Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1

Percentage Accurate: 100.0% → 100.0%

Time: 5.9s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x - y) / (z - 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 = (x - y) / (z - y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x - y) / (z - 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 = (x - y) / (z - y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x - y) / (z - 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 = (x - y) / (z - y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{z - y} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 68.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{-137}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;t\_0 \leq 40:\\ \;\;\;\;\frac{y + z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- z y))))
   (if (<= t_0 -1e+50)
     (/ x (- y))
     (if (<= t_0 4e-137)
       (/ x z)
       (if (<= t_0 5e-16)
         (/ (- y) z)
         (if (<= t_0 40.0) (/ (+ y z) y) (/ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x - y) / (z - y);
	double tmp;
	if (t_0 <= -1e+50) {
		tmp = x / -y;
	} else if (t_0 <= 4e-137) {
		tmp = x / z;
	} else if (t_0 <= 5e-16) {
		tmp = -y / z;
	} else if (t_0 <= 40.0) {
		tmp = (y + z) / y;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (x - y) / (z - y)
    if (t_0 <= (-1d+50)) then
        tmp = x / -y
    else if (t_0 <= 4d-137) then
        tmp = x / z
    else if (t_0 <= 5d-16) then
        tmp = -y / z
    else if (t_0 <= 40.0d0) then
        tmp = (y + z) / y
    else
        tmp = 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 - y);
	double tmp;
	if (t_0 <= -1e+50) {
		tmp = x / -y;
	} else if (t_0 <= 4e-137) {
		tmp = x / z;
	} else if (t_0 <= 5e-16) {
		tmp = -y / z;
	} else if (t_0 <= 40.0) {
		tmp = (y + z) / y;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - y) / (z - y)
	tmp = 0
	if t_0 <= -1e+50:
		tmp = x / -y
	elif t_0 <= 4e-137:
		tmp = x / z
	elif t_0 <= 5e-16:
		tmp = -y / z
	elif t_0 <= 40.0:
		tmp = (y + z) / y
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_0 <= -1e+50)
		tmp = Float64(x / Float64(-y));
	elseif (t_0 <= 4e-137)
		tmp = Float64(x / z);
	elseif (t_0 <= 5e-16)
		tmp = Float64(Float64(-y) / z);
	elseif (t_0 <= 40.0)
		tmp = Float64(Float64(y + z) / y);
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_0 <= -1e+50)
		tmp = x / -y;
	elseif (t_0 <= 4e-137)
		tmp = x / z;
	elseif (t_0 <= 5e-16)
		tmp = -y / z;
	elseif (t_0 <= 40.0)
		tmp = (y + z) / y;
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+50], N[(x / (-y)), $MachinePrecision], If[LessEqual[t$95$0, 4e-137], N[(x / z), $MachinePrecision], If[LessEqual[t$95$0, 5e-16], N[((-y) / z), $MachinePrecision], If[LessEqual[t$95$0, 40.0], N[(N[(y + z), $MachinePrecision] / y), $MachinePrecision], N[(x / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1.0000000000000001e50

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 86.5%

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

   if -1.0000000000000001e50 < (/.f64 (-.f64 x y) (-.f64 z y)) < 3.99999999999999991e-137 or 40 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 62.8

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

   5. Applied rewrites 62.8%

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

   if 3.99999999999999991e-137 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.0000000000000004e-16

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 68.1%

      \[\leadsto \frac{-y}{z} \]

   if 5.0000000000000004e-16 < (/.f64 (-.f64 x y) (-.f64 z y)) < 40

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate--l- N/A

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

      5. fp-cancel-sign-sub-inv N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. div-sub N/A

