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

Percentage Accurate: 88.4% → 99.9%

Time: 7.0s

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: 88.4% 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 89.3%

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

2. Taylor expanded in x around -inf 96.9%

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

   1. mul-1-neg 96.9%

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

   2. unsub-neg 96.9%

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

   3. associate-/l* 97.5%

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

   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%

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

4. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 78.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y + \frac{x}{z}\\ t_1 := \frac{-x}{\frac{z}{y}}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2300000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 12500000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ y (/ x z))) (t_1 (/ (- x) (/ z y))))
   (if (<= y -2.6e+42)
     t_0
     (if (<= y -2300000000.0)
       t_1
       (if (<= y 12500000000.0) t_0 (if (<= y 2.9e+88) t_1 (* z (/ y z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double t_1 = -x / (z / y);
	double tmp;
	if (y <= -2.6e+42) {
		tmp = t_0;
	} else if (y <= -2300000000.0) {
		tmp = t_1;
	} else if (y <= 12500000000.0) {
		tmp = t_0;
	} else if (y <= 2.9e+88) {
		tmp = t_1;
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y + (x / z)
    t_1 = -x / (z / y)
    if (y <= (-2.6d+42)) then
        tmp = t_0
    else if (y <= (-2300000000.0d0)) then
        tmp = t_1
    else if (y <= 12500000000.0d0) then
        tmp = t_0
    else if (y <= 2.9d+88) then
        tmp = t_1
    else
        tmp = z * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double t_1 = -x / (z / y);
	double tmp;
	if (y <= -2.6e+42) {
		tmp = t_0;
	} else if (y <= -2300000000.0) {
		tmp = t_1;
	} else if (y <= 12500000000.0) {
		tmp = t_0;
	} else if (y <= 2.9e+88) {
		tmp = t_1;
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y + (x / z)
	t_1 = -x / (z / y)
	tmp = 0
	if y <= -2.6e+42:
		tmp = t_0
	elif y <= -2300000000.0:
		tmp = t_1
	elif y <= 12500000000.0:
		tmp = t_0
	elif y <= 2.9e+88:
		tmp = t_1
	else:
		tmp = z * (y / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y + Float64(x / z))
	t_1 = Float64(Float64(-x) / Float64(z / y))
	tmp = 0.0
	if (y <= -2.6e+42)
		tmp = t_0;
	elseif (y <= -2300000000.0)
		tmp = t_1;
	elseif (y <= 12500000000.0)
		tmp = t_0;
	elseif (y <= 2.9e+88)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y + (x / z);
	t_1 = -x / (z / y);
	tmp = 0.0;
	if (y <= -2.6e+42)
		tmp = t_0;
	elseif (y <= -2300000000.0)
		tmp = t_1;
	elseif (y <= 12500000000.0)
		tmp = t_0;
	elseif (y <= 2.9e+88)
		tmp = t_1;
	else
		tmp = z * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[((-x) / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+42], t$95$0, If[LessEqual[y, -2300000000.0], t$95$1, If[LessEqual[y, 12500000000.0], t$95$0, If[LessEqual[y, 2.9e+88], t$95$1, N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5999999999999999e42 or -2.3e9 < y < 1.25e10

   1. Initial program 92.4%

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

   2. Taylor expanded in x around -inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. unsub-neg 97.9%

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

      3. associate-/l* 99.0%

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

      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 92.2%

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

      1. mul-1-neg 92.2%

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

      2. distribute-frac-neg 92.2%

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

   7. Simplified 92.2%

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

   8. Taylor expanded in y around 0 92.2%

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

      1. +-commutative 92.2%

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

   10. Simplified 92.2%

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

   if -2.5999999999999999e42 < y < -2.3e9 or 1.25e10 < y < 2.9e88

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 74.2%

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

      1. associate-/l* 65.7%

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

      2. associate-/r/ 74.2%

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

      3. mul-1-neg 74.2%

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

      4. unsub-neg 74.2%

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

   4. Simplified 74.2%

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

   5. Taylor expanded in y around inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. associate-/l* 64.6%

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

   7. Simplified 64.6%

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

   if 2.9e88 < y

   1. Initial program 66.5%

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

   2. Taylor expanded in y around inf 66.5%

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

   3. Taylor expanded in z around inf 28.4%

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

      1. associate-/l* 57.0%

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

      2. associate-/r/ 68.8%

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

   5. Applied egg-rr 68.8%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+42}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq -2300000000:\\ \;\;\;\;\frac{-x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 12500000000:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+88}:\\ \;\;\;\;\frac{-x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]

