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

Percentage Accurate: 88.8% → 99.5%

Time: 8.2s

Alternatives: 11

Speedup: 0.8×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.8% 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: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+122} \lor \neg \left(x \leq 10^{-40}\right):\\ \;\;\;\;y - \frac{x}{\frac{z}{y + -1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8e+122) (not (<= x 1e-40)))
   (- y (/ x (/ z (+ y -1.0))))
   (+ (/ x z) (* y (- 1.0 (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8e+122) || !(x <= 1e-40)) {
		tmp = y - (x / (z / (y + -1.0)));
	} else {
		tmp = (x / z) + (y * (1.0 - (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 <= (-8d+122)) .or. (.not. (x <= 1d-40))) then
        tmp = y - (x / (z / (y + (-1.0d0))))
    else
        tmp = (x / z) + (y * (1.0d0 - (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8e+122) || !(x <= 1e-40)) {
		tmp = y - (x / (z / (y + -1.0)));
	} else {
		tmp = (x / z) + (y * (1.0 - (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8e+122) or not (x <= 1e-40):
		tmp = y - (x / (z / (y + -1.0)))
	else:
		tmp = (x / z) + (y * (1.0 - (x / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8e+122) || !(x <= 1e-40))
		tmp = Float64(y - Float64(x / Float64(z / Float64(y + -1.0))));
	else
		tmp = Float64(Float64(x / z) + Float64(y * Float64(1.0 - Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8e+122) || ~((x <= 1e-40)))
		tmp = y - (x / (z / (y + -1.0)));
	else
		tmp = (x / z) + (y * (1.0 - (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8e+122], N[Not[LessEqual[x, 1e-40]], $MachinePrecision]], N[(y - N[(x / N[(z / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] + N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.00000000000000012e122 or 9.9999999999999993e-41 < x

   1. Initial program 90.7%

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

   2. Taylor expanded in y around 0 78.0%

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

   3. Taylor expanded in z around -inf 94.5%

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

      1. mul-1-neg 94.5%

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

      2. unsub-neg 94.5%

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

      3. distribute-rgt-out 94.5%

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

      4. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

   if -8.00000000000000012e122 < x < 9.9999999999999993e-41

   1. Initial program 91.5%

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

   2. Taylor expanded in y around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+122} \lor \neg \left(x \leq 10^{-40}\right):\\ \;\;\;\;y - \frac{x}{\frac{z}{y + -1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \]

Alternative 2: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+23} \lor \neg \left(y \leq 10^{+43}\right):\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{\frac{z}{y + -1}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.2e+23) (not (<= y 1e+43)))
   (/ y (/ z (- z x)))
   (- y (/ x (/ z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.2e+23) || !(y <= 1e+43)) {
		tmp = y / (z / (z - x));
	} else {
		tmp = y - (x / (z / (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.2d+23)) .or. (.not. (y <= 1d+43))) then
        tmp = y / (z / (z - x))
    else
        tmp = y - (x / (z / (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.2e+23) || !(y <= 1e+43)) {
		tmp = y / (z / (z - x));
	} else {
		tmp = y - (x / (z / (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.2e+23) or not (y <= 1e+43):
		tmp = y / (z / (z - x))
	else:
		tmp = y - (x / (z / (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.2e+23) || !(y <= 1e+43))
		tmp = Float64(y / Float64(z / Float64(z - x)));
	else
		tmp = Float64(y - Float64(x / Float64(z / Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.2e+23) || ~((y <= 1e+43)))
		tmp = y / (z / (z - x));
	else
		tmp = y - (x / (z / (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.2e+23], N[Not[LessEqual[y, 1e+43]], $MachinePrecision]], N[(y / N[(z / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y - N[(x / N[(z / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e23 or 1.00000000000000001e43 < y