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

      9. lower--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 98.9

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

   5. Applied rewrites 98.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 96.5%

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

Alternative 3: 68.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{-137}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-18}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;t\_0 \leq 40:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- z y))))
   (if (<= t_0 -1e+50)
     (/ x (- y))
     (if (<= t_0 4e-137)
       (/ x z)
       (if (<= t_0 2e-18) (/ (- y) z) (if (<= t_0 40.0) 1.0 (/ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x - y) / (z - y);
	double tmp;
	if (t_0 <= -1e+50) {
		tmp = x / -y;
	} else if (t_0 <= 4e-137) {
		tmp = x / z;
	} else if (t_0 <= 2e-18) {
		tmp = -y / z;
	} else if (t_0 <= 40.0) {
		tmp = 1.0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (x - y) / (z - y)
    if (t_0 <= (-1d+50)) then
        tmp = x / -y
    else if (t_0 <= 4d-137) then
        tmp = x / z
    else if (t_0 <= 2d-18) then
        tmp = -y / z
    else if (t_0 <= 40.0d0) then
        tmp = 1.0d0
    else
        tmp = 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 - y);
	double tmp;
	if (t_0 <= -1e+50) {
		tmp = x / -y;
	} else if (t_0 <= 4e-137) {
		tmp = x / z;
	} else if (t_0 <= 2e-18) {
		tmp = -y / z;
	} else if (t_0 <= 40.0) {
		tmp = 1.0;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - y) / (z - y)
	tmp = 0
	if t_0 <= -1e+50:
		tmp = x / -y
	elif t_0 <= 4e-137:
		tmp = x / z
	elif t_0 <= 2e-18:
		tmp = -y / z
	elif t_0 <= 40.0:
		tmp = 1.0
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_0 <= -1e+50)
		tmp = Float64(x / Float64(-y));
	elseif (t_0 <= 4e-137)
		tmp = Float64(x / z);
	elseif (t_0 <= 2e-18)
		tmp = Float64(Float64(-y) / z);
	elseif (t_0 <= 40.0)
		tmp = 1.0;
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_0 <= -1e+50)
		tmp = x / -y;
	elseif (t_0 <= 4e-137)
		tmp = x / z;
	elseif (t_0 <= 2e-18)
		tmp = -y / z;
	elseif (t_0 <= 40.0)
		tmp = 1.0;
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+50], N[(x / (-y)), $MachinePrecision], If[LessEqual[t$95$0, 4e-137], N[(x / z), $MachinePrecision], If[LessEqual[t$95$0, 2e-18], N[((-y) / z), $MachinePrecision], If[LessEqual[t$95$0, 40.0], 1.0, N[(x / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1.0000000000000001e50

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 86.5%

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

   if -1.0000000000000001e50 < (/.f64 (-.f64 x y) (-.f64 z y)) < 3.99999999999999991e-137 or 40 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 62.8

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

   5. Applied rewrites 62.8%

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

   if 3.99999999999999991e-137 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000001e-18

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 71.3%

      \[\leadsto \frac{-y}{z} \]

   if 2.0000000000000001e-18 < (/.f64 (-.f64 x y) (-.f64 z y)) < 40

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 95.3%

      \[\leadsto \color{blue}{1} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 98.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{z - y}\\ t_1 := \frac{x}{z - y}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.98:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;t\_0 \leq 40:\\ \;\;\;\;1 - \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- z y))) (t_1 (/ x (- z y))))
   (if (<= t_0 -2e+16)
     t_1
     (if (<= t_0 0.98)
       (/ (- x y) z)
       (if (<= t_0 40.0) (- 1.0 (/ (- x z) y)) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = (x - y) / (z - y);
	double t_1 = x / (z - y);
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = t_1;
	} else if (t_0 <= 0.98) {
		tmp = (x - y) / z;
	} else if (t_0 <= 40.0) {
		tmp = 1.0 - ((x - z) / y);
	} else {
		tmp = t_1;
	}
	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 = (x - y) / (z - y)
    t_1 = x / (z - y)
    if (t_0 <= (-2d+16)) then
        tmp = t_1
    else if (t_0 <= 0.98d0) then
        tmp = (x - y) / z
    else if (t_0 <= 40.0d0) then
        tmp = 1.0d0 - ((x - z) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x - y) / (z - y);
	double t_1 = x / (z - y);
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = t_1;
	} else if (t_0 <= 0.98) {
		tmp = (x - y) / z;
	} else if (t_0 <= 40.0) {
		tmp = 1.0 - ((x - z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - y) / (z - y)
	t_1 = x / (z - y)
	tmp = 0
	if t_0 <= -2e+16:
		tmp = t_1
	elif t_0 <= 0.98:
		tmp = (x - y) / z
	elif t_0 <= 40.0:
		tmp = 1.0 - ((x - z) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - y) / Float64(z - y))
	t_1 = Float64(x / Float64(z - y))
	tmp = 0.0
	if (t_0 <= -2e+16)
		tmp = t_1;
	elseif (t_0 <= 0.98)
		tmp = Float64(Float64(x - y) / z);
	elseif (t_0 <= 40.0)
		tmp = Float64(1.0 - Float64(Float64(x - z) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - y) / (z - y);
	t_1 = x / (z - y);
	tmp = 0.0;
	if (t_0 <= -2e+16)
		tmp = t_1;
	elseif (t_0 <= 0.98)
		tmp = (x - y) / z;
	elseif (t_0 <= 40.0)
		tmp = 1.0 - ((x - z) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+16], t$95$1, If[LessEqual[t$95$0, 0.98], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$0, 40.0], N[(1.0 - N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2e16 or 40 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 99.7

