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

Percentage Accurate: 99.8% → 100.0%

Time: 5.1s

Alternatives: 8

Speedup: 1.4×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - 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 * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - 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 * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 99.7%

      \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.75\right) - z\right)} \]

   2. +-commutative 99.7%

      \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.75 + x\right)} - z\right) \]

   3. fma-def 99.7%

      \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.75, x\right)} - z\right) \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.75, x\right) - z\right)} \]

4. Taylor expanded in y around 0 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 51.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \frac{x}{y}\\ t_1 := -4 \cdot \frac{z}{y}\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{-92}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-155}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-14}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.0 (/ x y))) (t_1 (* -4.0 (/ z y))))
   (if (<= x -2.7e-92)
     t_0
     (if (<= x -2.25e-299)
       t_1
       (if (<= x 1.5e-155)
         4.0
         (if (<= x 6.8e-46) t_1 (if (<= x 2.5e-14) 4.0 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double t_1 = -4.0 * (z / y);
	double tmp;
	if (x <= -2.7e-92) {
		tmp = t_0;
	} else if (x <= -2.25e-299) {
		tmp = t_1;
	} else if (x <= 1.5e-155) {
		tmp = 4.0;
	} else if (x <= 6.8e-46) {
		tmp = t_1;
	} else if (x <= 2.5e-14) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 4.0d0 * (x / y)
    t_1 = (-4.0d0) * (z / y)
    if (x <= (-2.7d-92)) then
        tmp = t_0
    else if (x <= (-2.25d-299)) then
        tmp = t_1
    else if (x <= 1.5d-155) then
        tmp = 4.0d0
    else if (x <= 6.8d-46) then
        tmp = t_1
    else if (x <= 2.5d-14) then
        tmp = 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.0 * (x / y);
	double t_1 = -4.0 * (z / y);
	double tmp;
	if (x <= -2.7e-92) {
		tmp = t_0;
	} else if (x <= -2.25e-299) {
		tmp = t_1;
	} else if (x <= 1.5e-155) {
		tmp = 4.0;
	} else if (x <= 6.8e-46) {
		tmp = t_1;
	} else if (x <= 2.5e-14) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 * (x / y)
	t_1 = -4.0 * (z / y)
	tmp = 0
	if x <= -2.7e-92:
		tmp = t_0
	elif x <= -2.25e-299:
		tmp = t_1
	elif x <= 1.5e-155:
		tmp = 4.0
	elif x <= 6.8e-46:
		tmp = t_1
	elif x <= 2.5e-14:
		tmp = 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 * Float64(x / y))
	t_1 = Float64(-4.0 * Float64(z / y))
	tmp = 0.0
	if (x <= -2.7e-92)
		tmp = t_0;
	elseif (x <= -2.25e-299)
		tmp = t_1;
	elseif (x <= 1.5e-155)
		tmp = 4.0;
	elseif (x <= 6.8e-46)
		tmp = t_1;
	elseif (x <= 2.5e-14)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 * (x / y);
	t_1 = -4.0 * (z / y);
	tmp = 0.0;
	if (x <= -2.7e-92)
		tmp = t_0;
	elseif (x <= -2.25e-299)
		tmp = t_1;
	elseif (x <= 1.5e-155)
		tmp = 4.0;
	elseif (x <= 6.8e-46)
		tmp = t_1;
	elseif (x <= 2.5e-14)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e-92], t$95$0, If[LessEqual[x, -2.25e-299], t$95$1, If[LessEqual[x, 1.5e-155], 4.0, If[LessEqual[x, 6.8e-46], t$95$1, If[LessEqual[x, 2.5e-14], 4.0, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.69999999999999995e-92 or 2.5000000000000001e-14 < x

   1. Initial program 99.3%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.75\right) - z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.75 + x\right)} - z\right) \]

      3. fma-def 99.7%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.75, x\right)} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.75, x\right) - z\right)} \]

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around inf 82.9%

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

   6. Taylor expanded in x around inf 64.0%

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

   if -2.69999999999999995e-92 < x < -2.25000000000000001e-299 or 1.49999999999999992e-155 < x < 6.79999999999999992e-46

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.75\right) - z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.75 + x\right)} - z\right) \]

      3. fma-def 99.7%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.75, x\right)} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.75, x\right) - z\right)} \]

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in y around 0 66.3%

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

   6. Taylor expanded in x around 0 58.2%

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

   if -2.25000000000000001e-299 < x < 1.49999999999999992e-155 or 6.79999999999999992e-46 < x < 2.5000000000000001e-14

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.75\right) - z\right)} \]

      2. +-commutative 99.9%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.75 + x\right)} - z\right) \]

      3. fma-def 99.9%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.75, x\right)} - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.75, x\right) - z\right)} \]