   1. Initial program 80.4%

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

   2. Taylor expanded in y around inf 80.4%

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

      1. associate-/l* 99.9%

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

   4. Simplified 99.9%

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

   if -1.2e23 < y < 1.00000000000000001e43

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 93.1%

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

   3. Taylor expanded in z around -inf 99.3%

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

      1. mul-1-neg 99.3%

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

      2. unsub-neg 99.3%

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

      3. distribute-rgt-out 99.4%

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

      4. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+23} \lor \neg \left(y \leq 10^{+43}\right):\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{\frac{z}{y + -1}}\\ \end{array} \]

Alternative 3: 99.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+50} \lor \neg \left(z \leq 2 \cdot 10^{-161}\right):\\ \;\;\;\;y - \frac{x}{\frac{z}{y + -1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2e+50) (not (<= z 2e-161)))
   (- y (/ x (/ z (+ y -1.0))))
   (/ (+ x (* y (- z x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2e+50) || !(z <= 2e-161)) {
		tmp = y - (x / (z / (y + -1.0)));
	} else {
		tmp = (x + (y * (z - 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 ((z <= (-2d+50)) .or. (.not. (z <= 2d-161))) then
        tmp = y - (x / (z / (y + (-1.0d0))))
    else
        tmp = (x + (y * (z - x))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2e+50) || !(z <= 2e-161)) {
		tmp = y - (x / (z / (y + -1.0)));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2e+50) or not (z <= 2e-161):
		tmp = y - (x / (z / (y + -1.0)))
	else:
		tmp = (x + (y * (z - x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2e+50) || !(z <= 2e-161))
		tmp = Float64(y - Float64(x / Float64(z / Float64(y + -1.0))));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z - x))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2e+50) || ~((z <= 2e-161)))
		tmp = y - (x / (z / (y + -1.0)));
	else
		tmp = (x + (y * (z - x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2e+50], N[Not[LessEqual[z, 2e-161]], $MachinePrecision]], N[(y - N[(x / N[(z / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000002e50 or 2.00000000000000006e-161 < z

   1. Initial program 83.3%

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

   2. Taylor expanded in y around 0 99.2%

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

   3. Taylor expanded in z around -inf 95.9%

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

      1. mul-1-neg 95.9%

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

      2. unsub-neg 95.9%

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

      3. distribute-rgt-out 95.9%

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

      4. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

   if -2.0000000000000002e50 < z < 2.00000000000000006e-161

   1. Initial program 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+50} \lor \neg \left(z \leq 2 \cdot 10^{-161}\right):\\ \;\;\;\;y - \frac{x}{\frac{z}{y + -1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \]

Alternative 4: 76.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+196} \lor \neg \left(y \leq -950000\right) \land y \leq 3.5 \cdot 10^{+87}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.75e+196) (and (not (<= y -950000.0)) (<= y 3.5e+87)))
   (+ y (/ x z))
   (* (/ x z) (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.75e+196) || (!(y <= -950000.0) && (y <= 3.5e+87))) {
		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 <= (-1.75d+196)) .or. (.not. (y <= (-950000.0d0))) .and. (y <= 3.5d+87)) 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 <= -1.75e+196) || (!(y <= -950000.0) && (y <= 3.5e+87))) {
		tmp = y + (x / z);
	} else {
		tmp = (x / z) * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.75e+196) or (not (y <= -950000.0) and (y <= 3.5e+87)):
		tmp = y + (x / z)
	else:
		tmp = (x / z) * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.75e+196) || (!(y <= -950000.0) && (y <= 3.5e+87)))
		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 <= -1.75e+196) || (~((y <= -950000.0)) && (y <= 3.5e+87)))
		tmp = y + (x / z);
	else
		tmp = (x / z) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.75e+196], And[N[Not[LessEqual[y, -950000.0]], $MachinePrecision], LessEqual[y, 3.5e+87]]], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7499999999999999e196 or -9.5e5 < y < 3.49999999999999986e87

   1. Initial program 93.7%

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

   2. Taylor expanded in y around 0 94.4%

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

   3. Taylor expanded in z around -inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. unsub-neg 97.9%

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

      3. distribute-rgt-out 97.9%

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

      4. associate-/l* 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in y around 0 90.7%

