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

Percentage Accurate: 88.5% → 96.6%

Time: 8.1s

Alternatives: 7

Speedup: 1.0×

• 20.6% 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: 88.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ y - \frac{x}{\frac{z}{y + -1}} \end{array} \]

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(x / Float64(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[(x / N[(z / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.6%

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

   1. div-inv 88.3%

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

   2. +-commutative 88.3%

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

   3. fma-def 88.3%

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

4. Applied egg-rr 88.3%

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

5. Taylor expanded in x around -inf 97.1%

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

   1. mul-1-neg 97.1%

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

   2. unsub-neg 97.1%

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

   3. associate-/l* 96.9%

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

   4. sub-neg 96.9%

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

   5. metadata-eval 96.9%

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

7. Simplified 96.9%

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

8. Final simplification 96.9%

   \[\leadsto y - \frac{x}{\frac{z}{y + -1}} \]
9. Add Preprocessing

Alternative 2: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+34} \lor \neg \left(x \leq 8.5 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.05e+34) (not (<= x 8.5e+20)))
   (* (/ x z) (- 1.0 y))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e+34) || !(x <= 8.5e+20)) {
		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 <= (-1.05d+34)) .or. (.not. (x <= 8.5d+20))) 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 <= -1.05e+34) || !(x <= 8.5e+20)) {
		tmp = (x / z) * (1.0 - y);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.05e+34) or not (x <= 8.5e+20):
		tmp = (x / z) * (1.0 - y)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.05e+34) || !(x <= 8.5e+20))
		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 <= -1.05e+34) || ~((x <= 8.5e+20)))
		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, -1.05e+34], N[Not[LessEqual[x, 8.5e+20]], $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 < -1.05000000000000009e34 or 8.5e20 < x

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 87.3%

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

      1. associate-*l/ 91.2%

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

      2. mul-1-neg 91.2%

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

      3. unsub-neg 91.2%

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

   5. Simplified 91.2%

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

   if -1.05000000000000009e34 < x < 8.5e20

   1. Initial program 87.3%

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

      1. div-inv 87.0%

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

      2. +-commutative 87.0%

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

      3. fma-def 87.0%

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

   4. Applied egg-rr 87.0%

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

   5. Taylor expanded in x around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. associate-/l* 94.4%

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

      4. sub-neg 94.4%

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

      5. metadata-eval 94.4%

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

   7. Simplified 94.4%

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

   8. Taylor expanded in y around 0 89.3%

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

      1. neg-mul-1 89.3%

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

      2. distribute-neg-frac 89.3%

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

   10. Simplified 89.3%

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

   11. Taylor expanded in y around 0 89.3%

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

       1. +-commutative 89.3%

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

   13. Simplified 89.3%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+34} \lor \neg \left(x \leq 8.5 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -260000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;\frac{y}{z} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -260000.0) (not (<= y 1.0))) (* (/ y z) (- z x)) (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -260000.0) || !(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 <= (-260000.0d0)) .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 <= -260000.0) || !(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 <= -260000.0) 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 <= -260000.0) || !(y <= 1.0))
		tmp = Float64(Float64(y / 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 <= -260000.0) || ~((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, -260000.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(N[(y / z), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e5 or 1 < y

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf 77.5%

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

      1. associate-*l/ 92.8%

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

   5. Simplified 92.8%

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

   if -2.6e5 < y < 1

   1. Initial program 99.9%

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

      1. div-inv 99.6%

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

      2. +-commutative 99.6%

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

      3. fma-def 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around -inf 100.0%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{x \cdot \left(y - 1\right)}{z}} \]
   6. 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. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-neg-frac 100.0%

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

   10. Simplified 100.0%

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

   11. Taylor expanded in y around 0 100.0%

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

       1. +-commutative 100.0%

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

   13. Simplified 100.0%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -260000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;\frac{y}{z} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-9} \lor \neg \left(y \leq 1.35 \cdot 10^{-36}\right):\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.8e-9) (not (<= y 1.35e-36))) (* z (/ y z)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e-9) || !(y <= 1.35e-36)) {
		tmp = z * (y / z);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-5.8d-9)) .or. (.not. (y <= 1.35d-36))) then
        tmp = z * (y / z)
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e-9) || !(y <= 1.35e-36)) {
		tmp = z * (y / z);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.8e-9) or not (y <= 1.35e-36):
		tmp = z * (y / z)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.8e-9) || !(y <= 1.35e-36))
		tmp = Float64(z * Float64(y / z));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.8e-9) || ~((y <= 1.35e-36)))
		tmp = z * (y / z);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.8e-9], N[Not[LessEqual[y, 1.35e-36]], $MachinePrecision]], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.79999999999999982e-9 or 1.35000000000000004e-36 < y

   1. Initial program 79.9%

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

   3. Taylor expanded in y around inf 77.4%

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

   4. Taylor expanded in z around inf 39.3%

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

      1. associate-/l* 55.0%

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

      2. associate-/r/ 57.5%

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

   6. Applied egg-rr 57.5%

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

   if -5.79999999999999982e-9 < y < 1.35000000000000004e-36

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 82.1%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-9} \lor \neg \left(y \leq 1.35 \cdot 10^{-36}\right):\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-9}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.8e-9) y (if (<= y 1.25e-37) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e-9) {
		tmp = y;
	} else if (y <= 1.25e-37) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.8d-9)) then
        tmp = y
    else if (y <= 1.25d-37) then
        tmp = x / z
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e-9) {
		tmp = y;
	} else if (y <= 1.25e-37) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.8e-9:
		tmp = y
	elif y <= 1.25e-37:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.8e-9)
		tmp = y;
	elseif (y <= 1.25e-37)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.8e-9)
		tmp = y;
	elseif (y <= 1.25e-37)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.8e-9], y, If[LessEqual[y, 1.25e-37], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -5.79999999999999982e-9 or 1.2499999999999999e-37 < y

   1. Initial program 80.0%

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

   3. Taylor expanded in x around 0 55.2%

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

   if -5.79999999999999982e-9 < y < 1.2499999999999999e-37

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 82.7%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-9}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ y + \frac{x}{z} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.6%

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

   1. div-inv 88.3%

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

   2. +-commutative 88.3%

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

   3. fma-def 88.3%

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

4. Applied egg-rr 88.3%

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

5. Taylor expanded in x around -inf 97.1%

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

   1. mul-1-neg 97.1%

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

   2. unsub-neg 97.1%

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

   3. associate-/l* 96.9%

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

   4. sub-neg 96.9%

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

   5. metadata-eval 96.9%

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

7. Simplified 96.9%

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

8. Taylor expanded in y around 0 77.5%

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

   1. neg-mul-1 77.5%

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

   2. distribute-neg-frac 77.5%

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

10. Simplified 77.5%

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

11. Taylor expanded in y around 0 77.5%

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

    1. +-commutative 77.5%

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

13. Simplified 77.5%

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

14. Final simplification 77.5%

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

Alternative 7: 40.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 88.6%

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

3. Taylor expanded in x around 0 39.4%

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

4. Final simplification 39.4%

   \[\leadsto y \]
5. Add Preprocessing

Developer target: 93.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024040 
(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))