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

Percentage Accurate: 87.5% → 99.9%

Time: 8.8s

Alternatives: 10

Speedup: 1.0×

• 21.8% 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: 87.5% 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: 99.9% 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 90.4%

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

3. Taylor expanded in x around -inf 98.8%

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

   1. mul-1-neg 98.8%

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

   2. unsub-neg 98.8%

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

   3. associate-/l* 95.2%

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

   4. associate-/r/ 100.0%

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

   5. sub-neg 100.0%

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

   6. metadata-eval 100.0%

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

5. Simplified 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 77.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{-y}{z}\\ \mathbf{if}\;y \leq -1.04 \cdot 10^{+270}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+22}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+119} \lor \neg \left(y \leq 3.8 \cdot 10^{+248}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ (- y) z))))
   (if (<= y -1.04e+270)
     t_0
     (if (<= y 6.4e+22)
       (+ y (/ x z))
       (if (or (<= y 3.8e+119) (not (<= y 3.8e+248))) t_0 (/ z (/ z y)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-y / z);
	double tmp;
	if (y <= -1.04e+270) {
		tmp = t_0;
	} else if (y <= 6.4e+22) {
		tmp = y + (x / z);
	} else if ((y <= 3.8e+119) || !(y <= 3.8e+248)) {
		tmp = t_0;
	} else {
		tmp = z / (z / 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 = x * (-y / z)
    if (y <= (-1.04d+270)) then
        tmp = t_0
    else if (y <= 6.4d+22) then
        tmp = y + (x / z)
    else if ((y <= 3.8d+119) .or. (.not. (y <= 3.8d+248))) then
        tmp = t_0
    else
        tmp = z / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-y / z);
	double tmp;
	if (y <= -1.04e+270) {
		tmp = t_0;
	} else if (y <= 6.4e+22) {
		tmp = y + (x / z);
	} else if ((y <= 3.8e+119) || !(y <= 3.8e+248)) {
		tmp = t_0;
	} else {
		tmp = z / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-y / z)
	tmp = 0
	if y <= -1.04e+270:
		tmp = t_0
	elif y <= 6.4e+22:
		tmp = y + (x / z)
	elif (y <= 3.8e+119) or not (y <= 3.8e+248):
		tmp = t_0
	else:
		tmp = z / (z / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(-y) / z))
	tmp = 0.0
	if (y <= -1.04e+270)
		tmp = t_0;
	elseif (y <= 6.4e+22)
		tmp = Float64(y + Float64(x / z));
	elseif ((y <= 3.8e+119) || !(y <= 3.8e+248))
		tmp = t_0;
	else
		tmp = Float64(z / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-y / z);
	tmp = 0.0;
	if (y <= -1.04e+270)
		tmp = t_0;
	elseif (y <= 6.4e+22)
		tmp = y + (x / z);
	elseif ((y <= 3.8e+119) || ~((y <= 3.8e+248)))
		tmp = t_0;
	else
		tmp = z / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.04e+270], t$95$0, If[LessEqual[y, 6.4e+22], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.8e+119], N[Not[LessEqual[y, 3.8e+248]], $MachinePrecision]], t$95$0, N[(z / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.04e270 or 6.4e22 < y < 3.7999999999999999e119 or 3.8000000000000001e248 < y

