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

Percentage Accurate: 88.2% → 99.9%

Time: 10.1s

Alternatives: 11

Speedup: 0.5×

• 21.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.2% 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, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y \cdot \left(z - x\right)}{z}\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 10^{+306}\right):\\ \;\;\;\;y + x \cdot \left(\frac{1}{z} - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot z - x \cdot y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x (* y (- z x))) z)))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 1e+306)))
     (+ y (* x (- (/ 1.0 z) (/ y z))))
     (/ (+ x (- (* y z) (* x y))) z))))

C

double code(double x, double y, double z) {
	double t_0 = (x + (y * (z - x))) / z;
	double tmp;
	if ((t_0 <= -((double) INFINITY)) || !(t_0 <= 1e+306)) {
		tmp = y + (x * ((1.0 / z) - (y / z)));
	} else {
		tmp = (x + ((y * z) - (x * y))) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + (y * (z - x))) / z;
	double tmp;
	if ((t_0 <= -Double.POSITIVE_INFINITY) || !(t_0 <= 1e+306)) {
		tmp = y + (x * ((1.0 / z) - (y / z)));
	} else {
		tmp = (x + ((y * z) - (x * y))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + (y * (z - x))) / z
	tmp = 0
	if (t_0 <= -math.inf) or not (t_0 <= 1e+306):
		tmp = y + (x * ((1.0 / z) - (y / z)))
	else:
		tmp = (x + ((y * z) - (x * y))) / z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + Float64(y * Float64(z - x))) / z)
	tmp = 0.0
	if ((t_0 <= Float64(-Inf)) || !(t_0 <= 1e+306))
		tmp = Float64(y + Float64(x * Float64(Float64(1.0 / z) - Float64(y / z))));
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) - Float64(x * y))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + (y * (z - x))) / z;
	tmp = 0.0;
	if ((t_0 <= -Inf) || ~((t_0 <= 1e+306)))
		tmp = y + (x * ((1.0 / z) - (y / z)));
	else
		tmp = (x + ((y * z) - (x * y))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[Or[LessEqual[t$95$0, (-Infinity)], N[Not[LessEqual[t$95$0, 1e+306]], $MachinePrecision]], N[(y + N[(x * N[(N[(1.0 / z), $MachinePrecision] - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (*.f64 y (-.f64 z x))) z) < -inf.0 or 1.00000000000000002e306 < (/.f64 (+.f64 x (*.f64 y (-.f64 z x))) z)

   1. Initial program 62.9%

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

   3. Taylor expanded in x around 0 100.0%

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

   if -inf.0 < (/.f64 (+.f64 x (*.f64 y (-.f64 z x))) z) < 1.00000000000000002e306

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 99.9%

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

   4. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y \cdot \left(z - x\right)}{z} \leq -\infty \lor \neg \left(\frac{x + y \cdot \left(z - x\right)}{z} \leq 10^{+306}\right):\\ \;\;\;\;y + x \cdot \left(\frac{1}{z} - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot z - x \cdot y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2000:\\ \;\;\;\;y - y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+27}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2000.0)
   (- y (* y (/ x z)))
   (if (<= y 6e+27) (/ (+ x (* y (- z x))) z) (* y (/ (- z x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2000.0) {
		tmp = y - (y * (x / z));
	} else if (y <= 6e+27) {
		tmp = (x + (y * (z - x))) / z;
	} else {
		tmp = 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 (y <= (-2000.0d0)) then
        tmp = y - (y * (x / z))
    else if (y <= 6d+27) then
        tmp = (x + (y * (z - x))) / z
    else
        tmp = y * ((z - x) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2000.0) {
		tmp = y - (y * (x / z));
	} else if (y <= 6e+27) {
		tmp = (x + (y * (z - x))) / z;
	} else {
		tmp = y * ((z - x) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2000.0:
		tmp = y - (y * (x / z))
	elif y <= 6e+27:
		tmp = (x + (y * (z - x))) / z
	else:
		tmp = y * ((z - x) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2000.0)
		tmp = Float64(y - Float64(y * Float64(x / z)));
	elseif (y <= 6e+27)
		tmp = Float64(Float64(x + Float64(y * Float64(z - x))) / z);
	else
		tmp = Float64(y * Float64(Float64(z - x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2000.0)
		tmp = y - (y * (x / z));
	elseif (y <= 6e+27)
		tmp = (x + (y * (z - x))) / z;
	else
		tmp = y * ((z - x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2000.0], N[(y - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+27], N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(y * N[(N[(z - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2e3

