot \left(1 - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 79.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{-x}{z}\\ \mathbf{if}\;y \leq 4.6 \cdot 10^{+14}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+192}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+260}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+279}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ (- x) z))))
   (if (<= y 4.6e+14)
     (+ y (/ x z))
     (if (<= y 1.45e+192)
       t_0
       (if (<= y 1.16e+260) (/ (* x y) x) (if (<= y 2.5e+279) t_0 y))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (-x / z);
	double tmp;
	if (y <= 4.6e+14) {
		tmp = y + (x / z);
	} else if (y <= 1.45e+192) {
		tmp = t_0;
	} else if (y <= 1.16e+260) {
		tmp = (x * y) / x;
	} else if (y <= 2.5e+279) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = y * (-x / z)
    if (y <= 4.6d+14) then
        tmp = y + (x / z)
    else if (y <= 1.45d+192) then
        tmp = t_0
    else if (y <= 1.16d+260) then
        tmp = (x * y) / x
    else if (y <= 2.5d+279) then
        tmp = t_0
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (-x / z);
	double tmp;
	if (y <= 4.6e+14) {
		tmp = y + (x / z);
	} else if (y <= 1.45e+192) {
		tmp = t_0;
	} else if (y <= 1.16e+260) {
		tmp = (x * y) / x;
	} else if (y <= 2.5e+279) {
		tmp = t_0;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (-x / z)
	tmp = 0
	if y <= 4.6e+14:
		tmp = y + (x / z)
	elif y <= 1.45e+192:
		tmp = t_0
	elif y <= 1.16e+260:
		tmp = (x * y) / x
	elif y <= 2.5e+279:
		tmp = t_0
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(Float64(-x) / z))
	tmp = 0.0
	if (y <= 4.6e+14)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 1.45e+192)
		tmp = t_0;
	elseif (y <= 1.16e+260)
		tmp = Float64(Float64(x * y) / x);
	elseif (y <= 2.5e+279)
		tmp = t_0;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (-x / z);
	tmp = 0.0;
	if (y <= 4.6e+14)
		tmp = y + (x / z);
	elseif (y <= 1.45e+192)
		tmp = t_0;
	elseif (y <= 1.16e+260)
		tmp = (x * y) / x;
	elseif (y <= 2.5e+279)
		tmp = t_0;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[((-x) / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 4.6e+14], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+192], t$95$0, If[LessEqual[y, 1.16e+260], N[(N[(x * y), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[y, 2.5e+279], t$95$0, y]]]]]

Derivation

1. Split input into 4 regimes

2. if y < 4.6e14

   1. Initial program 90.8%

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

   3. Taylor expanded in x around inf 90.6%

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

      1. associate-+r+ 90.6%

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

      2. +-commutative 90.6%

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

      3. mul-1-neg 90.6%

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

      4. unsub-neg 90.6%

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

      5. div-sub 90.6%

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

   5. Simplified 90.6%

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

   6. Taylor expanded in z around inf 97.2%

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

   7. Taylor expanded in y around 0 87.2%

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

   if 4.6e14 < y < 1.4500000000000001e192 or 1.16e260 < y < 2.5000000000000001e279

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf 92.3%

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

      1. associate-/l* 99.8%

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

      2. div-sub 99.8%

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

      3. *-inverses 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around inf 86.5%

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

      1. mul-1-neg 86.5%

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

      2. distribute-neg-frac2 86.5%

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

   8. Simplified 86.5%

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

   if 1.4500000000000001e192 < y < 1.16e260

   1. Initial program 57.4%

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

   3. Taylor expanded in x around inf 57.0%

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

      1. associate-+r+ 57.0%

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

      2. +-commutative 57.0%

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

      3. mul-1-neg 57.0%

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

      4. unsub-neg 57.0%

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

      5. div-sub 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in z around inf 27.1%

