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

Percentage Accurate: 87.9% → 99.9%

Time: 9.4s

Alternatives: 8

Speedup: 1.0×

• 20.0% 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: 87.9% 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: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (-1.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.5%

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

2. Taylor expanded in x around inf 97.7%

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

   1. +-commutative 97.7%

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

   2. distribute-rgt-in 97.8%

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

   3. *-commutative 97.8%

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

   4. associate-*r* 97.8%

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

   5. neg-mul-1 97.8%

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

   6. metadata-eval 97.8%

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

   7. distribute-lft-neg-in 97.8%

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

   8. distribute-rgt-neg-in 97.8%

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

   9. distribute-rgt-in 97.7%

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

   10. neg-mul-1 97.7%

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

   11. metadata-eval 97.7%

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

   12. sub-neg 97.7%

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

   13. associate-*r* 97.7%

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

   14. associate-*r/ 97.7%

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

   15. mul-1-neg 97.7%

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

   16. unsub-neg 97.7%

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

   17. associate-/l* 95.9%

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

   18. associate-/r/ 100.0%

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

   19. sub-neg 100.0%

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

   20. metadata-eval 100.0%

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

4. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 60.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.04 \cdot 10^{-132}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-192}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ y z))))
   (if (<= y -9.5e+16)
     t_0
     (if (<= y -1.04e-132)
       (/ x z)
       (if (<= y -3.35e-192) y (if (<= y 2.1e-45) (/ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y / z);
	double tmp;
	if (y <= -9.5e+16) {
		tmp = t_0;
	} else if (y <= -1.04e-132) {
		tmp = x / z;
	} else if (y <= -3.35e-192) {
		tmp = y;
	} else if (y <= 2.1e-45) {
		tmp = x / z;
	} 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 / z)
    if (y <= (-9.5d+16)) then
        tmp = t_0
    else if (y <= (-1.04d-132)) then
        tmp = x / z
    else if (y <= (-3.35d-192)) then
        tmp = y
    else if (y <= 2.1d-45) then
        tmp = x / z
    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 / z);
	double tmp;
	if (y <= -9.5e+16) {
		tmp = t_0;
	} else if (y <= -1.04e-132) {
		tmp = x / z;
	} else if (y <= -3.35e-192) {
		tmp = y;
	} else if (y <= 2.1e-45) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y / z)
	tmp = 0
	if y <= -9.5e+16:
		tmp = t_0
	elif y <= -1.04e-132:
		tmp = x / z
	elif y <= -3.35e-192:
		tmp = y
	elif y <= 2.1e-45:
		tmp = x / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y / z))
	tmp = 0.0
	if (y <= -9.5e+16)
		tmp = t_0;
	elseif (y <= -1.04e-132)
		tmp = Float64(x / z);
	elseif (y <= -3.35e-192)
		tmp = y;
	elseif (y <= 2.1e-45)
		tmp = Float64(x / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y / z);
	tmp = 0.0;
	if (y <= -9.5e+16)
		tmp = t_0;
	elseif (y <= -1.04e-132)
		tmp = x / z;
	elseif (y <= -3.35e-192)
		tmp = y;
	elseif (y <= 2.1e-45)
		tmp = x / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+16], t$95$0, If[LessEqual[y, -1.04e-132], N[(x / z), $MachinePrecision], If[LessEqual[y, -3.35e-192], y, If[LessEqual[y, 2.1e-45], N[(x / z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5e16 or 2.09999999999999995e-45 < y

   1. Initial program 83.8%

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

   2. Taylor expanded in z around inf 54.2%

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

   3. Taylor expanded in x around 0 47.1%

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

      1. *-commutative 47.1%

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

   5. Simplified 47.1%

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

      1. *-commutative 47.1%

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

      2. associate-/l* 60.4%

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

      3. associate-/r/ 61.6%

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

   7. Applied egg-rr 61.6%

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

   if -9.5e16 < y < -1.04e-132 or -3.34999999999999995e-192 < y < 2.09999999999999995e-45

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 77.8%

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

   if -1.04e-132 < y < -3.34999999999999995e-192

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 82.1%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -1.04 \cdot 10^{-132}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-192}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]