Alternative 3: 78.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y + \frac{x}{z}\\ t_1 := \frac{x}{z} \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+44}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2300000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 125000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+179}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ y (/ x z))) (t_1 (* (/ x z) (- y))))
   (if (<= y -5e+44)
     t_0
     (if (<= y -2300000000.0)
       t_1
       (if (<= y 125000000000.0)
         t_0
         (if (<= y 1.4e+179) t_1 (* z (/ y z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double t_1 = (x / z) * -y;
	double tmp;
	if (y <= -5e+44) {
		tmp = t_0;
	} else if (y <= -2300000000.0) {
		tmp = t_1;
	} else if (y <= 125000000000.0) {
		tmp = t_0;
	} else if (y <= 1.4e+179) {
		tmp = t_1;
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y + (x / z)
    t_1 = (x / z) * -y
    if (y <= (-5d+44)) then
        tmp = t_0
    else if (y <= (-2300000000.0d0)) then
        tmp = t_1
    else if (y <= 125000000000.0d0) then
        tmp = t_0
    else if (y <= 1.4d+179) then
        tmp = t_1
    else
        tmp = z * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double t_1 = (x / z) * -y;
	double tmp;
	if (y <= -5e+44) {
		tmp = t_0;
	} else if (y <= -2300000000.0) {
		tmp = t_1;
	} else if (y <= 125000000000.0) {
		tmp = t_0;
	} else if (y <= 1.4e+179) {
		tmp = t_1;
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y + (x / z)
	t_1 = (x / z) * -y
	tmp = 0
	if y <= -5e+44:
		tmp = t_0
	elif y <= -2300000000.0:
		tmp = t_1
	elif y <= 125000000000.0:
		tmp = t_0
	elif y <= 1.4e+179:
		tmp = t_1
	else:
		tmp = z * (y / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y + Float64(x / z))
	t_1 = Float64(Float64(x / z) * Float64(-y))
	tmp = 0.0
	if (y <= -5e+44)
		tmp = t_0;
	elseif (y <= -2300000000.0)
		tmp = t_1;
	elseif (y <= 125000000000.0)
		tmp = t_0;
	elseif (y <= 1.4e+179)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y + (x / z);
	t_1 = (x / z) * -y;
	tmp = 0.0;
	if (y <= -5e+44)
		tmp = t_0;
	elseif (y <= -2300000000.0)
		tmp = t_1;
	elseif (y <= 125000000000.0)
		tmp = t_0;
	elseif (y <= 1.4e+179)
		tmp = t_1;
	else
		tmp = z * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * (-y)), $MachinePrecision]}, If[LessEqual[y, -5e+44], t$95$0, If[LessEqual[y, -2300000000.0], t$95$1, If[LessEqual[y, 125000000000.0], t$95$0, If[LessEqual[y, 1.4e+179], t$95$1, N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999996e44 or -2.3e9 < y < 1.25e11

   1. Initial program 92.4%

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

   2. Taylor expanded in x around -inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. unsub-neg 97.9%

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

      3. associate-/l* 99.0%

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

      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 92.2%

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

      1. mul-1-neg 92.2%

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

      2. distribute-frac-neg 92.2%

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

   7. Simplified 92.2%

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

   8. Taylor expanded in y around 0 92.2%

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

      1. +-commutative 92.2%

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

   10. Simplified 92.2%

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

   if -4.9999999999999996e44 < y < -2.3e9 or 1.25e11 < y < 1.4e179

   1. Initial program 95.5%

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

   2. Taylor expanded in x around inf 67.8%

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

      1. associate-/l* 58.2%

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

      2. associate-/r/ 67.8%

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

      3. mul-1-neg 67.8%

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

      4. unsub-neg 67.8%

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

   4. Simplified 67.8%

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

   5. Taylor expanded in y around inf 67.1%

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

      1. associate-*l/ 67.1%

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

      2. neg-mul-1 67.1%

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

      3. distribute-rgt-neg-out 67.1%

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

   7. Simplified 67.1%

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

   if 1.4e179 < y

   1. Initial program 53.7%

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

   2. Taylor expanded in y around inf 53.7%

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

   3. Taylor expanded in z around inf 25.5%

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

      1. associate-/l* 64.1%

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

      2. associate-/r/ 79.3%

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

   5. Applied egg-rr 79.3%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+44}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq -2300000000:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 125000000000:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+179}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]

