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

Percentage Accurate: 87.8% → 99.9%

Time: 6.5s

Alternatives: 11

Speedup: 1.0×

• 20.7% 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: 87.8% 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. Taylor expanded in x around -inf 96.6%

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

   1. mul-1-neg 96.6%

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

   2. unsub-neg 96.6%

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

   3. associate-/l* 95.4%

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

   4. associate-/r/ 99.9%

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

   5. sub-neg 99.9%

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

   6. metadata-eval 99.9%

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

4. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 79.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7400000000:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+74} \lor \neg \left(y \leq 2.26 \cdot 10^{+108}\right) \land y \leq 1.7 \cdot 10^{+209}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 7400000000.0)
   (+ y (/ x z))
   (if (or (<= y 9e+74) (and (not (<= y 2.26e+108)) (<= y 1.7e+209)))
     (* (/ x z) (- y))
     (- y (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 7400000000.0) {
		tmp = y + (x / z);
	} else if ((y <= 9e+74) || (!(y <= 2.26e+108) && (y <= 1.7e+209))) {
		tmp = (x / z) * -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 (y <= 7400000000.0d0) then
        tmp = y + (x / z)
    else if ((y <= 9d+74) .or. (.not. (y <= 2.26d+108)) .and. (y <= 1.7d+209)) then
        tmp = (x / z) * -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 (y <= 7400000000.0) {
		tmp = y + (x / z);
	} else if ((y <= 9e+74) || (!(y <= 2.26e+108) && (y <= 1.7e+209))) {
		tmp = (x / z) * -y;
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 7400000000.0:
		tmp = y + (x / z)
	elif (y <= 9e+74) or (not (y <= 2.26e+108) and (y <= 1.7e+209)):
		tmp = (x / z) * -y
	else:
		tmp = y - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 7400000000.0)
		tmp = Float64(y + Float64(x / z));
	elseif ((y <= 9e+74) || (!(y <= 2.26e+108) && (y <= 1.7e+209)))
		tmp = Float64(Float64(x / z) * Float64(-y));
	else
		tmp = Float64(y - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 7400000000.0)
		tmp = y + (x / z);
	elseif ((y <= 9e+74) || (~((y <= 2.26e+108)) && (y <= 1.7e+209)))
		tmp = (x / z) * -y;
	else
		tmp = y - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 7400000000.0], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 9e+74], And[N[Not[LessEqual[y, 2.26e+108]], $MachinePrecision], LessEqual[y, 1.7e+209]]], N[(N[(x / z), $MachinePrecision] * (-y)), $MachinePrecision], N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.4e9

   1. Initial program 94.2%

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

   2. Taylor expanded in x around -inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. unsub-neg 98.9%

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

      3. associate-/l* 97.7%

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

      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%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 86.6%

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

      1. mul-1-neg 86.6%

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

      2. distribute-frac-neg 86.6%

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

   7. Simplified 86.6%

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

   8. Taylor expanded in y around 0 86.6%

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

      1. +-commutative 86.6%

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

   10. Simplified 86.6%

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

   if 7.4e9 < y < 8.9999999999999999e74 or 2.2599999999999999e108 < y < 1.6999999999999998e209

   1. Initial program 91.1%

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

   2. Taylor expanded in y around inf 90.4%

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

      1. associate-/l* 99.1%

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

      2. associate-/r/ 88.1%

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

   4. Simplified 88.1%

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

   5. Taylor expanded in z around 0 67.4%

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

      1. mul-1-neg 67.4%

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

      2. *-commutative 67.4%

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

      3. associate-*r/ 71.7%

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

      4. distribute-rgt-neg-out 71.7%

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

      5. distribute-frac-neg 71.7%

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

   7. Simplified 71.7%

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

   if 8.9999999999999999e74 < y < 2.2599999999999999e108 or 1.6999999999999998e209 < y

   1. Initial program 68.1%

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

   2. Taylor expanded in x around -inf 85.0%

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

      1. mul-1-neg 85.0%

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

      2. unsub-neg 85.0%

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

      3. associate-/l* 91.3%

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

      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%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 61.5%