Alternative 3: 58.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+16}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-133} \lor \neg \left(y \leq -3.35 \cdot 10^{-192}\right) \land y \leq 1.4 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.5e+16)
   y
   (if (or (<= y -5.1e-133) (and (not (<= y -3.35e-192)) (<= y 1.4e-45)))
     (/ x z)
     y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.5e+16) {
		tmp = y;
	} else if ((y <= -5.1e-133) || (!(y <= -3.35e-192) && (y <= 1.4e-45))) {
		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 (y <= (-9.5d+16)) then
        tmp = y
    else if ((y <= (-5.1d-133)) .or. (.not. (y <= (-3.35d-192))) .and. (y <= 1.4d-45)) 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 (y <= -9.5e+16) {
		tmp = y;
	} else if ((y <= -5.1e-133) || (!(y <= -3.35e-192) && (y <= 1.4e-45))) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.5e+16:
		tmp = y
	elif (y <= -5.1e-133) or (not (y <= -3.35e-192) and (y <= 1.4e-45)):
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.5e+16)
		tmp = y;
	elseif ((y <= -5.1e-133) || (!(y <= -3.35e-192) && (y <= 1.4e-45)))
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.5e+16)
		tmp = y;
	elseif ((y <= -5.1e-133) || (~((y <= -3.35e-192)) && (y <= 1.4e-45)))
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.5e+16], y, If[Or[LessEqual[y, -5.1e-133], And[N[Not[LessEqual[y, -3.35e-192]], $MachinePrecision], LessEqual[y, 1.4e-45]]], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5e16 or -5.0999999999999999e-133 < y < -3.34999999999999995e-192 or 1.4000000000000001e-45 < y

   1. Initial program 85.1%

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

   2. Taylor expanded in x around 0 62.0%

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

   if -9.5e16 < y < -5.0999999999999999e-133 or -3.34999999999999995e-192 < y < 1.4000000000000001e-45

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 77.8%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+16}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-133} \lor \neg \left(y \leq -3.35 \cdot 10^{-192}\right) \land y \leq 1.4 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 4: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+33} \lor \neg \left(x \leq 1.15 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.9e+33) (not (<= x 1.15e+44)))
   (* (/ x z) (- 1.0 y))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.9e+33) || !(x <= 1.15e+44)) {
		tmp = (x / z) * (1.0 - y);
	} 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 <= (-3.9d+33)) .or. (.not. (x <= 1.15d+44))) then
        tmp = (x / z) * (1.0d0 - y)
    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 <= -3.9e+33) || !(x <= 1.15e+44)) {
		tmp = (x / z) * (1.0 - y);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.9e+33) or not (x <= 1.15e+44):
		tmp = (x / z) * (1.0 - y)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.9e+33) || !(x <= 1.15e+44))
		tmp = Float64(Float64(x / z) * Float64(1.0 - y));
	else
		tmp = Float64(y + Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.9e+33) || ~((x <= 1.15e+44)))
		tmp = (x / z) * (1.0 - y);
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.9e+33], N[Not[LessEqual[x, 1.15e+44]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.9000000000000002e33 or 1.15000000000000002e44 < x

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf 90.8%

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

      1. associate-/l* 93.7%

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

      2. associate-/r/ 93.7%

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

      3. mul-1-neg 93.7%

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

      4. unsub-neg 93.7%

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

   4. Simplified 93.7%

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

   if -3.9000000000000002e33 < x < 1.15000000000000002e44

   1. Initial program 89.3%

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

   2. Taylor expanded in x around inf 99.4%

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

      1. +-commutative 99.4%

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

      2. distribute-rgt-in 99.4%

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

      3. *-commutative 99.4%

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

      4. associate-*r* 99.4%

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

      5. neg-mul-1 99.4%

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

      6. metadata-eval 99.4%

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

      7. distribute-lft-neg-in 99.4%

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

      8. distribute-rgt-neg-in 99.4%

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

      9. distribute-rgt-in 99.4%

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

      10. neg-mul-1 99.4%

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

      11. metadata-eval 99.4%

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

      12. sub-neg 99.4%

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

      13. associate-*r* 99.4%

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

      14. associate-*r/ 99.4%

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

      15. mul-1-neg 99.4%

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

      16. unsub-neg 99.4%

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

      17. associate-/l* 93.5%

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

      18. associate-/r/ 100.0%

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

      19. sub-neg 100.0%

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

      20. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 90.0%

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

      1. mul-1-neg 90.0%

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

      2. distribute-frac-neg 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in y around 0 90.0%

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

      1. +-commutative 90.0%

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

   10. Simplified 90.0%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+33} \lor \neg \left(x \leq 1.15 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 5: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 4.3 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 4.3e-12))) (/ y (/ z (- z x))) (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 4.3e-12)) {
		tmp = y / (z / (z - x));
	} 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 <= 4.3d-12))) then
        tmp = y / (z / (z - x))
    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 <= 4.3e-12)) {
		tmp = y / (z / (z - x));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 4.3e-12):
		tmp = y / (z / (z - x))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 4.3e-12))
		tmp = Float64(y / Float64(z / Float64(z - x)));
	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 <= 4.3e-12)))
		tmp = y / (z / (z - x));
	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, 4.3e-12]], $MachinePrecision]], N[(y / N[(z / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 4.29999999999999985e-12 < y

   1. Initial program 83.2%

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

   2. Taylor expanded in y around inf 81.8%

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

      1. associate-/l* 98.5%

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

   4. Simplified 98.5%

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

   if -1 < y < 4.29999999999999985e-12

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-rgt-in 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*r* 100.0%