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

   5. Applied rewrites 99.7%

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

   if -2e16 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.97999999999999998

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if 0.97999999999999998 < (/.f64 (-.f64 x y) (-.f64 z y)) < 40

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate--l- N/A

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

      5. fp-cancel-sign-sub-inv N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. div-sub N/A

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

      9. lower--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 99.9

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

   5. Applied rewrites 99.9%

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

Alternative 5: 98.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{z - y}\\ t_1 := \frac{x}{z - y}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.98:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;t\_0 \leq 40:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- z y))) (t_1 (/ x (- z y))))
   (if (<= t_0 -2e+16)
     t_1
     (if (<= t_0 0.98) (/ (- x y) z) (if (<= t_0 40.0) (- 1.0 (/ x y)) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = (x - y) / (z - y);
	double t_1 = x / (z - y);
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = t_1;
	} else if (t_0 <= 0.98) {
		tmp = (x - y) / z;
	} else if (t_0 <= 40.0) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = t_1;
	}
	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 = (x - y) / (z - y)
    t_1 = x / (z - y)
    if (t_0 <= (-2d+16)) then
        tmp = t_1
    else if (t_0 <= 0.98d0) then
        tmp = (x - y) / z
    else if (t_0 <= 40.0d0) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x - y) / (z - y);
	double t_1 = x / (z - y);
	double tmp;
	if (t_0 <= -2e+16) {
		tmp = t_1;
	} else if (t_0 <= 0.98) {
		tmp = (x - y) / z;
	} else if (t_0 <= 40.0) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - y) / (z - y)
	t_1 = x / (z - y)
	tmp = 0
	if t_0 <= -2e+16:
		tmp = t_1
	elif t_0 <= 0.98:
		tmp = (x - y) / z
	elif t_0 <= 40.0:
		tmp = 1.0 - (x / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - y) / Float64(z - y))
	t_1 = Float64(x / Float64(z - y))
	tmp = 0.0
	if (t_0 <= -2e+16)
		tmp = t_1;
	elseif (t_0 <= 0.98)
		tmp = Float64(Float64(x - y) / z);
	elseif (t_0 <= 40.0)
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - y) / (z - y);
	t_1 = x / (z - y);
	tmp = 0.0;
	if (t_0 <= -2e+16)
		tmp = t_1;
	elseif (t_0 <= 0.98)
		tmp = (x - y) / z;
	elseif (t_0 <= 40.0)
		tmp = 1.0 - (x / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+16], t$95$1, If[LessEqual[t$95$0, 0.98], N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$0, 40.0], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2e16 or 40 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 99.7

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

   5. Applied rewrites 99.7%

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

   if -2e16 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.97999999999999998

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if 0.97999999999999998 < (/.f64 (-.f64 x y) (-.f64 z y)) < 40

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate--l- N/A

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

      5. fp-cancel-sign-sub-inv N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. div-sub N/A