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

      1. mul-1-neg 61.5%

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

      2. distribute-frac-neg 61.5%

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

   7. Simplified 61.5%

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

      1. add-log-exp 10.5%

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

      2. log1p-expm1-u 4.1%

         \[\leadsto \log \left(e^{y}\right) - \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-x}{z}\right)\right)} \]

      3. log1p-udef 4.1%

         \[\leadsto \log \left(e^{y}\right) - \color{blue}{\log \left(1 + \mathsf{expm1}\left(\frac{-x}{z}\right)\right)} \]

      4. diff-log 4.1%

         \[\leadsto \color{blue}{\log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{-x}{z}\right)}\right)} \]

      5. add-sqr-sqrt 2.2%

         \[\leadsto \log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z}\right)}\right) \]

      6. sqrt-unprod 13.2%

         \[\leadsto \log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z}\right)}\right) \]

      7. sqr-neg 13.2%

         \[\leadsto \log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{z}\right)}\right) \]

      8. sqrt-unprod 11.3%

         \[\leadsto \log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z}\right)}\right) \]

      9. add-sqr-sqrt 19.9%

         \[\leadsto \log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{\color{blue}{x}}{z}\right)}\right) \]

   9. Applied egg-rr 19.9%

      \[\leadsto \color{blue}{\log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{x}{z}\right)}\right)} \]
   10. Step-by-step derivation

       1. log-div 19.9%

          \[\leadsto \color{blue}{\log \left(e^{y}\right) - \log \left(1 + \mathsf{expm1}\left(\frac{x}{z}\right)\right)} \]

       2. rem-log-exp 89.6%

          \[\leadsto \color{blue}{y} - \log \left(1 + \mathsf{expm1}\left(\frac{x}{z}\right)\right) \]

       3. log1p-def 89.6%

          \[\leadsto y - \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{z}\right)\right)} \]

       4. log1p-expm1 74.5%

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

   11. Simplified 74.5%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7400000000:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+74} \lor \neg \left(y \leq 2.26 \cdot 10^{+108}\right) \land y \leq 1.7 \cdot 10^{+209}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \]

Alternative 3: 79.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 780000000:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{y \cdot \left(-x\right)}{z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+107} \lor \neg \left(y \leq 1.05 \cdot 10^{+201}\right):\\ \;\;\;\;y - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 780000000.0)
   (+ y (/ x z))
   (if (<= y 1.2e+75)
     (/ (* y (- x)) z)
     (if (or (<= y 5.2e+107) (not (<= y 1.05e+201)))
       (- y (/ x z))
       (* (/ x z) (- y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 780000000.0) {
		tmp = y + (x / z);
	} else if (y <= 1.2e+75) {
		tmp = (y * -x) / z;
	} else if ((y <= 5.2e+107) || !(y <= 1.05e+201)) {
		tmp = y - (x / z);
	} else {
		tmp = (x / 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) :: tmp
    if (y <= 780000000.0d0) then
        tmp = y + (x / z)
    else if (y <= 1.2d+75) then
        tmp = (y * -x) / z
    else if ((y <= 5.2d+107) .or. (.not. (y <= 1.05d+201))) then
        tmp = y - (x / z)
    else
        tmp = (x / z) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 780000000.0) {
		tmp = y + (x / z);
	} else if (y <= 1.2e+75) {
		tmp = (y * -x) / z;
	} else if ((y <= 5.2e+107) || !(y <= 1.05e+201)) {
		tmp = y - (x / z);
	} else {
		tmp = (x / z) * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 780000000.0:
		tmp = y + (x / z)
	elif y <= 1.2e+75:
		tmp = (y * -x) / z
	elif (y <= 5.2e+107) or not (y <= 1.05e+201):
		tmp = y - (x / z)
	else:
		tmp = (x / z) * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 780000000.0)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 1.2e+75)
		tmp = Float64(Float64(y * Float64(-x)) / z);
	elseif ((y <= 5.2e+107) || !(y <= 1.05e+201))
		tmp = Float64(y - Float64(x / z));
	else
		tmp = Float64(Float64(x / z) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 780000000.0)
		tmp = y + (x / z);
	elseif (y <= 1.2e+75)
		tmp = (y * -x) / z;
	elseif ((y <= 5.2e+107) || ~((y <= 1.05e+201)))
		tmp = y - (x / z);
	else
		tmp = (x / z) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 780000000.0], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+75], N[(N[(y * (-x)), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[y, 5.2e+107], N[Not[LessEqual[y, 1.05e+201]], $MachinePrecision]], N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * (-y)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < 7.8e8

