Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C

Percentage Accurate: 99.9% → 100.0%

Time: 4.1s

Alternatives: 6

Speedup: 1.4×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - 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 = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - 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 = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ 4 \cdot \frac{x - z}{y} + 2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* 4.0 (/ (- x z) y)) 2.0))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - z) / y)) + 2.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (4.0d0 * ((x - z) / y)) + 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - z) / y)) + 2.0;
}

Python

def code(x, y, z):
	return (4.0 * ((x - z) / y)) + 2.0

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - z) / y)) + 2.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - z) / y)) + 2.0;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision]

Derivation

1. Initial program 99.2%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-/l* 99.8%

      \[\leadsto 1 + \color{blue}{\frac{4}{\frac{y}{\left(x + y \cdot 0.25\right) - z}}} \]

   2. associate--l+ 99.8%

      \[\leadsto 1 + \frac{4}{\frac{y}{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{1 + \frac{4}{\frac{y}{x + \left(y \cdot 0.25 - z\right)}}} \]

4. Taylor expanded in y around 0 100.0%

   \[\leadsto \color{blue}{2 + 4 \cdot \frac{x - z}{y}} \]
5. Step-by-step derivation

   1. +-commutative 100.0%

      \[\leadsto \color{blue}{4 \cdot \frac{x - z}{y} + 2} \]

6. Simplified 100.0%

   \[\leadsto \color{blue}{4 \cdot \frac{x - z}{y} + 2} \]

7. Final simplification 100.0%

   \[\leadsto 4 \cdot \frac{x - z}{y} + 2 \]

Alternative 2: 56.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + 4 \cdot \frac{x}{y}\\ t_1 := 1 + -4 \cdot \frac{z}{y}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-54}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-78}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-168}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-63}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* 4.0 (/ x y)))) (t_1 (+ 1.0 (* -4.0 (/ z y)))))
   (if (<= z -1.75e+120)
     t_1
     (if (<= z -9.8e-54)
       2.0
       (if (<= z -3.7e-78)
         t_0
         (if (<= z -4.7e-168) 2.0 (if (<= z 2.1e-63) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + (4.0 * (x / y));
	double t_1 = 1.0 + (-4.0 * (z / y));
	double tmp;
	if (z <= -1.75e+120) {
		tmp = t_1;
	} else if (z <= -9.8e-54) {
		tmp = 2.0;
	} else if (z <= -3.7e-78) {
		tmp = t_0;
	} else if (z <= -4.7e-168) {
		tmp = 2.0;
	} else if (z <= 2.1e-63) {
		tmp = t_0;
	} 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 = 1.0d0 + (4.0d0 * (x / y))
    t_1 = 1.0d0 + ((-4.0d0) * (z / y))
    if (z <= (-1.75d+120)) then
        tmp = t_1
    else if (z <= (-9.8d-54)) then
        tmp = 2.0d0
    else if (z <= (-3.7d-78)) then
        tmp = t_0
    else if (z <= (-4.7d-168)) then
        tmp = 2.0d0
    else if (z <= 2.1d-63) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + (4.0 * (x / y));
	double t_1 = 1.0 + (-4.0 * (z / y));
	double tmp;
	if (z <= -1.75e+120) {
		tmp = t_1;
	} else if (z <= -9.8e-54) {
		tmp = 2.0;
	} else if (z <= -3.7e-78) {
		tmp = t_0;
	} else if (z <= -4.7e-168) {
		tmp = 2.0;
	} else if (z <= 2.1e-63) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + (4.0 * (x / y))
	t_1 = 1.0 + (-4.0 * (z / y))
	tmp = 0
	if z <= -1.75e+120:
		tmp = t_1
	elif z <= -9.8e-54:
		tmp = 2.0
	elif z <= -3.7e-78:
		tmp = t_0
	elif z <= -4.7e-168:
		tmp = 2.0
	elif z <= 2.1e-63:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(4.0 * Float64(x / y)))
	t_1 = Float64(1.0 + Float64(-4.0 * Float64(z / y)))
	tmp = 0.0
	if (z <= -1.75e+120)
		tmp = t_1;
	elseif (z <= -9.8e-54)
		tmp = 2.0;
	elseif (z <= -3.7e-78)
		tmp = t_0;
	elseif (z <= -4.7e-168)
		tmp = 2.0;
	elseif (z <= 2.1e-63)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + (4.0 * (x / y));
	t_1 = 1.0 + (-4.0 * (z / y));
	tmp = 0.0;
	if (z <= -1.75e+120)
		tmp = t_1;
	elseif (z <= -9.8e-54)
		tmp = 2.0;
	elseif (z <= -3.7e-78)
		tmp = t_0;
	elseif (z <= -4.7e-168)
		tmp = 2.0;
	elseif (z <= 2.1e-63)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+120], t$95$1, If[LessEqual[z, -9.8e-54], 2.0, If[LessEqual[z, -3.7e-78], t$95$0, If[LessEqual[z, -4.7e-168], 2.0, If[LessEqual[z, 2.1e-63], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.75000000000000004e120 or 2.1e-63 < z