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

      5. neg-mul-1 100.0%

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

      6. metadata-eval 100.0%

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

      7. distribute-lft-neg-in 100.0%

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

      8. distribute-rgt-neg-in 100.0%

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

      9. distribute-rgt-in 100.0%

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

      10. neg-mul-1 100.0%

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

      11. metadata-eval 100.0%

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

      12. sub-neg 100.0%

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

      13. associate-*r* 100.0%

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

      14. associate-*r/ 100.0%

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

      15. mul-1-neg 100.0%

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

      16. unsub-neg 100.0%

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

      17. associate-/l* 100.0%

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

      18. associate-/r/ 100.0%

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

      19. sub-neg 100.0%

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

      20. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.0%

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

      1. mul-1-neg 99.0%

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

      2. distribute-frac-neg 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in y around 0 99.0%

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

      1. +-commutative 99.0%

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

   10. Simplified 99.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 4.3 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 6: 77.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.8 \cdot 10^{+206}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 2.8e+206) (+ y (/ x z)) (/ (- y) (/ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.8e+206) {
		tmp = y + (x / z);
	} else {
		tmp = -y / (z / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 2.8d+206) then
        tmp = y + (x / z)
    else
        tmp = -y / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.8e+206) {
		tmp = y + (x / z);
	} else {
		tmp = -y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2.8e+206:
		tmp = y + (x / z)
	else:
		tmp = -y / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2.8e+206)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(Float64(-y) / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 2.8e+206)
		tmp = y + (x / z);
	else
		tmp = -y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2.8e+206], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[((-y) / N[(z / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.7999999999999998e206

   1. Initial program 91.6%

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

   2. Taylor expanded in x around inf 98.4%

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

      1. +-commutative 98.4%

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

      2. distribute-rgt-in 98.4%

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

      3. *-commutative 98.4%

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

      4. associate-*r* 98.4%

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

      5. neg-mul-1 98.4%

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

      6. metadata-eval 98.4%

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

      7. distribute-lft-neg-in 98.4%

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

      8. distribute-rgt-neg-in 98.4%

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

      9. distribute-rgt-in 98.4%

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

      10. neg-mul-1 98.4%

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

      11. metadata-eval 98.4%

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

      12. sub-neg 98.4%

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

      13. associate-*r* 98.4%

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

      14. associate-*r/ 98.4%

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

      15. mul-1-neg 98.4%

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

      16. unsub-neg 98.4%

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

      17. associate-/l* 95.6%

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

      18. associate-/r/ 100.0%

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

      19. sub-neg 100.0%

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

      20. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 84.0%

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

      1. mul-1-neg 84.0%

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

      2. distribute-frac-neg 84.0%

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

   7. Simplified 84.0%

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

   8. Taylor expanded in y around 0 84.0%

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

      1. +-commutative 84.0%

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

   10. Simplified 84.0%

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

   if 2.7999999999999998e206 < x

   1. Initial program 90.0%

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

   2. Taylor expanded in x around inf 90.0%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 99.9%

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

      3. mul-1-neg 99.9%

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

      4. unsub-neg 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around inf 64.8%

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

      1. associate-*r/ 64.8%

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

      2. mul-1-neg 64.8%

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

      3. *-commutative 64.8%

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

      4. distribute-lft-neg-out 64.8%

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

      5. associate-/l* 84.6%

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

   7. Simplified 84.6%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.8 \cdot 10^{+206}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{z}{x}}\\ \end{array} \]

Alternative 7: 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 91.5%

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

2. Taylor expanded in x around inf 97.7%

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

   1. +-commutative 97.7%

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

   2. distribute-rgt-in 97.8%

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

   3. *-commutative 97.8%

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

   4. associate-*r* 97.8%

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

   5. neg-mul-1 97.8%

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

   6. metadata-eval 97.8%

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

   7. distribute-lft-neg-in 97.8%

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

   8. distribute-rgt-neg-in 97.8%

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

   9. distribute-rgt-in 97.7%

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

   10. neg-mul-1 97.7%

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

   11. metadata-eval 97.7%

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

   12. sub-neg 97.7%

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

   13. associate-*r* 97.7%

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

   14. associate-*r/ 97.7%

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

   15. mul-1-neg 97.7%

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

   16. unsub-neg 97.7%

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

   17. associate-/l* 95.9%

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

   18. associate-/r/ 100.0%

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

   19. sub-neg 100.0%

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

   20. metadata-eval 100.0%

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

4. Simplified 100.0%

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

5. Taylor expanded in y around 0 82.2%

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

   1. mul-1-neg 82.2%

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

   2. distribute-frac-neg 82.2%

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

7. Simplified 82.2%

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

8. Taylor expanded in y around 0 82.2%

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

   1. +-commutative 82.2%

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

10. Simplified 82.2%

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

11. Final simplification 82.2%

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

Alternative 8: 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 91.5%

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

2. Taylor expanded in x around 0 45.0%

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

3. Final simplification 45.0%

   \[\leadsto y \]

Developer target: 94.4% 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 2023301 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

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