   1. Initial program 94.2%

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

   2. Taylor expanded in x around -inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. unsub-neg 98.9%

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

      3. associate-/l* 97.7%

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

      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%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 86.6%

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

      1. mul-1-neg 86.6%

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

      2. distribute-frac-neg 86.6%

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

   7. Simplified 86.6%

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

   8. Taylor expanded in y around 0 86.6%

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

      1. +-commutative 86.6%

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

   10. Simplified 86.6%

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

   if 7.8e8 < y < 1.2e75

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 97.9%

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

   3. Taylor expanded in z around 0 78.9%

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

      1. mul-1-neg 78.9%

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

      2. distribute-lft-neg-out 78.9%

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

      3. *-commutative 78.9%

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

   5. Simplified 78.9%

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

   if 1.2e75 < y < 5.2000000000000002e107 or 1.05e201 < y

   1. Initial program 68.1%

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

   2. Taylor expanded in x around -inf 85.0%

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

      1. mul-1-neg 85.0%

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

      2. unsub-neg 85.0%

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

      3. associate-/l* 91.3%

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

      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%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 61.5%

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

      1. mul-1-neg 61.5%

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

      2. distribute-frac-neg 61.5%

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

   7. Simplified 61.5%

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

      1. add-log-exp 10.5%

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

      2. log1p-expm1-u 4.1%

         \[\leadsto \log \left(e^{y}\right) - \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-x}{z}\right)\right)} \]

      3. log1p-udef 4.1%

         \[\leadsto \log \left(e^{y}\right) - \color{blue}{\log \left(1 + \mathsf{expm1}\left(\frac{-x}{z}\right)\right)} \]

      4. diff-log 4.1%

         \[\leadsto \color{blue}{\log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{-x}{z}\right)}\right)} \]

      5. add-sqr-sqrt 2.2%

         \[\leadsto \log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z}\right)}\right) \]

      6. sqrt-unprod 13.2%

         \[\leadsto \log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z}\right)}\right) \]

      7. sqr-neg 13.2%

         \[\leadsto \log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{z}\right)}\right) \]

      8. sqrt-unprod 11.3%

         \[\leadsto \log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z}\right)}\right) \]

      9. add-sqr-sqrt 19.9%

         \[\leadsto \log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{\color{blue}{x}}{z}\right)}\right) \]

   9. Applied egg-rr 19.9%

      \[\leadsto \color{blue}{\log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{x}{z}\right)}\right)} \]
   10. Step-by-step derivation

       1. log-div 19.9%

          \[\leadsto \color{blue}{\log \left(e^{y}\right) - \log \left(1 + \mathsf{expm1}\left(\frac{x}{z}\right)\right)} \]

       2. rem-log-exp 89.6%

          \[\leadsto \color{blue}{y} - \log \left(1 + \mathsf{expm1}\left(\frac{x}{z}\right)\right) \]

       3. log1p-def 89.6%

          \[\leadsto y - \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{z}\right)\right)} \]

