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

Percentage Accurate: 88.1% → 99.5%

Time: 9.5s

Alternatives: 12

Speedup: 0.5×

• 20.4% 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: 88.1% 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, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + y \cdot \left(z - x\right)}{z}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+293} \lor \neg \left(t\_0 \leq 2 \cdot 10^{+300}\right):\\ \;\;\;\;y + x \cdot \left(\frac{1}{z} - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x (* y (- z x))) z)))
   (if (or (<= t_0 -4e+293) (not (<= t_0 2e+300)))
     (+ y (* x (- (/ 1.0 z) (/ y z))))
     (+ (/ x z) (* y (- 1.0 (/ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + (y * (z - x))) / z;
	double tmp;
	if ((t_0 <= -4e+293) || !(t_0 <= 2e+300)) {
		tmp = y + (x * ((1.0 / z) - (y / z)));
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (x + (y * (z - x))) / z
    if ((t_0 <= (-4d+293)) .or. (.not. (t_0 <= 2d+300))) then
        tmp = y + (x * ((1.0d0 / z) - (y / z)))
    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 t_0 = (x + (y * (z - x))) / z;
	double tmp;
	if ((t_0 <= -4e+293) || !(t_0 <= 2e+300)) {
		tmp = y + (x * ((1.0 / z) - (y / z)));
	} else {
		tmp = (x / z) + (y * (1.0 - (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + (y * (z - x))) / z
	tmp = 0
	if (t_0 <= -4e+293) or not (t_0 <= 2e+300):
		tmp = y + (x * ((1.0 / z) - (y / z)))
	else:
		tmp = (x / z) + (y * (1.0 - (x / 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 <= -4e+293) || !(t_0 <= 2e+300))
		tmp = Float64(y + Float64(x * Float64(Float64(1.0 / z) - Float64(y / z))));
	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)
	t_0 = (x + (y * (z - x))) / z;
	tmp = 0.0;
	if ((t_0 <= -4e+293) || ~((t_0 <= 2e+300)))
		tmp = y + (x * ((1.0 / z) - (y / z)));
	else
		tmp = (x / z) + (y * (1.0 - (x / 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, -4e+293], N[Not[LessEqual[t$95$0, 2e+300]], $MachinePrecision]], N[(y + N[(x * N[(N[(1.0 / z), $MachinePrecision] - N[(y / z), $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 (/.f64 (+.f64 x (*.f64 y (-.f64 z x))) z) < -3.9999999999999997e293 or 2.0000000000000001e300 < (/.f64 (+.f64 x (*.f64 y (-.f64 z x))) z)

   1. Initial program 70.7%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   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 -3.9999999999999997e293 < (/.f64 (+.f64 x (*.f64 y (-.f64 z x))) z) < 2.0000000000000001e300

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + y \cdot \left(z - x\right)}{z} \leq -4 \cdot 10^{+293} \lor \neg \left(\frac{x + y \cdot \left(z - x\right)}{z} \leq 2 \cdot 10^{+300}\right):\\ \;\;\;\;y + x \cdot \left(\frac{1}{z} - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+274}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{+174}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{elif}\;y \leq 8:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+92} \lor \neg \left(y \leq 2.6 \cdot 10^{+210}\right):\\ \;\;\;\;\frac{x \cdot y}{-z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ y z))))
   (if (<= y -1.7e+274)
     t_0
     (if (<= y -6.3e+174)
       (* y (/ (- x) z))
       (if (<= y 8.0)
         (+ y (/ x z))
         (if (or (<= y 1.26e+92) (not (<= y 2.6e+210)))
           (/ (* x y) (- z))
           t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y / z);
	double tmp;
	if (y <= -1.7e+274) {
		tmp = t_0;
	} else if (y <= -6.3e+174) {
		tmp = y * (-x / z);
	} else if (y <= 8.0) {
		tmp = y + (x / z);
	} else if ((y <= 1.26e+92) || !(y <= 2.6e+210)) {
		tmp = (x * y) / -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 <= (-1.7d+274)) then
        tmp = t_0
    else if (y <= (-6.3d+174)) then
        tmp = y * (-x / z)
    else if (y <= 8.0d0) then
        tmp = y + (x / z)
    else if ((y <= 1.26d+92) .or. (.not. (y <= 2.6d+210))) then
        tmp = (x * y) / -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 <= -1.7e+274) {
		tmp = t_0;
	} else if (y <= -6.3e+174) {
		tmp = y * (-x / z);
	} else if (y <= 8.0) {
		tmp = y + (x / z);
	} else if ((y <= 1.26e+92) || !(y <= 2.6e+210)) {
		tmp = (x * y) / -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y / z)
	tmp = 0
	if y <= -1.7e+274:
		tmp = t_0
	elif y <= -6.3e+174:
		tmp = y * (-x / z)
	elif y <= 8.0:
		tmp = y + (x / z)
	elif (y <= 1.26e+92) or not (y <= 2.6e+210):
		tmp = (x * y) / -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 <= -1.7e+274)
		tmp = t_0;
	elseif (y <= -6.3e+174)
		tmp = Float64(y * Float64(Float64(-x) / z));
	elseif (y <= 8.0)
		tmp = Float64(y + Float64(x / z));
	elseif ((y <= 1.26e+92) || !(y <= 2.6e+210))
		tmp = Float64(Float64(x * y) / Float64(-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 <= -1.7e+274)
		tmp = t_0;
	elseif (y <= -6.3e+174)
		tmp = y * (-x / z);
	elseif (y <= 8.0)
		tmp = y + (x / z);
	elseif ((y <= 1.26e+92) || ~((y <= 2.6e+210)))
		tmp = (x * y) / -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, -1.7e+274], t$95$0, If[LessEqual[y, -6.3e+174], N[(y * N[((-x) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.0], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.26e+92], N[Not[LessEqual[y, 2.6e+210]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] / (-z)), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.7e274 or 1.26e92 < y < 2.5999999999999999e210