   1. Initial program 98.3%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto 1 + \color{blue}{\frac{4}{\frac{y}{\left(x + y \cdot 0.25\right) - z}}} \]

      2. associate--l+ 99.7%

         \[\leadsto 1 + \frac{4}{\frac{y}{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{1 + \frac{4}{\frac{y}{x + \left(y \cdot 0.25 - z\right)}}} \]

   4. Taylor expanded in z around inf 71.5%

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

      1. *-commutative 71.5%

         \[\leadsto 1 + \color{blue}{\frac{z}{y} \cdot -4} \]

   6. Simplified 71.5%

      \[\leadsto 1 + \color{blue}{\frac{z}{y} \cdot -4} \]

   if -1.75000000000000004e120 < z < -9.80000000000000042e-54 or -3.70000000000000006e-78 < z < -4.70000000000000026e-168

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{\frac{y}{\left(x + y \cdot 0.25\right) - z}}} \]

      2. associate--l+ 99.8%

         \[\leadsto 1 + \frac{4}{\frac{y}{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{1 + \frac{4}{\frac{y}{x + \left(y \cdot 0.25 - z\right)}}} \]

   4. Taylor expanded in y around inf 60.8%

      \[\leadsto \color{blue}{2} \]

   if -9.80000000000000042e-54 < z < -3.70000000000000006e-78 or -4.70000000000000026e-168 < z < 2.1e-63

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto 1 + \color{blue}{\frac{4}{\frac{y}{\left(x + y \cdot 0.25\right) - z}}} \]

      2. associate--l+ 99.9%

         \[\leadsto 1 + \frac{4}{\frac{y}{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{1 + \frac{4}{\frac{y}{x + \left(y \cdot 0.25 - z\right)}}} \]

   4. Taylor expanded in x around inf 61.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+120}:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-54}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-78}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-168}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-63}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 3: 55.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+50} \lor \neg \left(x \leq 5.5 \cdot 10^{+32}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.7e+50) (not (<= x 5.5e+32))) (+ 1.0 (* 4.0 (/ x y))) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.7e+50) || !(x <= 5.5e+32)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0;
	}
	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 ((x <= (-3.7d+50)) .or. (.not. (x <= 5.5d+32))) then
        tmp = 1.0d0 + (4.0d0 * (x / y))
    else
        tmp = 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.7e+50) || !(x <= 5.5e+32)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.7e+50) or not (x <= 5.5e+32):
		tmp = 1.0 + (4.0 * (x / y))
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.7e+50) || !(x <= 5.5e+32))
		tmp = Float64(1.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.7e+50) || ~((x <= 5.5e+32)))
		tmp = 1.0 + (4.0 * (x / y));
	else
		tmp = 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.7e+50], N[Not[LessEqual[x, 5.5e+32]], $MachinePrecision]], N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0]