       4. log1p-expm1 74.5%

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

   11. Simplified 74.5%

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

   if 5.2000000000000002e107 < y < 1.05e201

   1. Initial program 85.9%

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

   2. Taylor expanded in y around inf 85.9%

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

      1. associate-/l* 99.8%

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

      2. associate-/r/ 85.8%

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

   4. Simplified 85.8%

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

   5. Taylor expanded in z around 0 60.6%

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

      1. mul-1-neg 60.6%

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

      2. *-commutative 60.6%

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

      3. associate-*r/ 67.5%

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

      4. distribute-rgt-neg-out 67.5%

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

      5. distribute-frac-neg 67.5%

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

   7. Simplified 67.5%

      \[\leadsto \color{blue}{y \cdot \frac{-x}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 780000000:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{y \cdot \left(-x\right)}{z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+107} \lor \neg \left(y \leq 1.05 \cdot 10^{+201}\right):\\ \;\;\;\;y - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \end{array} \]

Alternative 4: 85.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-9} \lor \neg \left(x \leq 6.4 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.2e-9) (not (<= x 6.4e+25)))
   (* (/ x z) (- 1.0 y))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.2e-9) || !(x <= 6.4e+25)) {
		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 <= (-2.2d-9)) .or. (.not. (x <= 6.4d+25))) 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 <= -2.2e-9) || !(x <= 6.4e+25)) {
		tmp = (x / z) * (1.0 - y);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.2e-9) or not (x <= 6.4e+25):
		tmp = (x / z) * (1.0 - y)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.2e-9) || !(x <= 6.4e+25))
		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 <= -2.2e-9) || ~((x <= 6.4e+25)))
		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, -2.2e-9], N[Not[LessEqual[x, 6.4e+25]], $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 < -2.1999999999999998e-9 or 6.3999999999999999e25 < x

   1. Initial program 93.4%

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

   2. Taylor expanded in x around inf 86.7%

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

      1. associate-/l* 89.6%

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

      2. associate-/r/ 89.6%

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

      3. mul-1-neg 89.6%

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

      4. unsub-neg 89.6%

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

   4. Simplified 89.6%

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

   if -2.1999999999999998e-9 < x < 6.3999999999999999e25

   1. Initial program 87.4%

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

   2. Taylor expanded in x around -inf 99.1%

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

      1. mul-1-neg 99.1%

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

      2. unsub-neg 99.1%

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

      3. associate-/l* 90.9%

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

      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%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. distribute-frac-neg 84.5%

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

   7. Simplified 84.5%

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

   8. Taylor expanded in y around 0 84.5%

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

      1. +-commutative 84.5%

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

   10. Simplified 84.5%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-9} \lor \neg \left(x \leq 6.4 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 5: 95.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -15000000 \lor \neg \left(y \leq 2.2 \cdot 10^{-5}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -15000000.0) (not (<= y 2.2e-5)))
   (* (- z x) (/ y z))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -15000000.0) || !(y <= 2.2e-5)) {
		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 <= (-15000000.0d0)) .or. (.not. (y <= 2.2d-5))) 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 <= -15000000.0) || !(y <= 2.2e-5)) {
		tmp = (z - x) * (y / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -15000000.0) or not (y <= 2.2e-5):
		tmp = (z - x) * (y / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -15000000.0) || !(y <= 2.2e-5))
		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 <= -15000000.0) || ~((y <= 2.2e-5)))
		tmp = (z - x) * (y / z);
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -15000000.0], N[Not[LessEqual[y, 2.2e-5]], $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 < -1.5e7 or 2.1999999999999999e-5 < y

   1. Initial program 82.1%

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

   2. Taylor expanded in y around inf 81.9%

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

      1. associate-/l* 99.6%

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

      2. associate-/r/ 90.7%

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

   4. Simplified 90.7%

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

   if -1.5e7 < y < 2.1999999999999999e-5

   1. Initial program 99.9%

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

   2. Taylor expanded in x around -inf 100.0%

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

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. distribute-frac-neg 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in y around 0 99.5%