   1. Initial program 59.2%

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

   3. Taylor expanded in z around inf 31.7%

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

   4. Taylor expanded in x around 0 30.0%

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

      1. *-commutative 30.0%

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

   6. Simplified 30.0%

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

      1. associate-/l* 74.9%

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

      2. *-commutative 74.9%

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

   8. Applied egg-rr 74.9%

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

   if -1.7e274 < y < -6.3000000000000001e174

   1. Initial program 84.4%

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

   3. Taylor expanded in y around inf 84.4%

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

      1. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 81.6%

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

      1. neg-mul-1 81.6%

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

   8. Simplified 81.6%

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

   if -6.3000000000000001e174 < y < 8

   1. Initial program 94.4%

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

   3. Taylor expanded in z around inf 87.8%

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

   4. Taylor expanded in x around 0 91.5%

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

      1. +-commutative 91.5%

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

   6. Simplified 91.5%

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

   if 8 < y < 1.26e92 or 2.5999999999999999e210 < y

   1. Initial program 93.6%

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

   3. Taylor expanded in y around inf 91.3%

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

      1. associate-/l* 97.4%

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

      2. div-sub 97.4%

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

      3. *-inverses 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in x around inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. *-commutative 74.1%

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

      3. distribute-frac-neg2 74.1%

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

   8. Simplified 74.1%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+274}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{+174}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{elif}\;y \leq 8:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+92} \lor \neg \left(y \leq 2.6 \cdot 10^{+210}\right):\\ \;\;\;\;\frac{x \cdot y}{-z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{y}{z}\\ t_1 := y \cdot \frac{-x}{z}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+269}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+92} \lor \neg \left(y \leq 8.8 \cdot 10^{+207}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ y z))) (t_1 (* y (/ (- x) z))))
   (if (<= y -2.6e+269)
     t_0
     (if (<= y -4.8e+173)
       t_1
       (if (<= y 9.0)
         (+ y (/ x z))
         (if (or (<= y 1.08e+92) (not (<= y 8.8e+207))) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y / z);
	double t_1 = y * (-x / z);
	double tmp;
	if (y <= -2.6e+269) {
		tmp = t_0;
	} else if (y <= -4.8e+173) {
		tmp = t_1;
	} else if (y <= 9.0) {
		tmp = y + (x / z);
	} else if ((y <= 1.08e+92) || !(y <= 8.8e+207)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = z * (y / z)
    t_1 = y * (-x / z)
    if (y <= (-2.6d+269)) then
        tmp = t_0
    else if (y <= (-4.8d+173)) then
        tmp = t_1
    else if (y <= 9.0d0) then
        tmp = y + (x / z)
    else if ((y <= 1.08d+92) .or. (.not. (y <= 8.8d+207))) then
        tmp = t_1
    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 t_1 = y * (-x / z);
	double tmp;
	if (y <= -2.6e+269) {
		tmp = t_0;
	} else if (y <= -4.8e+173) {
		tmp = t_1;
	} else if (y <= 9.0) {
		tmp = y + (x / z);
	} else if ((y <= 1.08e+92) || !(y <= 8.8e+207)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y / z)
	t_1 = y * (-x / z)
	tmp = 0
	if y <= -2.6e+269:
		tmp = t_0
	elif y <= -4.8e+173:
		tmp = t_1
	elif y <= 9.0:
		tmp = y + (x / z)
	elif (y <= 1.08e+92) or not (y <= 8.8e+207):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y / z))
	t_1 = Float64(y * Float64(Float64(-x) / z))
	tmp = 0.0
	if (y <= -2.6e+269)
		tmp = t_0;
	elseif (y <= -4.8e+173)
		tmp = t_1;
	elseif (y <= 9.0)
		tmp = Float64(y + Float64(x / z));
	elseif ((y <= 1.08e+92) || !(y <= 8.8e+207))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y / z);
	t_1 = y * (-x / z);
	tmp = 0.0;
	if (y <= -2.6e+269)
		tmp = t_0;
	elseif (y <= -4.8e+173)
		tmp = t_1;
	elseif (y <= 9.0)
		tmp = y + (x / z);
	elseif ((y <= 1.08e+92) || ~((y <= 8.8e+207)))
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(y * N[((-x) / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+269], t$95$0, If[LessEqual[y, -4.8e+173], t$95$1, If[LessEqual[y, 9.0], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.08e+92], N[Not[LessEqual[y, 8.8e+207]], $MachinePrecision]], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e269 or 1.08e92 < y < 8.80000000000000034e207