   1. Initial program 77.3%

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

   3. Taylor expanded in x around 0 92.7%

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

   4. Taylor expanded in y around inf 92.8%

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

      1. mul-1-neg 92.8%

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

      2. distribute-neg-frac2 92.8%

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

      3. associate-*r/ 92.6%

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

   6. Simplified 92.6%

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

      1. *-commutative 92.6%

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

      2. add-sqr-sqrt 41.8%

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

      3. sqrt-unprod 61.3%

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

      4. sqr-neg 61.3%

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

      5. sqrt-unprod 23.6%

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

      6. add-sqr-sqrt 48.1%

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

      7. cancel-sign-sub 48.1%

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

      8. distribute-frac-neg2 48.1%

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

      9. distribute-frac-neg2 48.1%

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

      10. distribute-frac-neg 48.1%

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

      11. div-inv 48.1%

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

      12. associate-*l* 52.2%

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

      13. add-sqr-sqrt 52.2%

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

      14. sqrt-unprod 26.1%

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

      15. sqr-neg 26.1%

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

      16. sqrt-unprod 0.0%

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

      17. add-sqr-sqrt 99.7%

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

      18. associate-*l/ 99.8%

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

      19. *-un-lft-identity 99.8%

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

   8. Applied egg-rr 99.8%

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

   if -2e3 < y < 5.99999999999999953e27

   1. Initial program 100.0%

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

   if 5.99999999999999953e27 < y

   1. Initial program 70.7%

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

   3. Taylor expanded in y around inf 70.7%

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

      1. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

Alternative 3: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2020 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \frac{z - x}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2020.0) (not (<= y 1.0))) (* y (/ (- z x) z)) (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2020.0) || !(y <= 1.0)) {
		tmp = y * ((z - 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 <= (-2020.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * ((z - 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 <= -2020.0) || !(y <= 1.0)) {
		tmp = y * ((z - x) / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2020.0) or not (y <= 1.0):
		tmp = y * ((z - x) / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2020.0) || !(y <= 1.0))
		tmp = Float64(y * Float64(Float64(z - 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 <= -2020.0) || ~((y <= 1.0)))
		tmp = y * ((z - x) / z);
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2020.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2020 or 1 < y

   1. Initial program 75.4%

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

   3. Taylor expanded in y around inf 75.3%

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

      1. associate-/l* 99.8%

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

   5. Simplified 99.8%

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

   if -2020 < y < 1

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 99.7%

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

   4. Taylor expanded in y around 0 98.1%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2020 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \frac{z - x}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+117} \lor \neg \left(x \leq 1.52 \cdot 10^{+71}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.5e+117) (not (<= x 1.52e+71)))
   (* x (/ (- 1.0 y) z))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.5e+117) || !(x <= 1.52e+71)) {
		tmp = x * ((1.0 - y) / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.5d+117)) .or. (.not. (x <= 1.52d+71))) then
        tmp = x * ((1.0d0 - y) / z)
    else
        tmp = y + (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.5e+117) || !(x <= 1.52e+71)) {
		tmp = x * ((1.0 - y) / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.5e+117) or not (x <= 1.52e+71):
		tmp = x * ((1.0 - y) / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.5e+117) || !(x <= 1.52e+71))
		tmp = Float64(x * Float64(Float64(1.0 - y) / z));
	else
		tmp = Float64(y + Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.5e+117) || ~((x <= 1.52e+71)))
		tmp = x * ((1.0 - y) / z);
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.5e+117], N[Not[LessEqual[x, 1.52e+71]], $MachinePrecision]], N[(x * N[(N[(1.0 - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5e117 or 1.5199999999999999e71 < x