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

      1. +-commutative 99.5%

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

   10. Simplified 99.5%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -15000000 \lor \neg \left(y \leq 2.2 \cdot 10^{-5}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 6: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -15000000 \lor \neg \left(y \leq 2.2 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -15000000.0) (not (<= y 2.2e-5)))
   (/ y (/ z (- z x)))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -15000000.0) || !(y <= 2.2e-5)) {
		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 <= (-15000000.0d0)) .or. (.not. (y <= 2.2d-5))) 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 <= -15000000.0) || !(y <= 2.2e-5)) {
		tmp = y / (z / (z - x));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -15000000.0) or not (y <= 2.2e-5):
		tmp = y / (z / (z - x))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -15000000.0) || !(y <= 2.2e-5))
		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 <= -15000000.0) || ~((y <= 2.2e-5)))
		tmp = y / (z / (z - x));
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -15000000.0], N[Not[LessEqual[y, 2.2e-5]], $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 < -1.5e7 or 2.1999999999999999e-5 < y

   1. Initial program 82.1%

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

   2. Taylor expanded in y around inf 81.9%

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

      1. associate-/l* 99.6%

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

   4. Simplified 99.6%

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

   if -1.5e7 < y < 2.1999999999999999e-5

   1. Initial program 99.9%

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

   2. Taylor expanded in x around -inf 100.0%

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

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. distribute-frac-neg 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in y around 0 99.5%

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

      1. +-commutative 99.5%

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

   10. Simplified 99.5%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -15000000 \lor \neg \left(y \leq 2.2 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 7: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-69} \lor \neg \left(y \leq 3.4 \cdot 10^{-6}\right):\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.4e-69) (not (<= y 3.4e-6))) (* z (/ y z)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e-69) || !(y <= 3.4e-6)) {
		tmp = z * (y / z);
	} else {
		tmp = 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 <= (-4.4d-69)) .or. (.not. (y <= 3.4d-6))) then
        tmp = z * (y / z)
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e-69) || !(y <= 3.4e-6)) {
		tmp = z * (y / z);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.4e-69) or not (y <= 3.4e-6):
		tmp = z * (y / z)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.4e-69) || !(y <= 3.4e-6))
		tmp = Float64(z * Float64(y / z));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.4e-69) || ~((y <= 3.4e-6)))
		tmp = z * (y / z);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.4e-69], N[Not[LessEqual[y, 3.4e-6]], $MachinePrecision]], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4e-69 or 3.40000000000000006e-6 < y

   1. Initial program 84.0%

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

   2. Taylor expanded in y around inf 83.2%

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

   3. Taylor expanded in z around inf 36.3%

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

      1. associate-/l* 49.2%

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

      2. associate-/r/ 52.5%

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

   5. Applied egg-rr 52.5%

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

   if -4.4e-69 < y < 3.40000000000000006e-6

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 80.8%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-69} \lor \neg \left(y \leq 3.4 \cdot 10^{-6}\right):\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 8: 60.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-69}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e-69) y (if (<= y 7.4e-8) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e-69) {
		tmp = y;
	} else if (y <= 7.4e-8) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6.5d-69)) then
        tmp = y
    else if (y <= 7.4d-8) then
        tmp = x / z
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e-69) {
		tmp = y;
	} else if (y <= 7.4e-8) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.5e-69:
		tmp = y
	elif y <= 7.4e-8:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e-69)
		tmp = y;
	elseif (y <= 7.4e-8)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.5e-69)
		tmp = y;
	elseif (y <= 7.4e-8)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e-69], y, If[LessEqual[y, 7.4e-8], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -6.49999999999999951e-69 or 7.4000000000000001e-8 < y

   1. Initial program 84.0%

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

   2. Taylor expanded in x around 0 49.2%

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

   if -6.49999999999999951e-69 < y < 7.4000000000000001e-8

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 80.8%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-69}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9: 81.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{-5}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.2e-5) (+ y (/ x z)) (- y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.2e-5) {
		tmp = y + (x / z);
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 2.2d-5) then
        tmp = y + (x / z)
    else
        tmp = y - (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.2e-5) {
		tmp = y + (x / z);
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.2e-5:
		tmp = y + (x / z)
	else:
		tmp = y - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.2e-5)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(y - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.2e-5)
		tmp = y + (x / z);
	else
		tmp = y - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.2e-5], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.1999999999999999e-5