Alternative 4: 77.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y + \frac{x}{z}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2300000000:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 160000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+176}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ y (/ x z))))
   (if (<= y -2.2e+42)
     t_0
     (if (<= y -2300000000.0)
       (* (/ x z) (- y))
       (if (<= y 160000.0)
         t_0
         (if (<= y 4.1e+176) (/ (* x (- y)) z) (* z (/ y z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double tmp;
	if (y <= -2.2e+42) {
		tmp = t_0;
	} else if (y <= -2300000000.0) {
		tmp = (x / z) * -y;
	} else if (y <= 160000.0) {
		tmp = t_0;
	} else if (y <= 4.1e+176) {
		tmp = (x * -y) / z;
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y + (x / z)
    if (y <= (-2.2d+42)) then
        tmp = t_0
    else if (y <= (-2300000000.0d0)) then
        tmp = (x / z) * -y
    else if (y <= 160000.0d0) then
        tmp = t_0
    else if (y <= 4.1d+176) then
        tmp = (x * -y) / z
    else
        tmp = z * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double tmp;
	if (y <= -2.2e+42) {
		tmp = t_0;
	} else if (y <= -2300000000.0) {
		tmp = (x / z) * -y;
	} else if (y <= 160000.0) {
		tmp = t_0;
	} else if (y <= 4.1e+176) {
		tmp = (x * -y) / z;
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y + (x / z)
	tmp = 0
	if y <= -2.2e+42:
		tmp = t_0
	elif y <= -2300000000.0:
		tmp = (x / z) * -y
	elif y <= 160000.0:
		tmp = t_0
	elif y <= 4.1e+176:
		tmp = (x * -y) / z
	else:
		tmp = z * (y / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y + Float64(x / z))
	tmp = 0.0
	if (y <= -2.2e+42)
		tmp = t_0;
	elseif (y <= -2300000000.0)
		tmp = Float64(Float64(x / z) * Float64(-y));
	elseif (y <= 160000.0)
		tmp = t_0;
	elseif (y <= 4.1e+176)
		tmp = Float64(Float64(x * Float64(-y)) / z);
	else
		tmp = Float64(z * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y + (x / z);
	tmp = 0.0;
	if (y <= -2.2e+42)
		tmp = t_0;
	elseif (y <= -2300000000.0)
		tmp = (x / z) * -y;
	elseif (y <= 160000.0)
		tmp = t_0;
	elseif (y <= 4.1e+176)
		tmp = (x * -y) / z;
	else
		tmp = z * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+42], t$95$0, If[LessEqual[y, -2300000000.0], N[(N[(x / z), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[y, 160000.0], t$95$0, If[LessEqual[y, 4.1e+176], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.2000000000000001e42 or -2.3e9 < y < 1.6e5

   1. Initial program 92.4%

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

   2. Taylor expanded in x around -inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. unsub-neg 97.9%

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

      3. associate-/l* 99.0%

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

      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 92.2%

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

      1. mul-1-neg 92.2%

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

      2. distribute-frac-neg 92.2%

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

   7. Simplified 92.2%

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

   8. Taylor expanded in y around 0 92.2%

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

      1. +-commutative 92.2%

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

   10. Simplified 92.2%

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

   if -2.2000000000000001e42 < y < -2.3e9

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 81.9%

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

      1. associate-/l* 81.7%

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

      2. associate-/r/ 82.0%

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

      3. mul-1-neg 82.0%

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

      4. unsub-neg 82.0%

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

   4. Simplified 82.0%

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

   5. Taylor expanded in y around inf 79.0%

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

      1. associate-*l/ 79.1%

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

      2. neg-mul-1 79.1%

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

      3. distribute-rgt-neg-out 79.1%

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

   7. Simplified 79.1%

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

   if 1.6e5 < y < 4.0999999999999999e176

   1. Initial program 94.2%

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

   2. Taylor expanded in y around inf 94.2%

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

   3. Taylor expanded in z around 0 63.3%

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

      1. mul-1-neg 63.3%

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

      2. distribute-lft-neg-out 63.3%

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

      3. *-commutative 63.3%

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

   5. Simplified 63.3%

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

   if 4.0999999999999999e176 < y

   1. Initial program 53.7%

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

   2. Taylor expanded in y around inf 53.7%

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

   3. Taylor expanded in z around inf 25.5%

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

      1. associate-/l* 64.1%

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

      2. associate-/r/ 79.3%

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

   5. Applied egg-rr 79.3%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+42}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq -2300000000:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 160000:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+176}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]

