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

Percentage Accurate: 88.4% → 99.9%

Time: 7.2s

Alternatives: 6

Speedup: 1.0×

• 22.2% 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 88.3%

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

3. Taylor expanded in x around -inf 96.2%

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

   1. mul-1-neg 96.2%

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

   2. unsub-neg 96.2%

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

   3. associate-/l* 94.5%

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

   4. associate-/r/ 100.0%

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

   5. sub-neg 100.0%

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

   6. metadata-eval 100.0%

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

5. Simplified 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 62.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -0.19:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-118}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-96}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ y z))))
   (if (<= y -0.19)
     t_0
     (if (<= y 1.7e-118)
       (/ x z)
       (if (<= y 3.8e-96) y (if (<= y 1.7e-22) (/ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y / z);
	double tmp;
	if (y <= -0.19) {
		tmp = t_0;
	} else if (y <= 1.7e-118) {
		tmp = x / z;
	} else if (y <= 3.8e-96) {
		tmp = y;
	} else if (y <= 1.7e-22) {
		tmp = x / z;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = z * (y / z)
    if (y <= (-0.19d0)) then
        tmp = t_0
    else if (y <= 1.7d-118) then
        tmp = x / z
    else if (y <= 3.8d-96) then
        tmp = y
    else if (y <= 1.7d-22) then
        tmp = x / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y / z);
	double tmp;
	if (y <= -0.19) {
		tmp = t_0;
	} else if (y <= 1.7e-118) {
		tmp = x / z;
	} else if (y <= 3.8e-96) {
		tmp = y;
	} else if (y <= 1.7e-22) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y / z)
	tmp = 0
	if y <= -0.19:
		tmp = t_0
	elif y <= 1.7e-118:
		tmp = x / z
	elif y <= 3.8e-96:
		tmp = y
	elif y <= 1.7e-22:
		tmp = x / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y / z))
	tmp = 0.0
	if (y <= -0.19)
		tmp = t_0;
	elseif (y <= 1.7e-118)
		tmp = Float64(x / z);
	elseif (y <= 3.8e-96)
		tmp = y;
	elseif (y <= 1.7e-22)
		tmp = Float64(x / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y / z);
	tmp = 0.0;
	if (y <= -0.19)
		tmp = t_0;
	elseif (y <= 1.7e-118)
		tmp = x / z;
	elseif (y <= 3.8e-96)
		tmp = y;
	elseif (y <= 1.7e-22)
		tmp = x / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.19], t$95$0, If[LessEqual[y, 1.7e-118], N[(x / z), $MachinePrecision], If[LessEqual[y, 3.8e-96], y, If[LessEqual[y, 1.7e-22], N[(x / z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.19 or 1.6999999999999999e-22 < y

   1. Initial program 77.5%

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

   3. Taylor expanded in x around 0 32.0%

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

      1. associate-/l* 50.6%

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

      2. associate-/r/ 56.6%

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

   5. Applied egg-rr 56.6%

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

   if -0.19 < y < 1.69999999999999995e-118 or 3.8000000000000001e-96 < y < 1.6999999999999999e-22