Derivation

1. Split input into 2 regimes

2. if x < -3.7000000000000001e50 or 5.49999999999999984e32 < x

   1. Initial program 99.1%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{\frac{y}{\left(x + y \cdot 0.25\right) - z}}} \]

      2. associate--l+ 99.8%

         \[\leadsto 1 + \frac{4}{\frac{y}{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{1 + \frac{4}{\frac{y}{x + \left(y \cdot 0.25 - z\right)}}} \]

   4. Taylor expanded in x around inf 70.4%

      \[\leadsto 1 + \color{blue}{4 \cdot \frac{x}{y}} \]

   if -3.7000000000000001e50 < x < 5.49999999999999984e32

   1. Initial program 99.3%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{\frac{y}{\left(x + y \cdot 0.25\right) - z}}} \]

      2. associate--l+ 99.8%

         \[\leadsto 1 + \frac{4}{\frac{y}{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{1 + \frac{4}{\frac{y}{x + \left(y \cdot 0.25 - z\right)}}} \]

   4. Taylor expanded in y around inf 48.3%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+50} \lor \neg \left(x \leq 5.5 \cdot 10^{+32}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 4: 80.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+172} \lor \neg \left(x \leq 2.4 \cdot 10^{+159}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + z \cdot \frac{-4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e+172) (not (<= x 2.4e+159)))
   (+ 1.0 (* 4.0 (/ x y)))
   (+ 2.0 (* z (/ -4.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e+172) || !(x <= 2.4e+159)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0 + (z * (-4.0 / 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 ((x <= (-5.8d+172)) .or. (.not. (x <= 2.4d+159))) then
        tmp = 1.0d0 + (4.0d0 * (x / y))
    else
        tmp = 2.0d0 + (z * ((-4.0d0) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e+172) || !(x <= 2.4e+159)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0 + (z * (-4.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.8e+172) or not (x <= 2.4e+159):
		tmp = 1.0 + (4.0 * (x / y))
	else:
		tmp = 2.0 + (z * (-4.0 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e+172) || !(x <= 2.4e+159))
		tmp = Float64(1.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(2.0 + Float64(z * Float64(-4.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.8e+172) || ~((x <= 2.4e+159)))
		tmp = 1.0 + (4.0 * (x / y));
	else
		tmp = 2.0 + (z * (-4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e+172], N[Not[LessEqual[x, 2.4e+159]], $MachinePrecision]], N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.7999999999999999e172 or 2.4e159 < x

   1. Initial program 98.2%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{\frac{y}{\left(x + y \cdot 0.25\right) - z}}} \]

      2. associate--l+ 99.8%

         \[\leadsto 1 + \frac{4}{\frac{y}{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{1 + \frac{4}{\frac{y}{x + \left(y \cdot 0.25 - z\right)}}} \]

   4. Taylor expanded in x around inf 90.1%

      \[\leadsto 1 + \color{blue}{4 \cdot \frac{x}{y}} \]

   if -5.7999999999999999e172 < x < 2.4e159

   1. Initial program 99.5%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{\frac{y}{\left(x + y \cdot 0.25\right) - z}}} \]

      2. associate--l+ 99.8%

         \[\leadsto 1 + \frac{4}{\frac{y}{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{1 + \frac{4}{\frac{y}{x + \left(y \cdot 0.25 - z\right)}}} \]

   4. Taylor expanded in x around 0 85.9%

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{0.25 \cdot y - z}{y}} \]

   6. Simplified 85.8%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+172} \lor \neg \left(x \leq 2.4 \cdot 10^{+159}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + z \cdot \frac{-4}{y}\\ \end{array} \]