   1. Initial program 59.2%

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

   3. Taylor expanded in z around inf 31.7%

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

   4. Taylor expanded in x around 0 30.0%

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

      1. *-commutative 30.0%

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

   6. Simplified 30.0%

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

      1. associate-/l* 74.9%

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

      2. *-commutative 74.9%

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

   8. Applied egg-rr 74.9%

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

   if -2.6e269 < y < -4.7999999999999998e173 or 9 < y < 1.08e92 or 8.80000000000000034e207 < y

   1. Initial program 90.9%

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

   3. Taylor expanded in y around inf 89.2%

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

      1. associate-/l* 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in z around 0 76.2%

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

      1. neg-mul-1 76.2%

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

   8. Simplified 76.2%

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

   if -4.7999999999999998e173 < y < 9

   1. Initial program 94.4%

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

   3. Taylor expanded in z around inf 87.8%

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

   4. Taylor expanded in x around 0 91.5%

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

      1. +-commutative 91.5%

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

   6. Simplified 91.5%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+269}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+173}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{elif}\;y \leq 9:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+92} \lor \neg \left(y \leq 8.8 \cdot 10^{+207}\right):\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.5:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+92} \lor \neg \left(y \leq 1.6 \cdot 10^{+211}\right):\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 5.5)
   (+ y (/ x z))
   (if (or (<= y 1.02e+92) (not (<= y 1.6e+211)))
     (* x (/ (- y) z))
     (* z (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.5) {
		tmp = y + (x / z);
	} else if ((y <= 1.02e+92) || !(y <= 1.6e+211)) {
		tmp = x * (-y / z);
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 5.5d0) then
        tmp = y + (x / z)
    else if ((y <= 1.02d+92) .or. (.not. (y <= 1.6d+211))) then
        tmp = x * (-y / z)
    else
        tmp = z * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.5) {
		tmp = y + (x / z);
	} else if ((y <= 1.02e+92) || !(y <= 1.6e+211)) {
		tmp = x * (-y / z);
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 5.5:
		tmp = y + (x / z)
	elif (y <= 1.02e+92) or not (y <= 1.6e+211):
		tmp = x * (-y / z)
	else:
		tmp = z * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 5.5)
		tmp = Float64(y + Float64(x / z));
	elseif ((y <= 1.02e+92) || !(y <= 1.6e+211))
		tmp = Float64(x * Float64(Float64(-y) / 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 <= 5.5)
		tmp = y + (x / z);
	elseif ((y <= 1.02e+92) || ~((y <= 1.6e+211)))
		tmp = x * (-y / z);
	else
		tmp = z * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 5.5], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.02e+92], N[Not[LessEqual[y, 1.6e+211]], $MachinePrecision]], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 5.5

   1. Initial program 91.7%

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

   3. Taylor expanded in z around inf 80.8%

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

   4. Taylor expanded in x around 0 86.5%

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

      1. +-commutative 86.5%

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

   6. Simplified 86.5%

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

   if 5.5 < y < 1.02000000000000003e92 or 1.59999999999999988e211 < y

   1. Initial program 93.6%

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

   3. Taylor expanded in x around inf 75.8%

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

      1. associate-/l* 70.4%

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

      2. mul-1-neg 70.4%

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

      3. unsub-neg 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in y around inf 68.6%