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

      1. associate-*r/ 76.4%

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

   8. Applied egg-rr 76.4%

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

   if 2.5000000000000001e279 < y

   1. Initial program 40.5%

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

   3. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+14}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+192}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+260}:\\ \;\;\;\;\frac{x \cdot y}{x}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+279}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+38} \lor \neg \left(x \leq 1.8 \cdot 10^{-30}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2e+38) (not (<= x 1.8e-30)))
   (* x (/ (- 1.0 y) z))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2e+38) || !(x <= 1.8e-30)) {
		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 <= (-2d+38)) .or. (.not. (x <= 1.8d-30))) 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 <= -2e+38) || !(x <= 1.8e-30)) {
		tmp = x * ((1.0 - y) / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2e+38) or not (x <= 1.8e-30):
		tmp = x * ((1.0 - y) / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2e+38) || !(x <= 1.8e-30))
		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 <= -2e+38) || ~((x <= 1.8e-30)))
		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, -2e+38], N[Not[LessEqual[x, 1.8e-30]], $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 < -1.99999999999999995e38 or 1.8000000000000002e-30 < x

   1. Initial program 89.7%

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

   3. Taylor expanded in x around inf 98.9%

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

      1. associate-+r+ 98.9%

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

      2. +-commutative 98.9%

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

      3. mul-1-neg 98.9%

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

      4. unsub-neg 98.9%

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

      5. div-sub 99.0%

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

   5. Simplified 99.0%

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

   6. Taylor expanded in z around 0 86.8%

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

   if -1.99999999999999995e38 < x < 1.8000000000000002e-30

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf 78.1%

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

      1. associate-+r+ 78.1%

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

      2. +-commutative 78.1%

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

      3. mul-1-neg 78.1%

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

      4. unsub-neg 78.1%

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

      5. div-sub 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in z around inf 99.3%

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

   7. Taylor expanded in y around 0 88.5%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+38} \lor \neg \left(x \leq 1.8 \cdot 10^{-30}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -24 \lor \neg \left(y \leq 2.1 \cdot 10^{-14}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -24.0) (not (<= y 2.1e-14)))
   (* y (- 1.0 (/ x z)))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -24.0) || !(y <= 2.1e-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 <= (-24.0d0)) .or. (.not. (y <= 2.1d-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 <= -24.0) || !(y <= 2.1e-14)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -24.0) or not (y <= 2.1e-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 <= -24.0) || !(y <= 2.1e-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 <= -24.0) || ~((y <= 2.1e-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, -24.0], N[Not[LessEqual[y, 2.1e-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 < -24 or 2.0999999999999999e-14 < y

   1. Initial program 77.4%

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

   3. Taylor expanded in y around inf 76.4%

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

      1. associate-/l* 98.9%

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

      2. div-sub 98.9%

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

      3. *-inverses 98.9%

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

   5. Simplified 98.9%

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

   if -24 < y < 2.0999999999999999e-14

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 99.8%

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

      1. associate-+r+ 99.8%

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

      2. +-commutative 99.8%

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

      3. mul-1-neg 99.8%

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

      4. unsub-neg 99.8%

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

      5. div-sub 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 100.0%

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

   7. Taylor expanded in y around 0 99.5%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -24 \lor \neg \left(y \leq 2.1 \cdot 10^{-14}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+14}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+191}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 4.6e+14) (+ y (/ x z)) (if (<= y 2.45e+191) (* x (/ (- y) z)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.6e+14) {
		tmp = y + (x / z);
	} else if (y <= 2.45e+191) {
		tmp = x * (-y / 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 (y <= 4.6d+14) then
        tmp = y + (x / z)
    else if (y <= 2.45d+191) then
        tmp = x * (-y / z)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.6e+14) {
		tmp = y + (x / z);
	} else if (y <= 2.45e+191) {
		tmp = x * (-y / z);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 4.6e+14:
		tmp = y + (x / z)
	elif y <= 2.45e+191:
		tmp = x * (-y / z)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 4.6e+14)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 2.45e+191)
		tmp = Float64(x * Float64(Float64(-y) / z));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 4.6e+14)
		tmp = y + (x / z);
	elseif (y <= 2.45e+191)
		tmp = x * (-y / z);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 4.6e+14], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45e+191], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < 4.6e14

   1. Initial program 90.8%

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

   3. Taylor expanded in x around inf 90.6%

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

      1. associate-+r+ 90.6%

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

      2. +-commutative 90.6%

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

      3. mul-1-neg 90.6%

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

      4. unsub-neg 90.6%

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

      5. div-sub 90.6%

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

   5. Simplified 90.6%

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

   6. Taylor expanded in z around inf 97.2%

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

   7. Taylor expanded in y around 0 87.2%

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

   if 4.6e14 < y < 2.45e191

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 91.5%

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

      1. associate-/l* 99.8%

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

      2. div-sub 99.8%

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

      3. *-inverses 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around inf 79.5%