Alternative 5: 80.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+172} \lor \neg \left(x \leq 3.9 \cdot 10^{+167}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e+172) (not (<= x 3.9e+167)))
   (+ 1.0 (* 4.0 (/ x y)))
   (+ 2.0 (* -4.0 (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e+172) || !(x <= 3.9e+167)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0 + (-4.0 * (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 ((x <= (-5.5d+172)) .or. (.not. (x <= 3.9d+167))) then
        tmp = 1.0d0 + (4.0d0 * (x / y))
    else
        tmp = 2.0d0 + ((-4.0d0) * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e+172) || !(x <= 3.9e+167)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0 + (-4.0 * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5e+172) or not (x <= 3.9e+167):
		tmp = 1.0 + (4.0 * (x / y))
	else:
		tmp = 2.0 + (-4.0 * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e+172) || !(x <= 3.9e+167))
		tmp = Float64(1.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(2.0 + Float64(-4.0 * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.5e+172) || ~((x <= 3.9e+167)))
		tmp = 1.0 + (4.0 * (x / y));
	else
		tmp = 2.0 + (-4.0 * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e+172], N[Not[LessEqual[x, 3.9e+167]], $MachinePrecision]], N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.4999999999999999e172 or 3.8999999999999998e167 < x

   1. Initial program 98.2%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{\frac{y}{\left(x + y \cdot 0.25\right) - z}}} \]

      2. associate--l+ 99.8%

         \[\leadsto 1 + \frac{4}{\frac{y}{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{1 + \frac{4}{\frac{y}{x + \left(y \cdot 0.25 - z\right)}}} \]

   4. Taylor expanded in x around inf 90.1%

      \[\leadsto 1 + \color{blue}{4 \cdot \frac{x}{y}} \]

   if -5.4999999999999999e172 < x < 3.8999999999999998e167

   1. Initial program 99.5%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{\frac{y}{\left(x + y \cdot 0.25\right) - z}}} \]

      2. associate--l+ 99.8%

         \[\leadsto 1 + \frac{4}{\frac{y}{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{1 + \frac{4}{\frac{y}{x + \left(y \cdot 0.25 - z\right)}}} \]

   4. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{2 + 4 \cdot \frac{x - z}{y}} \]
   5. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \color{blue}{4 \cdot \frac{x - z}{y} + 2} \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{4 \cdot \frac{x - z}{y} + 2} \]

   7. Taylor expanded in x around 0 85.9%

      \[\leadsto 4 \cdot \color{blue}{\left(-1 \cdot \frac{z}{y}\right)} + 2 \]
   8. Step-by-step derivation

      1. neg-mul-1 85.9%

         \[\leadsto 4 \cdot \color{blue}{\left(-\frac{z}{y}\right)} + 2 \]

      2. distribute-neg-frac 85.9%

         \[\leadsto 4 \cdot \color{blue}{\frac{-z}{y}} + 2 \]

   9. Simplified 85.9%

      \[\leadsto 4 \cdot \color{blue}{\frac{-z}{y}} + 2 \]

   10. Taylor expanded in z around 0 85.9%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+172} \lor \neg \left(x \leq 3.9 \cdot 10^{+167}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 6: 33.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 2.0)

C

double code(double x, double y, double z) {
	return 2.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 2.0;
}

Python

def code(x, y, z):
	return 2.0

Julia

function code(x, y, z)
	return 2.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0;
end

Wolfram

code[x_, y_, z_] := 2.0

Derivation

1. Initial program 99.2%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-/l* 99.8%

      \[\leadsto 1 + \color{blue}{\frac{4}{\frac{y}{\left(x + y \cdot 0.25\right) - z}}} \]

   2. associate--l+ 99.8%

      \[\leadsto 1 + \frac{4}{\frac{y}{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{1 + \frac{4}{\frac{y}{x + \left(y \cdot 0.25 - z\right)}}} \]

4. Taylor expanded in y around inf 36.9%

   \[\leadsto \color{blue}{2} \]

5. Final simplification 36.9%

   \[\leadsto 2 \]

Reproduce

herbie shell --seed 2023200 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))