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

      1. neg-mul-1 68.6%

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

   8. Simplified 68.6%

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

   if 1.02000000000000003e92 < y < 1.59999999999999988e211

   1. Initial program 59.7%

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

   3. Taylor expanded in z around inf 31.0%

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

   4. Taylor expanded in x around 0 31.5%

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

      1. *-commutative 31.5%

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

   6. Simplified 31.5%

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

      1. associate-/l* 68.9%

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

      2. *-commutative 68.9%

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

   8. Applied egg-rr 68.9%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.5:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+92} \lor \neg \left(y \leq 1.6 \cdot 10^{+211}\right):\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-25} \lor \neg \left(z \leq 3 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1e-25) (not (<= z 3e-36)))
   (+ (/ x z) (* y (- 1.0 (/ x z))))
   (/ (+ x (* y (- z x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e-25) || !(z <= 3e-36)) {
		tmp = (x / z) + (y * (1.0 - (x / z)));
	} 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 <= (-1d-25)) .or. (.not. (z <= 3d-36))) then
        tmp = (x / z) + (y * (1.0d0 - (x / z)))
    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 <= -1e-25) || !(z <= 3e-36)) {
		tmp = (x / z) + (y * (1.0 - (x / z)));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1e-25) or not (z <= 3e-36):
		tmp = (x / z) + (y * (1.0 - (x / z)))
	else:
		tmp = (x + (y * (z - x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1e-25) || !(z <= 3e-36))
		tmp = Float64(Float64(x / z) + Float64(y * Float64(1.0 - Float64(x / z))));
	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 <= -1e-25) || ~((z <= 3e-36)))
		tmp = (x / z) + (y * (1.0 - (x / z)));
	else
		tmp = (x + (y * (z - x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1e-25], N[Not[LessEqual[z, 3e-36]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] + N[(y * N[(1.0 - N[(x / z), $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 < -1.00000000000000004e-25 or 3.0000000000000002e-36 < z

   1. Initial program 77.0%

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

   3. Taylor expanded in y around 0 99.9%

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

   if -1.00000000000000004e-25 < z < 3.0000000000000002e-36

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-25} \lor \neg \left(z \leq 3 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+31} \lor \neg \left(y \leq 3 \cdot 10^{+75}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.8e+31) (not (<= y 3e+75)))
   (* y (- 1.0 (/ x z)))
   (/ (+ x (* y (- z x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.8e+31) || !(y <= 3e+75)) {
		tmp = y * (1.0 - (x / z));
	} 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 ((y <= (-2.8d+31)) .or. (.not. (y <= 3d+75))) then
        tmp = y * (1.0d0 - (x / z))
    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 ((y <= -2.8e+31) || !(y <= 3e+75)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.8e+31) or not (y <= 3e+75):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = (x + (y * (z - x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.8e+31) || !(y <= 3e+75))
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	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 ((y <= -2.8e+31) || ~((y <= 3e+75)))
		tmp = y * (1.0 - (x / z));
	else
		tmp = (x + (y * (z - x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.8e+31], N[Not[LessEqual[y, 3e+75]], $MachinePrecision]], N[(y * N[(1.0 - N[(x / z), $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 y < -2.80000000000000017e31 or 3e75 < y

   1. Initial program 74.1%

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

   3. Taylor expanded in y around inf 74.1%

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

      1. associate-/l* 99.9%

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

      2. div-sub 99.9%

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

      3. *-inverses 99.9%

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

   5. Simplified 99.9%

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

   if -2.80000000000000017e31 < y < 3e75

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+31} \lor \neg \left(y \leq 3 \cdot 10^{+75}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -23500000 \lor \neg \left(y \leq 0.0052\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -23500000.0) (not (<= y 0.0052)))
   (* y (- 1.0 (/ x z)))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -23500000.0) || !(y <= 0.0052)) {
		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 <= (-23500000.0d0)) .or. (.not. (y <= 0.0052d0))) 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 <= -23500000.0) || !(y <= 0.0052)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -23500000.0) or not (y <= 0.0052):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -23500000.0) || !(y <= 0.0052))
		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 <= -23500000.0) || ~((y <= 0.0052)))
		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, -23500000.0], N[Not[LessEqual[y, 0.0052]], $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 < -2.35e7 or 0.0051999999999999998 < y