   1. Initial program 82.0%

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

   3. Taylor expanded in y around inf 82.0%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in z around 0 71.7%

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

      1. mul-1-neg 71.7%

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

      2. associate-*r/ 71.7%

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

      3. distribute-rgt-neg-in 71.7%

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

      4. distribute-neg-frac 71.7%

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

   8. Simplified 71.7%

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

   if -1.04e270 < y < 6.4e22

   1. Initial program 95.0%

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

   3. Taylor expanded in x around -inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

      3. associate-/l* 96.6%

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

      4. associate-/r/ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 89.3%

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

      1. mul-1-neg 89.3%

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

      2. distribute-neg-frac 89.3%

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

   8. Simplified 89.3%

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

   9. Taylor expanded in y around 0 89.3%

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

       1. +-commutative 89.3%

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

   11. Simplified 89.3%

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

   if 3.7999999999999999e119 < y < 3.8000000000000001e248

   1. Initial program 65.3%

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

   3. Taylor expanded in y around inf 65.3%

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

   4. Taylor expanded in z around inf 39.0%

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

      1. associate-/l* 73.6%

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

      2. associate-/r/ 77.7%

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

   6. Applied egg-rr 77.7%

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

      1. *-commutative 77.7%

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

      2. clear-num 77.5%

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

      3. un-div-inv 77.8%

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

   8. Applied egg-rr 77.8%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.04 \cdot 10^{+270}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+22}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+119} \lor \neg \left(y \leq 3.8 \cdot 10^{+248}\right):\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{\frac{-z}{x}}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+268}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+22}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+113} \lor \neg \left(y \leq 1.35 \cdot 10^{+258}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (/ (- z) x))))
   (if (<= y -4e+268)
     t_0
     (if (<= y 2.4e+22)
       (+ y (/ x z))
       (if (or (<= y 1.6e+113) (not (<= y 1.35e+258))) t_0 (/ z (/ z y)))))))

C

double code(double x, double y, double z) {
	double t_0 = y / (-z / x);
	double tmp;
	if (y <= -4e+268) {
		tmp = t_0;
	} else if (y <= 2.4e+22) {
		tmp = y + (x / z);
	} else if ((y <= 1.6e+113) || !(y <= 1.35e+258)) {
		tmp = t_0;
	} else {
		tmp = z / (z / 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 / (-z / x)
    if (y <= (-4d+268)) then
        tmp = t_0
    else if (y <= 2.4d+22) then
        tmp = y + (x / z)
    else if ((y <= 1.6d+113) .or. (.not. (y <= 1.35d+258))) then
        tmp = t_0
    else
        tmp = z / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / (-z / x);
	double tmp;
	if (y <= -4e+268) {
		tmp = t_0;
	} else if (y <= 2.4e+22) {
		tmp = y + (x / z);
	} else if ((y <= 1.6e+113) || !(y <= 1.35e+258)) {
		tmp = t_0;
	} else {
		tmp = z / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (-z / x)
	tmp = 0
	if y <= -4e+268:
		tmp = t_0
	elif y <= 2.4e+22:
		tmp = y + (x / z)
	elif (y <= 1.6e+113) or not (y <= 1.35e+258):
		tmp = t_0
	else:
		tmp = z / (z / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(Float64(-z) / x))
	tmp = 0.0
	if (y <= -4e+268)
		tmp = t_0;
	elseif (y <= 2.4e+22)
		tmp = Float64(y + Float64(x / z));
	elseif ((y <= 1.6e+113) || !(y <= 1.35e+258))
		tmp = t_0;
	else
		tmp = Float64(z / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (-z / x);
	tmp = 0.0;
	if (y <= -4e+268)
		tmp = t_0;
	elseif (y <= 2.4e+22)
		tmp = y + (x / z);
	elseif ((y <= 1.6e+113) || ~((y <= 1.35e+258)))
		tmp = t_0;
	else
		tmp = z / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[((-z) / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e+268], t$95$0, If[LessEqual[y, 2.4e+22], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.6e+113], N[Not[LessEqual[y, 1.35e+258]], $MachinePrecision]], t$95$0, N[(z / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9999999999999999e268 or 2.4e22 < y < 1.5999999999999999e113 or 1.34999999999999998e258 < y

   1. Initial program 82.0%

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

   3. Taylor expanded in y around inf 82.0%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in y around 0 82.0%

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

      1. associate-/l* 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in z around 0 76.3%