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

      9. lower--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 99.4%

      \[\leadsto 1 - \frac{x}{\color{blue}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 83.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{z - y}\\ t_1 := \frac{x}{z - y}\\ \mathbf{if}\;t\_0 \leq 4 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.98:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;t\_0 \leq 40:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- z y))) (t_1 (/ x (- z y))))
   (if (<= t_0 4e-137)
     t_1
     (if (<= t_0 0.98) (/ (- y) z) (if (<= t_0 40.0) (- 1.0 (/ x y)) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = (x - y) / (z - y);
	double t_1 = x / (z - y);
	double tmp;
	if (t_0 <= 4e-137) {
		tmp = t_1;
	} else if (t_0 <= 0.98) {
		tmp = -y / z;
	} else if (t_0 <= 40.0) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = t_1;
	}
	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 = (x - y) / (z - y)
    t_1 = x / (z - y)
    if (t_0 <= 4d-137) then
        tmp = t_1
    else if (t_0 <= 0.98d0) then
        tmp = -y / z
    else if (t_0 <= 40.0d0) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x - y) / (z - y);
	double t_1 = x / (z - y);
	double tmp;
	if (t_0 <= 4e-137) {
		tmp = t_1;
	} else if (t_0 <= 0.98) {
		tmp = -y / z;
	} else if (t_0 <= 40.0) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - y) / (z - y)
	t_1 = x / (z - y)
	tmp = 0
	if t_0 <= 4e-137:
		tmp = t_1
	elif t_0 <= 0.98:
		tmp = -y / z
	elif t_0 <= 40.0:
		tmp = 1.0 - (x / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - y) / Float64(z - y))
	t_1 = Float64(x / Float64(z - y))
	tmp = 0.0
	if (t_0 <= 4e-137)
		tmp = t_1;
	elseif (t_0 <= 0.98)
		tmp = Float64(Float64(-y) / z);
	elseif (t_0 <= 40.0)
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - y) / (z - y);
	t_1 = x / (z - y);
	tmp = 0.0;
	if (t_0 <= 4e-137)
		tmp = t_1;
	elseif (t_0 <= 0.98)
		tmp = -y / z;
	elseif (t_0 <= 40.0)
		tmp = 1.0 - (x / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 4e-137], t$95$1, If[LessEqual[t$95$0, 0.98], N[((-y) / z), $MachinePrecision], If[LessEqual[t$95$0, 40.0], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 3.99999999999999991e-137 or 40 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 85.3

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

   5. Applied rewrites 85.3%

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

   if 3.99999999999999991e-137 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.97999999999999998

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 65.1%

      \[\leadsto \frac{-y}{z} \]

   if 0.97999999999999998 < (/.f64 (-.f64 x y) (-.f64 z y)) < 40

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate--l- N/A

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

      5. fp-cancel-sign-sub-inv N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. div-sub N/A

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

      9. lower--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 99.9

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 99.4%

      \[\leadsto 1 - \frac{x}{\color{blue}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 69.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{-137}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;t\_0 \leq 0.98:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- z y))))
   (if (<= t_0 -1e+50)
     (/ x (- y))
     (if (<= t_0 4e-137)
       (/ x z)
       (if (<= t_0 0.98) (/ (- y) z) (- 1.0 (/ x y)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x - y) / (z - y);
	double tmp;
	if (t_0 <= -1e+50) {
		tmp = x / -y;
	} else if (t_0 <= 4e-137) {
		tmp = x / z;
	} else if (t_0 <= 0.98) {
		tmp = -y / z;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x - y) / (z - y)
    if (t_0 <= (-1d+50)) then
        tmp = x / -y
    else if (t_0 <= 4d-137) then
        tmp = x / z
    else if (t_0 <= 0.98d0) then
        tmp = -y / z
    else
        tmp = 1.0d0 - (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x - y) / (z - y);
	double tmp;
	if (t_0 <= -1e+50) {
		tmp = x / -y;
	} else if (t_0 <= 4e-137) {
		tmp = x / z;
	} else if (t_0 <= 0.98) {
		tmp = -y / z;
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - y) / (z - y)
	tmp = 0
	if t_0 <= -1e+50:
		tmp = x / -y
	elif t_0 <= 4e-137:
		tmp = x / z
	elif t_0 <= 0.98:
		tmp = -y / z
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_0 <= -1e+50)
		tmp = Float64(x / Float64(-y));
	elseif (t_0 <= 4e-137)
		tmp = Float64(x / z);
	elseif (t_0 <= 0.98)
		tmp = Float64(Float64(-y) / z);
	else
		tmp = Float64(1.0 - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_0 <= -1e+50)
		tmp = x / -y;
	elseif (t_0 <= 4e-137)
		tmp = x / z;
	elseif (t_0 <= 0.98)
		tmp = -y / z;
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+50], N[(x / (-y)), $MachinePrecision], If[LessEqual[t$95$0, 4e-137], N[(x / z), $MachinePrecision], If[LessEqual[t$95$0, 0.98], N[((-y) / z), $MachinePrecision], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1.0000000000000001e50

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 86.5%

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

   if -1.0000000000000001e50 < (/.f64 (-.f64 x y) (-.f64 z y)) < 3.99999999999999991e-137