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

      1. associate-*r/ 90.7%

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

      2. neg-mul-1 90.7%

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

   8. Simplified 90.7%

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

   9. Taylor expanded in y around 0 90.7%

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

       1. +-commutative 90.7%

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

   11. Simplified 90.7%

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

   if -1.7499999999999999e196 < y < -9.5e5 or 3.49999999999999986e87 < y

   1. Initial program 85.5%

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

   2. Taylor expanded in y around inf 84.8%

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

      1. associate-/l* 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in z around 0 66.7%

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

      1. associate-*r/ 66.7%

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

      2. neg-mul-1 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in y around 0 65.7%

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

      1. mul-1-neg 65.7%

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

      2. associate-*r/ 66.8%

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

      3. distribute-rgt-neg-in 66.8%

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

      4. mul-1-neg 66.8%

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

      5. associate-*r/ 66.8%

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

      6. neg-mul-1 66.8%

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

   10. Simplified 66.8%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+196} \lor \neg \left(y \leq -950000\right) \land y \leq 3.5 \cdot 10^{+87}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \end{array} \]

Alternative 5: 75.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y + \frac{x}{z}\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+191}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -950000:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+86}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ y (/ x z))))
   (if (<= y -4.3e+191)
     t_0
     (if (<= y -950000.0)
       (/ (* x (- y)) z)
       (if (<= y 4.4e+86) t_0 (* (/ x z) (- y)))))))

C

double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double tmp;
	if (y <= -4.3e+191) {
		tmp = t_0;
	} else if (y <= -950000.0) {
		tmp = (x * -y) / z;
	} else if (y <= 4.4e+86) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = y + (x / z)
    if (y <= (-4.3d+191)) then
        tmp = t_0
    else if (y <= (-950000.0d0)) then
        tmp = (x * -y) / z
    else if (y <= 4.4d+86) then
        tmp = t_0
    else
        tmp = (x / z) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double tmp;
	if (y <= -4.3e+191) {
		tmp = t_0;
	} else if (y <= -950000.0) {
		tmp = (x * -y) / z;
	} else if (y <= 4.4e+86) {
		tmp = t_0;
	} else {
		tmp = (x / z) * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y + (x / z)
	tmp = 0
	if y <= -4.3e+191:
		tmp = t_0
	elif y <= -950000.0:
		tmp = (x * -y) / z
	elif y <= 4.4e+86:
		tmp = t_0
	else:
		tmp = (x / z) * -y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y + Float64(x / z))
	tmp = 0.0
	if (y <= -4.3e+191)
		tmp = t_0;
	elseif (y <= -950000.0)
		tmp = Float64(Float64(x * Float64(-y)) / z);
	elseif (y <= 4.4e+86)
		tmp = t_0;
	else
		tmp = Float64(Float64(x / z) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y + (x / z);
	tmp = 0.0;
	if (y <= -4.3e+191)
		tmp = t_0;
	elseif (y <= -950000.0)
		tmp = (x * -y) / z;
	elseif (y <= 4.4e+86)
		tmp = t_0;
	else
		tmp = (x / z) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e+191], t$95$0, If[LessEqual[y, -950000.0], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 4.4e+86], t$95$0, N[(N[(x / z), $MachinePrecision] * (-y)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2999999999999998e191 or -9.5e5 < y < 4.40000000000000006e86

   1. Initial program 93.7%

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

   2. Taylor expanded in y around 0 94.4%

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

   3. Taylor expanded in z around -inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. unsub-neg 97.9%

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

      3. distribute-rgt-out 97.9%

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

      4. associate-/l* 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in y around 0 90.7%

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

      1. associate-*r/ 90.7%

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

      2. neg-mul-1 90.7%

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

   8. Simplified 90.7%

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

   9. Taylor expanded in y around 0 90.7%

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

       1. +-commutative 90.7%

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

   11. Simplified 90.7%

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

   if -4.2999999999999998e191 < y < -9.5e5

   1. Initial program 80.8%

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

   2. Taylor expanded in y around inf 79.4%

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

   3. Taylor expanded in z around 0 65.3%

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

      1. mul-1-neg 65.3%

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

      2. distribute-rgt-neg-out 65.3%

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

   5. Simplified 65.3%

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

   if 4.40000000000000006e86 < y

   1. Initial program 89.2%

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

   2. Taylor expanded in y around inf 89.2%

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

      1. associate-/l* 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around 0 67.9%