   1. Initial program 94.1%

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

   2. Taylor expanded in x around -inf 98.8%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{x \cdot \left(y - 1\right)}{z}} \]
   3. 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* 97.6%

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

      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%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 86.4%

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

      1. mul-1-neg 86.4%

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

      2. distribute-frac-neg 86.4%

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

   7. Simplified 86.4%

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

   8. Taylor expanded in y around 0 86.4%

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

      1. +-commutative 86.4%

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

   10. Simplified 86.4%

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

   if 2.1999999999999999e-5 < y

   1. Initial program 81.9%

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

   2. Taylor expanded in x around -inf 91.4%

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

      1. mul-1-neg 91.4%

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

      2. unsub-neg 91.4%

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

      3. associate-/l* 90.4%

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

      4. associate-/r/ 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 42.6%

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

      1. mul-1-neg 42.6%

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

      2. distribute-frac-neg 42.6%

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

   7. Simplified 42.6%

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

      1. add-log-exp 14.2%

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

      2. log1p-expm1-u 4.6%

         \[\leadsto \log \left(e^{y}\right) - \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-x}{z}\right)\right)} \]

      3. log1p-udef 4.6%

         \[\leadsto \log \left(e^{y}\right) - \color{blue}{\log \left(1 + \mathsf{expm1}\left(\frac{-x}{z}\right)\right)} \]

      4. diff-log 4.6%

         \[\leadsto \color{blue}{\log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{-x}{z}\right)}\right)} \]

      5. add-sqr-sqrt 1.2%

         \[\leadsto \log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z}\right)}\right) \]

      6. sqrt-unprod 13.7%

         \[\leadsto \log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z}\right)}\right) \]

      7. sqr-neg 13.7%

         \[\leadsto \log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{z}\right)}\right) \]

      8. sqrt-unprod 12.6%

         \[\leadsto \log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z}\right)}\right) \]

      9. add-sqr-sqrt 19.3%

         \[\leadsto \log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{\color{blue}{x}}{z}\right)}\right) \]

   9. Applied egg-rr 19.3%

      \[\leadsto \color{blue}{\log \left(\frac{e^{y}}{1 + \mathsf{expm1}\left(\frac{x}{z}\right)}\right)} \]
   10. Step-by-step derivation

       1. log-div 19.3%

          \[\leadsto \color{blue}{\log \left(e^{y}\right) - \log \left(1 + \mathsf{expm1}\left(\frac{x}{z}\right)\right)} \]

       2. rem-log-exp 75.0%

          \[\leadsto \color{blue}{y} - \log \left(1 + \mathsf{expm1}\left(\frac{x}{z}\right)\right) \]

       3. log1p-def 75.0%

          \[\leadsto y - \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{z}\right)\right)} \]

       4. log1p-expm1 58.0%

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

   11. Simplified 58.0%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{-5}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \]

Alternative 10: 78.0% 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. Taylor expanded in x around -inf 96.6%

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

   1. mul-1-neg 96.6%

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

   2. unsub-neg 96.6%

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

   3. associate-/l* 95.4%

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

   4. associate-/r/ 99.9%

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

   5. sub-neg 99.9%

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

   6. metadata-eval 99.9%

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

4. Simplified 99.9%

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

5. Taylor expanded in y around 0 73.0%

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

   1. mul-1-neg 73.0%

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

   2. distribute-frac-neg 73.0%

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

7. Simplified 73.0%

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

8. Taylor expanded in y around 0 73.0%

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

   1. +-commutative 73.0%

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

10. Simplified 73.0%

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

11. Final simplification 73.0%

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

Alternative 11: 41.3% 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 90.4%

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

2. Taylor expanded in x around 0 37.8%

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

3. Final simplification 37.8%

   \[\leadsto y \]

Developer target: 93.9% 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 2023271 
(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))