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 65.8

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

   5. Applied rewrites 65.8%

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

   if 3.99999999999999991e-137 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.97999999999999998

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 65.1%

      \[\leadsto \frac{-y}{z} \]

   if 0.97999999999999998 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. associate--l- N/A

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

      5. fp-cancel-sign-sub-inv N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. div-sub N/A

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

      9. lower--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 84.7

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

   5. Applied rewrites 84.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 84.4%

      \[\leadsto 1 - \frac{x}{\color{blue}{y}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 68.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;t\_0 \leq 0.98 \lor \neg \left(t\_0 \leq 40\right):\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- z y))))
   (if (<= t_0 -1e+50)
     (/ x (- y))
     (if (or (<= t_0 0.98) (not (<= t_0 40.0))) (/ x z) 1.0))))

C

double code(double x, double y, double z) {
	double t_0 = (x - y) / (z - y);
	double tmp;
	if (t_0 <= -1e+50) {
		tmp = x / -y;
	} else if ((t_0 <= 0.98) || !(t_0 <= 40.0)) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x - y) / (z - y)
    if (t_0 <= (-1d+50)) then
        tmp = x / -y
    else if ((t_0 <= 0.98d0) .or. (.not. (t_0 <= 40.0d0))) then
        tmp = x / z
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x - y) / (z - y);
	double tmp;
	if (t_0 <= -1e+50) {
		tmp = x / -y;
	} else if ((t_0 <= 0.98) || !(t_0 <= 40.0)) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - y) / (z - y)
	tmp = 0
	if t_0 <= -1e+50:
		tmp = x / -y
	elif (t_0 <= 0.98) or not (t_0 <= 40.0):
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_0 <= -1e+50)
		tmp = Float64(x / Float64(-y));
	elseif ((t_0 <= 0.98) || !(t_0 <= 40.0))
		tmp = Float64(x / z);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_0 <= -1e+50)
		tmp = x / -y;
	elseif ((t_0 <= 0.98) || ~((t_0 <= 40.0)))
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+50], N[(x / (-y)), $MachinePrecision], If[Or[LessEqual[t$95$0, 0.98], N[Not[LessEqual[t$95$0, 40.0]], $MachinePrecision]], N[(x / z), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1.0000000000000001e50

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 86.5%

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

   if -1.0000000000000001e50 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.97999999999999998 or 40 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 59.0

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

   5. Applied rewrites 59.0%

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

   if 0.97999999999999998 < (/.f64 (-.f64 x y) (-.f64 z y)) < 40

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.1%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.98 \lor \neg \left(\frac{x - y}{z - y} \leq 40\right):\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_0 \leq 0.98 \lor \neg \left(t\_0 \leq 40\right):\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- z y))))
   (if (or (<= t_0 0.98) (not (<= t_0 40.0))) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double t_0 = (x - y) / (z - y);
	double tmp;
	if ((t_0 <= 0.98) || !(t_0 <= 40.0)) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x - y) / (z - y)
    if ((t_0 <= 0.98d0) .or. (.not. (t_0 <= 40.0d0))) then
        tmp = x / z
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x - y) / (z - y);
	double tmp;
	if ((t_0 <= 0.98) || !(t_0 <= 40.0)) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - y) / (z - y)
	tmp = 0
	if (t_0 <= 0.98) or not (t_0 <= 40.0):
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if ((t_0 <= 0.98) || !(t_0 <= 40.0))
		tmp = Float64(x / z);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - y) / (z - y);
	tmp = 0.0;
	if ((t_0 <= 0.98) || ~((t_0 <= 40.0)))
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.98], N[Not[LessEqual[t$95$0, 40.0]], $MachinePrecision]], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.97999999999999998 or 40 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 53.2

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

   5. Applied rewrites 53.2%

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

   if 0.97999999999999998 < (/.f64 (-.f64 x y) (-.f64 z y)) < 40

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.1%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 0.98 \lor \neg \left(\frac{x - y}{z - y} \leq 40\right):\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.5% accurate, 18.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 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 = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{z - y} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{1} \]
4. Step-by-step derivation

5. Applied rewrites 36.2%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Developer Target 1: 100.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x / (z - y)) - (y / (z - 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 = (x / (z - y)) - (y / (z - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024339 
(FPCore (x y z)
  :name "Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1"
  :precision binary64

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

  (/ (- x y) (- z y)))