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

      1. associate-*r/ 67.9%

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

      2. neg-mul-1 67.9%

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

   7. Simplified 67.9%

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

   8. Taylor expanded in y around 0 66.0%

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

      1. mul-1-neg 66.0%

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

      2. associate-*r/ 68.1%

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

      3. distribute-rgt-neg-in 68.1%

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

      4. mul-1-neg 68.1%

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

      5. associate-*r/ 68.1%

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

      6. neg-mul-1 68.1%

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

   10. Simplified 68.1%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+191}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq -950000:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+86}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \end{array} \]

Alternative 6: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+31} \lor \neg \left(x \leq 2.8 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.4e+31) (not (<= x 2.8e+91)))
   (* (/ x z) (- 1.0 y))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e+31) || !(x <= 2.8e+91)) {
		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 <= (-1.4d+31)) .or. (.not. (x <= 2.8d+91))) 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 <= -1.4e+31) || !(x <= 2.8e+91)) {
		tmp = (x / z) * (1.0 - y);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.4e+31) or not (x <= 2.8e+91):
		tmp = (x / z) * (1.0 - y)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4e+31) || !(x <= 2.8e+91))
		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 <= -1.4e+31) || ~((x <= 2.8e+91)))
		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, -1.4e+31], N[Not[LessEqual[x, 2.8e+91]], $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 < -1.40000000000000008e31 or 2.7999999999999999e91 < x

   1. Initial program 92.6%

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

   2. Taylor expanded in x around inf 89.9%

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

      1. *-commutative 89.9%

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

      2. associate-/l* 93.0%

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

      3. mul-1-neg 93.0%

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

      4. unsub-neg 93.0%

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

   4. Simplified 93.0%

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

      1. associate-/r/ 93.0%

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

   6. Applied egg-rr 93.0%

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

   if -1.40000000000000008e31 < x < 2.7999999999999999e91

   1. Initial program 90.4%

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

   2. Taylor expanded in y around 0 100.0%

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

   3. Taylor expanded in z around -inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

      3. distribute-rgt-out 99.5%

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

      4. associate-/l* 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in y around 0 84.5%

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

      1. associate-*r/ 84.5%

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

      2. neg-mul-1 84.5%

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

   8. Simplified 84.5%

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

   9. Taylor expanded in y around 0 84.5%

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

       1. +-commutative 84.5%

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

   11. Simplified 84.5%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+31} \lor \neg \left(x \leq 2.8 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 7: 99.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -118 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -118.0) (not (<= y 1.0))) (/ y (/ z (- z x))) (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -118.0) || !(y <= 1.0)) {
		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 <= (-118.0d0)) .or. (.not. (y <= 1.0d0))) 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 <= -118.0) || !(y <= 1.0)) {
		tmp = y / (z / (z - x));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -118.0) or not (y <= 1.0):
		tmp = y / (z / (z - x))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -118.0) || !(y <= 1.0))
		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 <= -118.0) || ~((y <= 1.0)))
		tmp = y / (z / (z - x));
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -118.0], N[Not[LessEqual[y, 1.0]], $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 < -118 or 1 < y