Alternative 5: 99.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \lor \neg \left(y \leq 0.64\right):\\ \;\;\;\;y \cdot \left(\left(z - x\right) \cdot \frac{1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.6) (not (<= y 0.64)))
   (* y (* (- z x) (/ 1.0 z)))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.6) || !(y <= 0.64)) {
		tmp = y * ((z - x) * (1.0 / 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 <= (-2.6d0)) .or. (.not. (y <= 0.64d0))) then
        tmp = y * ((z - x) * (1.0d0 / 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 <= -2.6) || !(y <= 0.64)) {
		tmp = y * ((z - x) * (1.0 / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.6) or not (y <= 0.64):
		tmp = y * ((z - x) * (1.0 / z))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.6) || !(y <= 0.64))
		tmp = Float64(y * Float64(Float64(z - x) * Float64(1.0 / 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 <= -2.6) || ~((y <= 0.64)))
		tmp = y * ((z - x) * (1.0 / z));
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.6], N[Not[LessEqual[y, 0.64]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.60000000000000009 or 0.640000000000000013 < y

   1. Initial program 78.1%

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

   2. Taylor expanded in y around inf 77.8%

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

      1. div-inv 77.7%

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

      2. associate-*l* 99.6%

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

   4. Applied egg-rr 99.6%

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

   if -2.60000000000000009 < y < 0.640000000000000013

   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 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \lor \neg \left(y \leq 0.64\right):\\ \;\;\;\;y \cdot \left(\left(z - x\right) \cdot \frac{1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 6: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-97} \lor \neg \left(z \leq 6800000000\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4e-97) (not (<= z 6800000000.0)))
   (+ y (/ x z))
   (* (/ x z) (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4e-97) || !(z <= 6800000000.0)) {
		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 <= (-4d-97)) .or. (.not. (z <= 6800000000.0d0))) 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 <= -4e-97) || !(z <= 6800000000.0)) {
		tmp = y + (x / z);
	} else {
		tmp = (x / z) * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4e-97) or not (z <= 6800000000.0):
		tmp = y + (x / z)
	else:
		tmp = (x / z) * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4e-97) || !(z <= 6800000000.0))
		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 <= -4e-97) || ~((z <= 6800000000.0)))
		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, -4e-97], N[Not[LessEqual[z, 6800000000.0]], $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 < -4.00000000000000014e-97 or 6.8e9 < z

   1. Initial program 81.1%

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

   2. Taylor expanded in x around -inf 94.6%

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

      1. mul-1-neg 94.6%

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

      2. unsub-neg 94.6%

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

      3. associate-/l* 99.3%

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

      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 88.0%

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

      1. mul-1-neg 88.0%

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

      2. distribute-frac-neg 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in y around 0 88.0%

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

      1. +-commutative 88.0%

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

   10. Simplified 88.0%

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

   if -4.00000000000000014e-97 < z < 6.8e9

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 90.7%

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

      1. associate-/l* 86.8%

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

      2. associate-/r/ 90.7%

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

      3. mul-1-neg 90.7%

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

      4. unsub-neg 90.7%

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

   4. Simplified 90.7%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-97} \lor \neg \left(z \leq 6800000000\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 7: 95.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \lor \neg \left(y \leq 0.64\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.6) (not (<= y 0.64))) (* (- z x) (/ y z)) (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.6) || !(y <= 0.64)) {
		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 <= (-2.6d0)) .or. (.not. (y <= 0.64d0))) 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 <= -2.6) || !(y <= 0.64)) {
		tmp = (z - x) * (y / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.6) or not (y <= 0.64):
		tmp = (z - x) * (y / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.6) || !(y <= 0.64))
		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 <= -2.6) || ~((y <= 0.64)))
		tmp = (z - x) * (y / z);
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.6], N[Not[LessEqual[y, 0.64]], $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 < -2.60000000000000009 or 0.640000000000000013 < y