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 81.0%

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

   if 1.69999999999999995e-118 < y < 3.8000000000000001e-96

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 77.3%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.19:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-118}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-96}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-48}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-118} \lor \neg \left(y \leq 3.65 \cdot 10^{-96}\right) \land y \leq 2.2 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.2e-48)
   y
   (if (or (<= y 1.7e-118) (and (not (<= y 3.65e-96)) (<= y 2.2e-22)))
     (/ x z)
     y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.2e-48) {
		tmp = y;
	} else if ((y <= 1.7e-118) || (!(y <= 3.65e-96) && (y <= 2.2e-22))) {
		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 <= (-8.2d-48)) then
        tmp = y
    else if ((y <= 1.7d-118) .or. (.not. (y <= 3.65d-96)) .and. (y <= 2.2d-22)) 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 <= -8.2e-48) {
		tmp = y;
	} else if ((y <= 1.7e-118) || (!(y <= 3.65e-96) && (y <= 2.2e-22))) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.2e-48:
		tmp = y
	elif (y <= 1.7e-118) or (not (y <= 3.65e-96) and (y <= 2.2e-22)):
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.2e-48)
		tmp = y;
	elseif ((y <= 1.7e-118) || (!(y <= 3.65e-96) && (y <= 2.2e-22)))
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.2e-48)
		tmp = y;
	elseif ((y <= 1.7e-118) || (~((y <= 3.65e-96)) && (y <= 2.2e-22)))
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.2e-48], y, If[Or[LessEqual[y, 1.7e-118], And[N[Not[LessEqual[y, 3.65e-96]], $MachinePrecision], LessEqual[y, 2.2e-22]]], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -8.20000000000000028e-48 or 1.69999999999999995e-118 < y < 3.64999999999999997e-96 or 2.2000000000000001e-22 < y

   1. Initial program 80.9%

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

   3. Taylor expanded in x around 0 52.4%

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

   if -8.20000000000000028e-48 < y < 1.69999999999999995e-118 or 3.64999999999999997e-96 < y < 2.2000000000000001e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.0%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-48}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-118} \lor \neg \left(y \leq 3.65 \cdot 10^{-96}\right) \land y \leq 2.2 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+24} \lor \neg \left(y \leq 3.2 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.35e+24) (not (<= y 3.2e-6)))
   (* y (- 1.0 (/ x z)))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.35e+24) || !(y <= 3.2e-6)) {
		tmp = y * (1.0 - (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 <= (-1.35d+24)) .or. (.not. (y <= 3.2d-6))) then
        tmp = y * (1.0d0 - (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 <= -1.35e+24) || !(y <= 3.2e-6)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.35e+24) or not (y <= 3.2e-6):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.35e+24) || !(y <= 3.2e-6))
		tmp = Float64(y * Float64(1.0 - 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 <= -1.35e+24) || ~((y <= 3.2e-6)))
		tmp = y * (1.0 - (x / z));
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.35e+24], N[Not[LessEqual[y, 3.2e-6]], $MachinePrecision]], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e24 or 3.1999999999999999e-6 < y

   1. Initial program 76.3%

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

   3. Taylor expanded in x around -inf 92.4%

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

      1. mul-1-neg 92.4%

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

      2. unsub-neg 92.4%

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

      3. associate-/l* 88.8%

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

      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%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around inf 99.9%

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

   if -1.35e24 < y < 3.1999999999999999e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in x around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-/l* 100.0%

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

      4. associate-/r/ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in y around 0 98.4%

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

      1. associate-*r/ 98.4%

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

      2. neg-mul-1 98.4%

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

   10. Simplified 98.4%

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

   11. Taylor expanded in y around 0 98.4%

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

       1. +-commutative 98.4%

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

   13. Simplified 98.4%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+24} \lor \neg \left(y \leq 3.2 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.4% 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 88.3%

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

3. Taylor expanded in x around -inf 96.2%

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

   1. mul-1-neg 96.2%

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

   2. unsub-neg 96.2%

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

   3. associate-/l* 94.5%

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

   4. associate-/r/ 100.0%

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

   5. sub-neg 100.0%

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

   6. metadata-eval 100.0%

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

5. Simplified 100.0%

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

   1. *-commutative 100.0%

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

   2. clear-num 99.8%

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

   3. un-div-inv 99.8%

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

7. Applied egg-rr 99.8%

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

8. Taylor expanded in y around 0 76.5%

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

   1. associate-*r/ 76.5%

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

   2. neg-mul-1 76.5%

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

10. Simplified 76.5%

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

11. Taylor expanded in y around 0 76.5%

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

    1. +-commutative 76.5%

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

13. Simplified 76.5%

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

14. Final simplification 76.5%

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

Alternative 6: 39.8% 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 88.3%

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

3. Taylor expanded in x around 0 38.2%

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

4. Final simplification 38.2%

   \[\leadsto y \]
5. Add Preprocessing

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 2024024 
(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))