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

       1. neg-mul-1 76.3%

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

       2. distribute-neg-frac 76.3%

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

   11. Simplified 76.3%

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

   if -3.9999999999999999e268 < y < 2.4e22

   1. Initial program 95.0%

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

   3. Taylor expanded in x around -inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

      3. associate-/l* 96.6%

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

      4. associate-/r/ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 89.3%

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

      1. mul-1-neg 89.3%

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

      2. distribute-neg-frac 89.3%

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

   8. Simplified 89.3%

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

   9. Taylor expanded in y around 0 89.3%

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

       1. +-commutative 89.3%

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

   11. Simplified 89.3%

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

   if 1.5999999999999999e113 < y < 1.34999999999999998e258

   1. Initial program 65.3%

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

   3. Taylor expanded in y around inf 65.3%

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

   4. Taylor expanded in z around inf 39.0%

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

      1. associate-/l* 73.6%

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

      2. associate-/r/ 77.7%

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

   6. Applied egg-rr 77.7%

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

      1. *-commutative 77.7%

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

      2. clear-num 77.5%

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

      3. un-div-inv 77.8%

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

   8. Applied egg-rr 77.8%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+268}:\\ \;\;\;\;\frac{y}{\frac{-z}{x}}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+22}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+113} \lor \neg \left(y \leq 1.35 \cdot 10^{+258}\right):\\ \;\;\;\;\frac{y}{\frac{-z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{+49} \lor \neg \left(x \leq 4.1 \cdot 10^{+65}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.7e+49) (not (<= x 4.1e+65)))
   (* x (/ (- 1.0 y) z))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.7e+49) || !(x <= 4.1e+65)) {
		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 <= (-5.7d+49)) .or. (.not. (x <= 4.1d+65))) 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 <= -5.7e+49) || !(x <= 4.1e+65)) {
		tmp = x * ((1.0 - y) / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.7e+49) or not (x <= 4.1e+65):
		tmp = x * ((1.0 - y) / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.7e+49) || !(x <= 4.1e+65))
		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 <= -5.7e+49) || ~((x <= 4.1e+65)))
		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, -5.7e+49], N[Not[LessEqual[x, 4.1e+65]], $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 < -5.6999999999999998e49 or 4.1000000000000001e65 < x

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 92.0%

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

      1. mul-1-neg 92.0%

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

      2. unsub-neg 92.0%

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

   5. Simplified 92.0%

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

   6. Taylor expanded in y around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. associate-*l/ 77.9%

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

      3. *-commutative 77.9%

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

      4. distribute-lft-neg-out 77.9%

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

      5. distribute-lft1-in 94.0%

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

      6. +-commutative 94.0%

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

      7. sub-neg 94.0%

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

      8. associate-*r/ 92.0%

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

      9. associate-*l/ 93.8%

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

      10. *-commutative 93.8%

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

   8. Simplified 93.8%

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

   if -5.6999999999999998e49 < x < 4.1000000000000001e65

   1. Initial program 87.2%

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

   3. Taylor expanded in x around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. associate-/l* 92.5%

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

      4. associate-/r/ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. distribute-neg-frac 84.8%

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

   8. Simplified 84.8%

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

   9. Taylor expanded in y around 0 84.8%

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

       1. +-commutative 84.8%

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

   11. Simplified 84.8%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{+49} \lor \neg \left(x \leq 4.1 \cdot 10^{+65}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-100} \lor \neg \left(z \leq 5.8 \cdot 10^{-146}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.5e-100) (not (<= z 5.8e-146)))
   (+ y (/ x z))
   (* (/ x z) (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e-100) || !(z <= 5.8e-146)) {
		tmp = y + (x / z);
	} else {
		tmp = (x / z) * (1.0 - 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 <= (-8.5d-100)) .or. (.not. (z <= 5.8d-146))) then
        tmp = y + (x / z)
    else
        tmp = (x / z) * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e-100) || !(z <= 5.8e-146)) {
		tmp = y + (x / z);
	} else {
		tmp = (x / z) * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.5e-100) or not (z <= 5.8e-146):
		tmp = y + (x / z)
	else:
		tmp = (x / z) * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.5e-100) || !(z <= 5.8e-146))
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.5e-100) || ~((z <= 5.8e-146)))
		tmp = y + (x / z);
	else
		tmp = (x / z) * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.5e-100], N[Not[LessEqual[z, 5.8e-146]], $MachinePrecision]], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000017e-100 or 5.80000000000000022e-146 < z

   1. Initial program 85.7%

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

   3. Taylor expanded in x around -inf 98.3%

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

      1. mul-1-neg 98.3%

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

      2. unsub-neg 98.3%

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

      3. associate-/l* 100.0%

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

      4. associate-/r/ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 86.2%

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

      1. mul-1-neg 86.2%

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

      2. distribute-neg-frac 86.2%

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

   8. Simplified 86.2%

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

   9. Taylor expanded in y around 0 86.2%

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

       1. +-commutative 86.2%

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

   11. Simplified 86.2%

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

   if -8.50000000000000017e-100 < z < 5.80000000000000022e-146

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 94.4%

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

      1. associate-/l* 84.2%

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

      2. associate-/r/ 94.5%

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

      3. mul-1-neg 94.5%

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

      4. unsub-neg 94.5%

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

   5. Simplified 94.5%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-100} \lor \neg \left(z \leq 5.8 \cdot 10^{-146}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.55\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.55))) (* (- z x) (/ y z)) (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.55)) {
		tmp = (z - x) * (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 ((y <= (-1.0d0)) .or. (.not. (y <= 0.55d0))) then
        tmp = (z - x) * (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 ((y <= -1.0) || !(y <= 0.55)) {
		tmp = (z - x) * (y / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.55):
		tmp = (z - x) * (y / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.55))
		tmp = Float64(Float64(z - x) * Float64(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 ((y <= -1.0) || ~((y <= 0.55)))
		tmp = (z - x) * (y / 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, 0.55]], $MachinePrecision]], N[(N[(z - x), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.55000000000000004 < y