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

      1. mul-1-neg 79.5%

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

      2. distribute-neg-frac2 79.5%

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

      3. associate-*r/ 70.8%

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

   8. Simplified 70.8%

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

   if 2.45e191 < y

   1. Initial program 64.0%

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

   3. Taylor expanded in x around 0 59.9%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.6 \cdot 10^{+14}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+191}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.2 \cdot 10^{-20}:\\ \;\;\;\;y + \frac{x \cdot \left(1 - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{1 - y}{z} + \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 4.2e-20)
   (+ y (/ (* x (- 1.0 y)) z))
   (* x (+ (/ (- 1.0 y) z) (/ y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.2e-20) {
		tmp = y + ((x * (1.0 - y)) / z);
	} else {
		tmp = x * (((1.0 - y) / z) + (y / 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 (x <= 4.2d-20) then
        tmp = y + ((x * (1.0d0 - y)) / z)
    else
        tmp = x * (((1.0d0 - y) / z) + (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.2e-20) {
		tmp = y + ((x * (1.0 - y)) / z);
	} else {
		tmp = x * (((1.0 - y) / z) + (y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 4.2e-20:
		tmp = y + ((x * (1.0 - y)) / z)
	else:
		tmp = x * (((1.0 - y) / z) + (y / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 4.2e-20)
		tmp = Float64(y + Float64(Float64(x * Float64(1.0 - y)) / z));
	else
		tmp = Float64(x * Float64(Float64(Float64(1.0 - y) / z) + Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 4.2e-20)
		tmp = y + ((x * (1.0 - y)) / z);
	else
		tmp = x * (((1.0 - y) / z) + (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 4.2e-20], N[(y + N[(N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(1.0 - y), $MachinePrecision] / z), $MachinePrecision] + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.1999999999999998e-20

   1. Initial program 89.8%

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

   3. Taylor expanded in x around inf 82.9%

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

      1. associate-+r+ 82.9%

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

      2. +-commutative 82.9%

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

      3. mul-1-neg 82.9%

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

      4. unsub-neg 82.9%

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

      5. div-sub 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in z around inf 98.0%

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

   if 4.1999999999999998e-20 < x

   1. Initial program 86.6%

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

   3. Taylor expanded in x around inf 99.8%

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

      1. associate-+r+ 99.8%

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

      2. +-commutative 99.8%

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

      3. mul-1-neg 99.8%

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

      4. unsub-neg 99.8%

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

      5. div-sub 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.2 \cdot 10^{-20}:\\ \;\;\;\;y + \frac{x \cdot \left(1 - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{1 - y}{z} + \frac{y}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-59}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.1e-59) y (if (<= z 2.65e+23) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.1e-59) {
		tmp = y;
	} else if (z <= 2.65e+23) {
		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 (z <= (-2.1d-59)) then
        tmp = y
    else if (z <= 2.65d+23) 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 (z <= -2.1e-59) {
		tmp = y;
	} else if (z <= 2.65e+23) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.1e-59:
		tmp = y
	elif z <= 2.65e+23:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.1e-59)
		tmp = y;
	elseif (z <= 2.65e+23)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.1e-59)
		tmp = y;
	elseif (z <= 2.65e+23)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.1e-59], y, If[LessEqual[z, 2.65e+23], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if z < -2.09999999999999997e-59 or 2.6500000000000001e23 < z

   1. Initial program 76.2%

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

   3. Taylor expanded in x around 0 72.6%

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

   if -2.09999999999999997e-59 < z < 2.6500000000000001e23

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 54.2%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-59}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.2% 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 89.0%

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

3. Taylor expanded in x around inf 87.0%

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

   1. associate-+r+ 87.0%

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

   2. +-commutative 87.0%

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

   3. mul-1-neg 87.0%

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

   4. unsub-neg 87.0%

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

   5. div-sub 87.0%

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

5. Simplified 87.0%

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

6. Taylor expanded in z around inf 95.9%

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

7. Taylor expanded in y around 0 76.1%

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

8. Final simplification 76.1%

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

Alternative 9: 40.3% 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 89.0%

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

3. Taylor expanded in x around 0 40.0%

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

4. Final simplification 40.0%

   \[\leadsto y \]
5. Add Preprocessing

Developer target: 94.0% 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 2024053 
(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))