   1. Initial program 82.3%

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

   2. Taylor expanded in y around inf 80.9%

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

      1. associate-/l* 98.5%

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

   4. Simplified 98.5%

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

   if -118 < y < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 93.8%

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

   3. Taylor expanded in z around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. distribute-rgt-out 100.0%

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

      4. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 98.4%

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

      1. associate-*r/ 98.4%

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

      2. neg-mul-1 98.4%

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

   8. Simplified 98.4%

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

   9. Taylor expanded in y around 0 98.4%

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

       1. +-commutative 98.4%

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

   11. Simplified 98.4%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -118 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 8: 57.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+44}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.55e+44) y (if (<= z 1.5e+29) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e+44) {
		tmp = y;
	} else if (z <= 1.5e+29) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.55d+44)) then
        tmp = y
    else if (z <= 1.5d+29) then
        tmp = x / z
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e+44) {
		tmp = y;
	} else if (z <= 1.5e+29) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.55e+44:
		tmp = y
	elif z <= 1.5e+29:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.55e+44)
		tmp = y;
	elseif (z <= 1.5e+29)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.55e+44)
		tmp = y;
	elseif (z <= 1.5e+29)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.55e+44], y, If[LessEqual[z, 1.5e+29], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if z < -1.54999999999999998e44 or 1.5e29 < z

   1. Initial program 78.3%

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

   2. Taylor expanded in x around 0 75.0%

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

   if -1.54999999999999998e44 < z < 1.5e29

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 50.8%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+44}:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9: 79.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.0) {
		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 <= 1.0d0) 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 <= 1.0) {
		tmp = y + (x / z);
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < 1

   1. Initial program 92.1%

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

   2. Taylor expanded in y around 0 95.8%

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

   3. Taylor expanded in z around -inf 99.0%

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

      1. mul-1-neg 99.0%

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

      2. unsub-neg 99.0%

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

      3. distribute-rgt-out 99.0%

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

      4. associate-/l* 95.1%

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

   5. Simplified 95.1%

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

   6. Taylor expanded in y around 0 86.8%

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

      1. associate-*r/ 86.8%

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

      2. neg-mul-1 86.8%

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

   8. Simplified 86.8%

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

   9. Taylor expanded in y around 0 86.8%

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

       1. +-commutative 86.8%

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

   11. Simplified 86.8%

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

   if 1 < y

   1. Initial program 88.4%

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

   2. Taylor expanded in y around inf 87.5%

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

   3. Taylor expanded in z around inf 36.7%

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

      1. associate-/l* 42.5%

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

      2. associate-/r/ 48.5%

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

   5. Applied egg-rr 48.5%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]

Alternative 10: 81.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.0) {
		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 <= 1.0d0) 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 <= 1.0) {
		tmp = y + (x / z);
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < 1