   1. Initial program 80.0%

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

   3. Taylor expanded in y around inf 79.1%

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

      1. associate-/l* 99.1%

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

      2. associate-/r/ 89.2%

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

   5. Simplified 89.2%

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

   if -1 < y < 0.55000000000000004

   1. Initial program 99.9%

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

   3. Taylor expanded in x around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-/l* 100.0%

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

      4. associate-/r/ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 98.7%

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

      1. mul-1-neg 98.7%

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

      2. distribute-neg-frac 98.7%

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

   8. Simplified 98.7%

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

   9. Taylor expanded in y around 0 98.7%

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

       1. +-commutative 98.7%

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

   11. Simplified 98.7%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.55\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.55\right):\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.55))) (/ y (/ z (- z x))) (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.55)) {
		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 <= 0.55d0))) 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 <= 0.55)) {
		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 <= 0.55):
		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 <= 0.55))
		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 <= 0.55)))
		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, 0.55]], $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 0.55000000000000004 < y

   1. Initial program 80.0%

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

   3. Taylor expanded in y around inf 79.1%

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

      1. associate-/l* 99.1%

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

      2. associate-/r/ 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in y around 0 79.1%

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

      1. associate-/l* 99.1%

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

   8. Simplified 99.1%

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

   if -1 < y < 0.55000000000000004

   1. Initial program 99.9%

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

   3. Taylor expanded in x around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-/l* 100.0%

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

      4. associate-/r/ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 98.7%

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

      1. mul-1-neg 98.7%

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

      2. distribute-neg-frac 98.7%

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

   8. Simplified 98.7%

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

   9. Taylor expanded in y around 0 98.7%

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

       1. +-commutative 98.7%

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

   11. Simplified 98.7%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.55\right):\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-6} \lor \neg \left(x \leq 1.7 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.9e-6) (not (<= x 1.7e+34))) (/ x z) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.9e-6) || !(x <= 1.7e+34)) {
		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 <= (-2.9d-6)) .or. (.not. (x <= 1.7d+34))) 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 <= -2.9e-6) || !(x <= 1.7e+34)) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.9e-6) or not (x <= 1.7e+34):
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.9e-6) || !(x <= 1.7e+34))
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.9e-6) || ~((x <= 1.7e+34)))
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.9e-6], N[Not[LessEqual[x, 1.7e+34]], $MachinePrecision]], N[(x / z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -2.9000000000000002e-6 or 1.7e34 < x

   1. Initial program 95.5%

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

   3. Taylor expanded in y around 0 60.8%

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

   if -2.9000000000000002e-6 < x < 1.7e34

   1. Initial program 86.5%

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

   3. Taylor expanded in x around 0 63.6%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-6} \lor \neg \left(x \leq 1.7 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.1% 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 90.4%

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

3. Taylor expanded in x around -inf 98.8%

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

   1. mul-1-neg 98.8%

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

   2. unsub-neg 98.8%

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

   3. associate-/l* 95.2%

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

   4. associate-/r/ 100.0%

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

   5. sub-neg 100.0%

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

   6. metadata-eval 100.0%

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

5. Simplified 100.0%

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

6. Taylor expanded in y around 0 78.3%

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

   1. mul-1-neg 78.3%

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

   2. distribute-neg-frac 78.3%

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

8. Simplified 78.3%

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

9. Taylor expanded in y around 0 78.3%

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

    1. +-commutative 78.3%

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

11. Simplified 78.3%

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

12. Final simplification 78.3%

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

Alternative 10: 40.7% 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 90.4%

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

3. Taylor expanded in x around 0 41.3%

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

4. Final simplification 41.3%

   \[\leadsto y \]
5. Add Preprocessing

Developer target: 93.6% 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 2024014 
(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))