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

Percentage Accurate: 100.0% → 100.0%

Time: 7.7s

Alternatives: 6

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: 75.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+46} \lor \neg \left(y \leq 2.4 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.8e+46) (not (<= y 2.4e+76))) (/ y (- y z)) (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e+46) || !(y <= 2.4e+76)) {
		tmp = y / (y - z);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4.8d+46)) .or. (.not. (y <= 2.4d+76))) then
        tmp = y / (y - z)
    else
        tmp = x / (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e+46) || !(y <= 2.4e+76)) {
		tmp = y / (y - z);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.8e+46) or not (y <= 2.4e+76):
		tmp = y / (y - z)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.8e+46) || !(y <= 2.4e+76))
		tmp = Float64(y / Float64(y - z));
	else
		tmp = Float64(x / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.8e+46) || ~((y <= 2.4e+76)))
		tmp = y / (y - z);
	else
		tmp = x / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.8e+46], N[Not[LessEqual[y, 2.4e+76]], $MachinePrecision]], N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.80000000000000017e46 or 2.4e76 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 86.6%

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

      1. neg-mul-1 86.6%

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

      2. distribute-neg-frac2 86.6%

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

      3. sub-neg 86.6%

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

      4. +-commutative 86.6%

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

      5. distribute-neg-in 86.6%

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

      6. remove-double-neg 86.6%

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

      7. sub-neg 86.6%

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

   5. Simplified 86.6%

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

   if -4.80000000000000017e46 < y < 2.4e76

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.8%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+46} \lor \neg \left(y \leq 2.4 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.15 \cdot 10^{-20} \lor \neg \left(y \leq 1.55 \cdot 10^{+27}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.15e-20) (not (<= y 1.55e+27)))
   (- 1.0 (/ x y))
   (/ x (- z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.15e-20) || !(y <= 1.55e+27)) {
		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 <= (-4.15d-20)) .or. (.not. (y <= 1.55d+27))) 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 <= -4.15e-20) || !(y <= 1.55e+27)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.15e-20) or not (y <= 1.55e+27):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (z - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.15e-20) || !(y <= 1.55e+27))
		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 <= -4.15e-20) || ~((y <= 1.55e+27)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.15e-20], N[Not[LessEqual[y, 1.55e+27]], $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 < -4.14999999999999995e-20 or 1.54999999999999998e27 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 78.4%

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

      1. associate-*r/ 78.4%

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

      2. neg-mul-1 78.4%

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

      3. sub-neg 78.4%

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

      4. +-commutative 78.4%

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

      5. distribute-neg-in 78.4%

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

      6. remove-double-neg 78.4%

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

      7. sub-neg 78.4%

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

      8. div-sub 78.4%

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

      9. *-inverses 78.4%

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

   5. Simplified 78.4%

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

   if -4.14999999999999995e-20 < y < 1.54999999999999998e27

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.15 \cdot 10^{-20} \lor \neg \left(y \leq 1.55 \cdot 10^{+27}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-61} \lor \neg \left(y \leq 3 \cdot 10^{-18}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.15e-61) (not (<= y 3e-18))) (- 1.0 (/ x y)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15e-61) || !(y <= 3e-18)) {
		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 <= (-1.15d-61)) .or. (.not. (y <= 3d-18))) 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 <= -1.15e-61) || !(y <= 3e-18)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.15e-61) or not (y <= 3e-18):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.15e-61) || !(y <= 3e-18))
		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 <= -1.15e-61) || ~((y <= 3e-18)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.15e-61], N[Not[LessEqual[y, 3e-18]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.14999999999999996e-61 or 2.99999999999999983e-18 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 76.4%

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

      1. associate-*r/ 76.4%

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

      2. neg-mul-1 76.4%

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

      3. sub-neg 76.4%

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

      4. +-commutative 76.4%

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

      5. distribute-neg-in 76.4%

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

      6. remove-double-neg 76.4%

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

      7. sub-neg 76.4%

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

      8. div-sub 76.4%

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

      9. *-inverses 76.4%

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

   5. Simplified 76.4%

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

   if -1.14999999999999996e-61 < y < 2.99999999999999983e-18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 71.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-61} \lor \neg \left(y \leq 3 \cdot 10^{-18}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-46}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.1e-46) 1.0 (if (<= y 1.95e+27) (/ x z) 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.1e-46) {
		tmp = 1.0;
	} else if (y <= 1.95e+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 <= (-2.1d-46)) then
        tmp = 1.0d0
    else if (y <= 1.95d+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 <= -2.1e-46) {
		tmp = 1.0;
	} else if (y <= 1.95e+27) {
		tmp = x / z;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.1e-46:
		tmp = 1.0
	elif y <= 1.95e+27:
		tmp = x / z
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.1e-46)
		tmp = 1.0;
	elseif (y <= 1.95e+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 <= -2.1e-46)
		tmp = 1.0;
	elseif (y <= 1.95e+27)
		tmp = x / z;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.1e-46], 1.0, If[LessEqual[y, 1.95e+27], N[(x / z), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.09999999999999987e-46 or 1.9499999999999999e27 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 59.9%

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

   if -2.09999999999999987e-46 < y < 1.9499999999999999e27

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 68.6%

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

Alternative 6: 35.5% 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 35.7%

   \[\leadsto \color{blue}{1} \]
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 2024157 
(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)))