   1. Initial program 78.1%

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

   2. Taylor expanded in y around inf 77.8%

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

      1. associate-/l* 99.6%

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

      2. associate-/r/ 93.6%

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

   4. Simplified 93.6%

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

   if -2.60000000000000009 < y < 0.640000000000000013

   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 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \lor \neg \left(y \leq 0.64\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 8: 95.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 0.64:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.6)
   (* (- z x) (/ y z))
   (if (<= y 0.64) (+ y (/ x z)) (- y (/ (* y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.6) {
		tmp = (z - x) * (y / z);
	} else if (y <= 0.64) {
		tmp = y + (x / z);
	} else {
		tmp = y - ((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 <= (-2.6d0)) then
        tmp = (z - x) * (y / z)
    else if (y <= 0.64d0) then
        tmp = y + (x / z)
    else
        tmp = y - ((y * x) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.6) {
		tmp = (z - x) * (y / z);
	} else if (y <= 0.64) {
		tmp = y + (x / z);
	} else {
		tmp = y - ((y * x) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.6:
		tmp = (z - x) * (y / z)
	elif y <= 0.64:
		tmp = y + (x / z)
	else:
		tmp = y - ((y * x) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.6)
		tmp = Float64(Float64(z - x) * Float64(y / z));
	elseif (y <= 0.64)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(y - Float64(Float64(y * x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.6)
		tmp = (z - x) * (y / z);
	elseif (y <= 0.64)
		tmp = y + (x / z);
	else
		tmp = y - ((y * x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.6], N[(N[(z - x), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.64], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y - N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.60000000000000009

   1. Initial program 77.9%

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

   2. Taylor expanded in y around inf 77.4%

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

      1. associate-/l* 99.4%

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

      2. associate-/r/ 96.4%

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

   4. Simplified 96.4%

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

   if -2.60000000000000009 < y < 0.640000000000000013

   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 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   10. Simplified 100.0%

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

   if 0.640000000000000013 < y

   1. Initial program 78.2%

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

   2. Taylor expanded in x around -inf 93.5%

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

      1. mul-1-neg 93.5%

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

      2. unsub-neg 93.5%

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

      3. associate-/l* 92.7%

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

      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 inf 93.5%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 0.64:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{y \cdot x}{z}\\ \end{array} \]

Alternative 9: 58.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-43} \lor \neg \left(x \leq 2.9 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.1e-43) (not (<= x 2.9e+41))) (/ x z) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e-43) || !(x <= 2.9e+41)) {
		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 <= (-2.1d-43)) .or. (.not. (x <= 2.9d+41))) 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 <= -2.1e-43) || !(x <= 2.9e+41)) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.1e-43) or not (x <= 2.9e+41):
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.1e-43) || !(x <= 2.9e+41))
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.1e-43) || ~((x <= 2.9e+41)))
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.1e-43], N[Not[LessEqual[x, 2.9e+41]], $MachinePrecision]], N[(x / z), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -2.1000000000000001e-43 or 2.89999999999999988e41 < x

   1. Initial program 92.9%

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

   2. Taylor expanded in y around 0 61.2%

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

   if -2.1000000000000001e-43 < x < 2.89999999999999988e41

   1. Initial program 85.5%

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

   2. Taylor expanded in x around 0 67.1%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-43} \lor \neg \left(x \leq 2.9 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 10: 79.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.64:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 0.64) (+ y (/ x z)) (* z (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.64) {
		tmp = y + (x / z);
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 0.64d0) then
        tmp = y + (x / z)
    else
        tmp = z * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.64) {
		tmp = y + (x / z);
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 0.64:
		tmp = y + (x / z)
	else:
		tmp = z * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 0.64)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(z * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 0.64)
		tmp = y + (x / z);
	else
		tmp = z * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 0.64], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 0.640000000000000013

   1. Initial program 92.7%

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

   2. Taylor expanded in x around -inf 98.0%

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

      1. mul-1-neg 98.0%

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

      2. unsub-neg 98.0%

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

      3. associate-/l* 99.0%

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

      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 88.3%

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

      1. mul-1-neg 88.3%

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

      2. distribute-frac-neg 88.3%

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

   7. Simplified 88.3%

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

   8. Taylor expanded in y around 0 88.3%

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

      1. +-commutative 88.3%

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

   10. Simplified 88.3%

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

   if 0.640000000000000013 < y

   1. Initial program 78.2%

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

   2. Taylor expanded in y around inf 78.2%

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

   3. Taylor expanded in z around inf 31.2%

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

      1. associate-/l* 49.7%

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

      2. associate-/r/ 57.3%

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

   5. Applied egg-rr 57.3%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.64:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]

Alternative 11: 40.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 89.3%

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

2. Taylor expanded in x around 0 40.0%

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

3. Final simplification 40.0%

   \[\leadsto y \]

Developer target: 94.2% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023315 
(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))