   1. Initial program 92.2%

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

   3. Taylor expanded in x around inf 87.7%

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

      1. associate-/l* 91.6%

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

      2. mul-1-neg 91.6%

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

      3. unsub-neg 91.6%

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

   5. Simplified 91.6%

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

   if -1.5e117 < x < 1.5199999999999999e71

   1. Initial program 83.5%

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

   3. Taylor expanded in x around 0 93.2%

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

   4. Taylor expanded in y around 0 85.4%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+117} \lor \neg \left(x \leq 1.52 \cdot 10^{+71}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2020:\\ \;\;\;\;y - y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2020.0)
   (- y (* y (/ x z)))
   (if (<= y 1.0) (+ y (/ x z)) (* y (/ (- z x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2020.0) {
		tmp = y - (y * (x / z));
	} else if (y <= 1.0) {
		tmp = y + (x / z);
	} else {
		tmp = 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 (y <= (-2020.0d0)) then
        tmp = y - (y * (x / z))
    else if (y <= 1.0d0) then
        tmp = y + (x / z)
    else
        tmp = y * ((z - x) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2020.0) {
		tmp = y - (y * (x / z));
	} else if (y <= 1.0) {
		tmp = y + (x / z);
	} else {
		tmp = y * ((z - x) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2020.0:
		tmp = y - (y * (x / z))
	elif y <= 1.0:
		tmp = y + (x / z)
	else:
		tmp = y * ((z - x) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2020.0)
		tmp = Float64(y - Float64(y * Float64(x / z)));
	elseif (y <= 1.0)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(y * Float64(Float64(z - x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2020.0)
		tmp = y - (y * (x / z));
	elseif (y <= 1.0)
		tmp = y + (x / z);
	else
		tmp = y * ((z - x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2020.0], N[(y - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2020

   1. Initial program 78.5%

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

   3. Taylor expanded in x around 0 92.6%

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

   4. Taylor expanded in y around inf 92.7%

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

      1. mul-1-neg 92.7%

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

      2. distribute-neg-frac2 92.7%

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

      3. associate-*r/ 92.5%

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

   6. Simplified 92.5%

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

      1. *-commutative 92.5%

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

      2. add-sqr-sqrt 42.5%

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

      3. sqrt-unprod 60.7%

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

      4. sqr-neg 60.7%

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

      5. sqrt-unprod 22.4%

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

      6. add-sqr-sqrt 47.4%

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

      7. cancel-sign-sub 47.4%

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

      8. distribute-frac-neg2 47.4%

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

      9. distribute-frac-neg2 47.4%

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

      10. distribute-frac-neg 47.4%

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

      11. div-inv 47.4%

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

      12. associate-*l* 51.5%

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

      13. add-sqr-sqrt 51.5%

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

      14. sqrt-unprod 24.9%

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

      15. sqr-neg 24.9%

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

      16. sqrt-unprod 0.0%

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

      17. add-sqr-sqrt 99.7%

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

      18. associate-*l/ 99.8%

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

      19. *-un-lft-identity 99.8%

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

   8. Applied egg-rr 99.8%

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

   if -2020 < y < 1

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 99.7%

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

   4. Taylor expanded in y around 0 98.1%

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

   if 1 < y

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf 72.4%

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

      1. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

Alternative 6: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4.5 \cdot 10^{-287} \lor \neg \left(z \leq 7.2 \cdot 10^{-198}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z 4.5e-287) (not (<= z 7.2e-198)))
   (+ y (/ x z))
   (* (/ x z) (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= 4.5e-287) || !(z <= 7.2e-198)) {
		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 ((z <= 4.5d-287) .or. (.not. (z <= 7.2d-198))) 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 ((z <= 4.5e-287) || !(z <= 7.2e-198)) {
		tmp = y + (x / z);
	} else {
		tmp = (x / z) * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= 4.5e-287) or not (z <= 7.2e-198):
		tmp = y + (x / z)
	else:
		tmp = (x / z) * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= 4.5e-287) || !(z <= 7.2e-198))
		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 ((z <= 4.5e-287) || ~((z <= 7.2e-198)))
		tmp = y + (x / z);
	else
		tmp = (x / z) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, 4.5e-287], N[Not[LessEqual[z, 7.2e-198]], $MachinePrecision]], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.50000000000000017e-287 or 7.19999999999999996e-198 < z

