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

Percentage Accurate: 100.0% → 100.0%

Time: 7.1s

Alternatives: 5

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: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-21} \lor \neg \left(y \leq 7.4 \cdot 10^{-68}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.5e-21) (not (<= y 7.4e-68))) (- 1.0 (/ x y)) (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.5e-21) || !(y <= 7.4e-68)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-9.5d-21)) .or. (.not. (y <= 7.4d-68))) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = x / (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.5e-21) || !(y <= 7.4e-68)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.5e-21) or not (y <= 7.4e-68):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.5e-21) || !(y <= 7.4e-68))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -9.5e-21) || ~((y <= 7.4e-68)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9.5e-21], N[Not[LessEqual[y, 7.4e-68]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.4999999999999994e-21 or 7.40000000000000004e-68 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 77.3%

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

      1. associate-*r/ 77.3%

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

      2. neg-mul-1 77.3%

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

      3. sub-neg 77.3%

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

      4. +-commutative 77.3%

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

      5. distribute-neg-in 77.3%

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

      6. remove-double-neg 77.3%

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

      7. sub-neg 77.3%

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

      8. div-sub 77.4%

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

      9. *-inverses 77.4%

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

   5. Simplified 77.4%

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

   if -9.4999999999999994e-21 < y < 7.40000000000000004e-68

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 81.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-21} \lor \neg \left(y \leq 7.4 \cdot 10^{-68}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-86} \lor \neg \left(y \leq 9.5 \cdot 10^{-107}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.6e-86) (not (<= y 9.5e-107))) (- 1.0 (/ x y)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.6e-86) || !(y <= 9.5e-107)) {
		tmp = 1.0 - (x / 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) :: tmp
    if ((y <= (-3.6d-86)) .or. (.not. (y <= 9.5d-107))) then
        tmp = 1.0d0 - (x / y)
    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 <= -3.6e-86) || !(y <= 9.5e-107)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.6e-86) or not (y <= 9.5e-107):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.6e-86) || !(y <= 9.5e-107))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.6e-86) || ~((y <= 9.5e-107)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.6e-86], N[Not[LessEqual[y, 9.5e-107]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.59999999999999966e-86 or 9.4999999999999999e-107 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 73.1%

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

      1. associate-*r/ 73.1%

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

      2. neg-mul-1 73.1%

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

      3. sub-neg 73.1%

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

      4. +-commutative 73.1%

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

      5. distribute-neg-in 73.1%

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

      6. remove-double-neg 73.1%

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

      7. sub-neg 73.1%

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

      8. div-sub 73.2%

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

      9. *-inverses 73.2%

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

   5. Simplified 73.2%

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

   if -3.59999999999999966e-86 < y < 9.4999999999999999e-107

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 69.5%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-86} \lor \neg \left(y \leq 9.5 \cdot 10^{-107}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.46 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.46e-21) 1.0 (if (<= y 2.8e-27) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.46e-21) {
		tmp = 1.0;
	} else if (y <= 2.8e-27) {
		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) :: tmp
    if (y <= (-1.46d-21)) then
        tmp = 1.0d0
    else if (y <= 2.8d-27) 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 tmp;
	if (y <= -1.46e-21) {
		tmp = 1.0;
	} else if (y <= 2.8e-27) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.46e-21:
		tmp = 1.0
	elif y <= 2.8e-27:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.46e-21)
		tmp = 1.0;
	elseif (y <= 2.8e-27)
		tmp = Float64(x / z);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.46e-21)
		tmp = 1.0;
	elseif (y <= 2.8e-27)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.46e-21], 1.0, If[LessEqual[y, 2.8e-27], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.46000000000000006e-21 or 2.8e-27 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 57.7%

      \[\leadsto \color{blue}{1} \]

   if -1.46000000000000006e-21 < y < 2.8e-27

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 62.0%

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

Alternative 5: 35.1% accurate, 7.0× 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 35.2%

   \[\leadsto \color{blue}{1} \]
4. 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 2024139 
(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)))