   1. Initial program 92.1%

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

   2. Taylor expanded in y around 0 95.8%

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

   3. Taylor expanded in z around -inf 99.0%

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

      1. mul-1-neg 99.0%

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

      2. unsub-neg 99.0%

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

      3. distribute-rgt-out 99.0%

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

      4. associate-/l* 95.1%

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

   5. Simplified 95.1%

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

   6. Taylor expanded in y around 0 86.8%

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

      1. associate-*r/ 86.8%

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

      2. neg-mul-1 86.8%

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

   8. Simplified 86.8%

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

   9. Taylor expanded in y around 0 86.8%

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

       1. +-commutative 86.8%

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

   11. Simplified 86.8%

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

   if 1 < y

   1. Initial program 88.4%

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

   2. Taylor expanded in y around 0 78.1%

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

   3. Taylor expanded in z around -inf 94.2%

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

      1. mul-1-neg 94.2%

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

      2. unsub-neg 94.2%

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

      3. distribute-rgt-out 94.3%

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

      4. associate-/l* 87.9%

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

   5. Simplified 87.9%

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

   6. Taylor expanded in y around 0 41.3%

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

      1. associate-*r/ 41.3%

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

      2. neg-mul-1 41.3%

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

   8. Simplified 41.3%

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

      1. add-sqr-sqrt 41.0%

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

      2. add-sqr-sqrt 22.3%

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

      3. difference-of-squares 22.3%

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

      4. add-sqr-sqrt 10.9%

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

      5. sqrt-unprod 15.8%

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

      6. sqr-neg 15.8%

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

      7. sqrt-unprod 4.7%

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

      8. add-sqr-sqrt 7.8%

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

      9. add-sqr-sqrt 3.1%

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

      10. sqrt-unprod 29.8%

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

      11. sqr-neg 29.8%

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

      12. sqrt-unprod 23.7%

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

      13. add-sqr-sqrt 37.7%

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

   10. Applied egg-rr 37.7%

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

       1. /-rgt-identity 37.7%

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

       2. *-inverses 37.7%

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

       3. associate-/r/ 32.0%

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

       4. *-commutative 32.0%

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

       5. unpow1/2 32.0%

          \[\leadsto \left(\color{blue}{{\left(z \cdot \frac{y}{z}\right)}^{0.5}} + \sqrt{\frac{x}{z}}\right) \cdot \left(\sqrt{y} - \sqrt{\frac{x}{z}}\right) \]

       6. metadata-eval 32.0%

          \[\leadsto \left({\left(z \cdot \frac{y}{z}\right)}^{\color{blue}{\left(\frac{1}{2}\right)}} + \sqrt{\frac{x}{z}}\right) \cdot \left(\sqrt{y} - \sqrt{\frac{x}{z}}\right) \]

       7. /-rgt-identity 32.0%

          \[\leadsto \left({\left(z \cdot \frac{y}{z}\right)}^{\left(\frac{1}{2}\right)} + \sqrt{\frac{x}{z}}\right) \cdot \left(\sqrt{\color{blue}{\frac{y}{1}}} - \sqrt{\frac{x}{z}}\right) \]

       8. *-inverses 32.0%

          \[\leadsto \left({\left(z \cdot \frac{y}{z}\right)}^{\left(\frac{1}{2}\right)} + \sqrt{\frac{x}{z}}\right) \cdot \left(\sqrt{\frac{y}{\color{blue}{\frac{z}{z}}}} - \sqrt{\frac{x}{z}}\right) \]

       9. associate-/r/ 24.2%

          \[\leadsto \left({\left(z \cdot \frac{y}{z}\right)}^{\left(\frac{1}{2}\right)} + \sqrt{\frac{x}{z}}\right) \cdot \left(\sqrt{\color{blue}{\frac{y}{z} \cdot z}} - \sqrt{\frac{x}{z}}\right) \]

       10. *-commutative 24.2%

           \[\leadsto \left({\left(z \cdot \frac{y}{z}\right)}^{\left(\frac{1}{2}\right)} + \sqrt{\frac{x}{z}}\right) \cdot \left(\sqrt{\color{blue}{z \cdot \frac{y}{z}}} - \sqrt{\frac{x}{z}}\right) \]

       11. unpow1/2 24.2%

           \[\leadsto \left({\left(z \cdot \frac{y}{z}\right)}^{\left(\frac{1}{2}\right)} + \sqrt{\frac{x}{z}}\right) \cdot \left(\color{blue}{{\left(z \cdot \frac{y}{z}\right)}^{0.5}} - \sqrt{\frac{x}{z}}\right) \]

       12. metadata-eval 24.2%

           \[\leadsto \left({\left(z \cdot \frac{y}{z}\right)}^{\left(\frac{1}{2}\right)} + \sqrt{\frac{x}{z}}\right) \cdot \left({\left(z \cdot \frac{y}{z}\right)}^{\color{blue}{\left(\frac{1}{2}\right)}} - \sqrt{\frac{x}{z}}\right) \]

       13. difference-of-squares 24.2%

           \[\leadsto \color{blue}{{\left(z \cdot \frac{y}{z}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(z \cdot \frac{y}{z}\right)}^{\left(\frac{1}{2}\right)} - \sqrt{\frac{x}{z}} \cdot \sqrt{\frac{x}{z}}} \]

       14. sqr-pow 24.3%

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

       15. unpow1 24.3%

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

       16. rem-square-sqrt 53.6%

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

   12. Simplified 64.3%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \]

Alternative 11: 40.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 91.2%

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

2. Taylor expanded in x around 0 40.5%

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

3. Final simplification 40.5%

   \[\leadsto y \]

Developer target: 93.8% 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 2023279 
(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))