   1. Initial program 78.0%

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

   3. Taylor expanded in y around inf 77.3%

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

      1. associate-/l* 99.1%

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

      2. div-sub 99.1%

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

      3. *-inverses 99.1%

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

   5. Simplified 99.1%

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

   if -2.35e7 < y < 0.0051999999999999998

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 98.0%

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

   4. Taylor expanded in x around 0 98.0%

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

      1. +-commutative 98.0%

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

   6. Simplified 98.0%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -23500000 \lor \neg \left(y \leq 0.0052\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \lor \neg \left(x \leq 3.5 \cdot 10^{+137}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.2) (not (<= x 3.5e+137)))
   (* x (/ (- 1.0 y) z))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.2) || !(x <= 3.5e+137)) {
		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 <= (-1.2d0)) .or. (.not. (x <= 3.5d+137))) 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 <= -1.2) || !(x <= 3.5e+137)) {
		tmp = x * ((1.0 - y) / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.2) or not (x <= 3.5e+137):
		tmp = x * ((1.0 - y) / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.2) || !(x <= 3.5e+137))
		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 <= -1.2) || ~((x <= 3.5e+137)))
		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, -1.2], N[Not[LessEqual[x, 3.5e+137]], $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 < -1.19999999999999996 or 3.5000000000000001e137 < x

   1. Initial program 89.0%

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

   3. Taylor expanded in x around inf 83.1%

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

      1. associate-/l* 89.5%

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

      2. mul-1-neg 89.5%

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

      3. unsub-neg 89.5%

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

   5. Simplified 89.5%

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

   if -1.19999999999999996 < x < 3.5000000000000001e137

   1. Initial program 86.9%

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

   3. Taylor expanded in z around inf 69.8%

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

   4. Taylor expanded in x around 0 82.9%

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

      1. +-commutative 82.9%

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

   6. Simplified 82.9%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \lor \neg \left(x \leq 3.5 \cdot 10^{+137}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0095 \lor \neg \left(y \leq 0.00195\right):\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0095) (not (<= y 0.00195))) (* z (/ y z)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0095) || !(y <= 0.00195)) {
		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 <= (-0.0095d0)) .or. (.not. (y <= 0.00195d0))) 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 <= -0.0095) || !(y <= 0.00195)) {
		tmp = z * (y / z);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0095) or not (y <= 0.00195):
		tmp = z * (y / z)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0095) || !(y <= 0.00195))
		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 <= -0.0095) || ~((y <= 0.00195)))
		tmp = z * (y / z);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0095], N[Not[LessEqual[y, 0.00195]], $MachinePrecision]], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00949999999999999976 or 0.0019499999999999999 < y

   1. Initial program 78.3%

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

   3. Taylor expanded in z around inf 36.9%

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

   4. Taylor expanded in x around 0 28.8%

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

      1. *-commutative 28.8%

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

   6. Simplified 28.8%

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

      1. associate-/l* 55.0%

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

      2. *-commutative 55.0%

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

   8. Applied egg-rr 55.0%

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

   if -0.00949999999999999976 < y < 0.0019499999999999999

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 79.0%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0095 \lor \neg \left(y \leq 0.00195\right):\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0056:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.00145:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.0056) y (if (<= y 0.00145) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.0056) {
		tmp = y;
	} else if (y <= 0.00145) {
		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 <= (-0.0056d0)) then
        tmp = y
    else if (y <= 0.00145d0) 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 <= -0.0056) {
		tmp = y;
	} else if (y <= 0.00145) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.0056:
		tmp = y
	elif y <= 0.00145:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.0056)
		tmp = y;
	elseif (y <= 0.00145)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.0056)
		tmp = y;
	elseif (y <= 0.00145)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.0056], y, If[LessEqual[y, 0.00145], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00559999999999999994 or 0.00145 < y

   1. Initial program 78.3%

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

   3. Taylor expanded in x around 0 44.3%

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

   if -0.00559999999999999994 < y < 0.00145

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 79.0%

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

Alternative 11: 79.2% accurate, 0.9× 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 91.7%

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

   3. Taylor expanded in z around inf 80.8%

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

   4. Taylor expanded in x around 0 86.5%

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

      1. +-commutative 86.5%

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

   6. Simplified 86.5%

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

   if 1 < y

   1. Initial program 78.7%

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

   3. Taylor expanded in z around inf 23.7%

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

   4. Taylor expanded in x around 0 24.5%

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

      1. *-commutative 24.5%

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

   6. Simplified 24.5%

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

      1. associate-/l* 48.8%

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

      2. *-commutative 48.8%

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

   8. Applied egg-rr 48.8%

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

4. Final simplification 75.4%

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

Alternative 12: 41.0% 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 87.9%

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

3. Taylor expanded in x around 0 33.4%

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

Developer Target 1: 94.2% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024123 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- (+ y (/ x z)) (/ y (/ z x))))

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