   1. Initial program 85.7%

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

   3. Taylor expanded in x around 0 96.6%

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

   4. Taylor expanded in y around 0 80.4%

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

   if 4.50000000000000017e-287 < z < 7.19999999999999996e-198

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 92.2%

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

      1. mul-1-neg 92.2%

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

      2. distribute-lft-neg-out 92.2%

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

      3. *-commutative 92.2%

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

   5. Simplified 92.2%

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

      1. *-un-lft-identity 92.2%

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

      2. distribute-rgt-neg-out 92.2%

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

      3. distribute-lft-neg-in 92.2%

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

      4. distribute-rgt-in 92.1%

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

      5. sub-neg 92.1%

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

      6. *-commutative 92.1%

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

      7. associate-*l/ 84.2%

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

      8. div-inv 84.3%

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

      9. associate-*l* 92.2%

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

      10. associate-*l/ 92.2%

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

      11. *-un-lft-identity 92.2%

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

   7. Applied egg-rr 92.2%

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

   8. Taylor expanded in y around inf 77.7%

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

      1. neg-mul-1 77.7%

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

   10. Simplified 77.7%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.5 \cdot 10^{-287} \lor \neg \left(z \leq 7.2 \cdot 10^{-198}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-41}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.2e-41) y (if (<= y 1.2e-11) (/ x z) (* z (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.2e-41) {
		tmp = y;
	} else if (y <= 1.2e-11) {
		tmp = 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 <= (-6.2d-41)) then
        tmp = y
    else if (y <= 1.2d-11) then
        tmp = 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 <= -6.2e-41) {
		tmp = y;
	} else if (y <= 1.2e-11) {
		tmp = x / z;
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.2e-41:
		tmp = y
	elif y <= 1.2e-11:
		tmp = x / z
	else:
		tmp = z * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.2e-41)
		tmp = y;
	elseif (y <= 1.2e-11)
		tmp = 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 <= -6.2e-41)
		tmp = y;
	elseif (y <= 1.2e-11)
		tmp = x / z;
	else
		tmp = z * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.2e-41], y, If[LessEqual[y, 1.2e-11], N[(x / z), $MachinePrecision], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.20000000000000001e-41

   1. Initial program 79.5%

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

   3. Taylor expanded in x around 0 52.6%

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

   if -6.20000000000000001e-41 < y < 1.2000000000000001e-11

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.3%

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

   if 1.2000000000000001e-11 < y

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf 72.4%

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

   4. Taylor expanded in z around inf 31.5%

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

      1. *-commutative 31.5%

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

      2. associate-/l* 54.8%

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

   6. Applied egg-rr 54.8%

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

Alternative 8: 60.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-39}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.45e-39) y (if (<= y 8e-12) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.45e-39) {
		tmp = y;
	} else if (y <= 8e-12) {
		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 <= (-1.45d-39)) then
        tmp = y
    else if (y <= 8d-12) 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 <= -1.45e-39) {
		tmp = y;
	} else if (y <= 8e-12) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.45e-39:
		tmp = y
	elif y <= 8e-12:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.45e-39)
		tmp = y;
	elseif (y <= 8e-12)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.45e-39)
		tmp = y;
	elseif (y <= 8e-12)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.45e-39], y, If[LessEqual[y, 8e-12], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.44999999999999994e-39 or 7.99999999999999984e-12 < y

   1. Initial program 76.1%

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

   3. Taylor expanded in x around 0 53.1%

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

   if -1.44999999999999994e-39 < y < 7.99999999999999984e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.3%

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

Alternative 9: 81.6% accurate, 0.9× 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 91.9%

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

   3. Taylor expanded in x around 0 97.2%

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

   4. Taylor expanded in y around 0 85.7%

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

   if 1 < y

   1. Initial program 72.4%

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

   3. Taylor expanded in x around 0 91.5%

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

   4. Taylor expanded in y around 0 53.1%

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

      1. add-sqr-sqrt 25.8%

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

      2. sqrt-unprod 59.1%

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

      3. sqr-neg 59.1%

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

      4. sqrt-unprod 33.7%

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

      5. add-sqr-sqrt 63.1%

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

      6. distribute-frac-neg 63.1%

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

      7. sub-neg 63.1%

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

   6. Applied egg-rr 63.1%

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

Alternative 10: 78.0% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.7%

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

3. Taylor expanded in x around 0 95.7%

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

4. Taylor expanded in y around 0 77.1%

   \[\leadsto y + \color{blue}{\frac{x}{z}} \]
5. Add Preprocessing

Alternative 11: 40.4% 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 86.7%

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

3. Taylor expanded in x around 0 39.4%

   \[\leadsto \color{blue}{y} \]
4. Add Preprocessing

Developer target: 93.7% 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 2024110 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :alt
  (- (+ y (/ x z)) (/ y (/ z x)))

  (/ (+ x (* y (- z x))) z))