   4. Taylor expanded in y around inf 74.9%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-92}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-299}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-155}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-46}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-14}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 3: 85.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+101} \lor \neg \left(y \leq 1.05 \cdot 10^{+23}\right):\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8e+101) (not (<= y 1.05e+23)))
   (+ 4.0 (* -4.0 (/ z y)))
   (* 4.0 (/ (- x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8e+101) || !(y <= 1.05e+23)) {
		tmp = 4.0 + (-4.0 * (z / y));
	} else {
		tmp = 4.0 * ((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 <= (-8d+101)) .or. (.not. (y <= 1.05d+23))) then
        tmp = 4.0d0 + ((-4.0d0) * (z / y))
    else
        tmp = 4.0d0 * ((x - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8e+101) || !(y <= 1.05e+23)) {
		tmp = 4.0 + (-4.0 * (z / y));
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8e+101) or not (y <= 1.05e+23):
		tmp = 4.0 + (-4.0 * (z / y))
	else:
		tmp = 4.0 * ((x - z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8e+101) || !(y <= 1.05e+23))
		tmp = Float64(4.0 + Float64(-4.0 * Float64(z / y)));
	else
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8e+101) || ~((y <= 1.05e+23)))
		tmp = 4.0 + (-4.0 * (z / y));
	else
		tmp = 4.0 * ((x - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8e+101], N[Not[LessEqual[y, 1.05e+23]], $MachinePrecision]], N[(4.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.9999999999999998e101 or 1.0500000000000001e23 < y

   1. Initial program 98.7%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.75\right) - z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.75 + x\right)} - z\right) \]

      3. fma-def 99.7%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.75, x\right)} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.75, x\right) - z\right)} \]

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around 0 83.0%

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

   if -7.9999999999999998e101 < y < 1.0500000000000001e23

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.75\right) - z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.75 + x\right)} - z\right) \]

      3. fma-def 99.7%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.75, x\right)} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.75, x\right) - z\right)} \]

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in y around 0 87.1%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+101} \lor \neg \left(y \leq 1.05 \cdot 10^{+23}\right):\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]

Alternative 4: 84.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+16} \lor \neg \left(y \leq 1.1 \cdot 10^{-55}\right):\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.8e+16) (not (<= y 1.1e-55)))
   (+ 4.0 (* 4.0 (/ x y)))
   (* 4.0 (/ (- x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.8e+16) || !(y <= 1.1e-55)) {
		tmp = 4.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 * ((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 <= (-3.8d+16)) .or. (.not. (y <= 1.1d-55))) then
        tmp = 4.0d0 + (4.0d0 * (x / y))
    else
        tmp = 4.0d0 * ((x - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.8e+16) || !(y <= 1.1e-55)) {
		tmp = 4.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 * ((x - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.8e+16) or not (y <= 1.1e-55):
		tmp = 4.0 + (4.0 * (x / y))
	else:
		tmp = 4.0 * ((x - z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.8e+16) || !(y <= 1.1e-55))
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.8e+16) || ~((y <= 1.1e-55)))
		tmp = 4.0 + (4.0 * (x / y));
	else
		tmp = 4.0 * ((x - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.8e+16], N[Not[LessEqual[y, 1.1e-55]], $MachinePrecision]], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8e16 or 1.1e-55 < y

   1. Initial program 99.1%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.75\right) - z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.75 + x\right)} - z\right) \]

      3. fma-def 99.7%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.75, x\right)} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.75, x\right) - z\right)} \]

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around inf 86.4%

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

   if -3.8e16 < y < 1.1e-55

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.75\right) - z\right)} \]

      2. +-commutative 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.75 + x\right)} - z\right) \]

      3. fma-def 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.75, x\right)} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.75, x\right) - z\right)} \]

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in y around 0 92.6%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+16} \lor \neg \left(y \leq 1.1 \cdot 10^{-55}\right):\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \end{array} \]

Alternative 5: 80.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+165}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+94}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e+165) 4.0 (if (<= y 1.8e+94) (* 4.0 (/ (- x z) y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+165) {
		tmp = 4.0;
	} else if (y <= 1.8e+94) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0;
	}
	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 <= (-3.8d+165)) then
        tmp = 4.0d0
    else if (y <= 1.8d+94) then
        tmp = 4.0d0 * ((x - z) / y)
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+165) {
		tmp = 4.0;
	} else if (y <= 1.8e+94) {
		tmp = 4.0 * ((x - z) / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e+165:
		tmp = 4.0
	elif y <= 1.8e+94:
		tmp = 4.0 * ((x - z) / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e+165)
		tmp = 4.0;
	elseif (y <= 1.8e+94)
		tmp = Float64(4.0 * Float64(Float64(x - z) / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.8e+165)
		tmp = 4.0;
	elseif (y <= 1.8e+94)
		tmp = 4.0 * ((x - z) / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e+165], 4.0, If[LessEqual[y, 1.8e+94], N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7999999999999999e165 or 1.79999999999999996e94 < y

   1. Initial program 99.8%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.75\right) - z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.75 + x\right)} - z\right) \]

      3. fma-def 99.7%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.75, x\right)} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.75, x\right) - z\right)} \]

   4. Taylor expanded in y around inf 77.7%

      \[\leadsto \color{blue}{4} \]

   if -3.7999999999999999e165 < y < 1.79999999999999996e94

   1. Initial program 99.5%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.75\right) - z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.75 + x\right)} - z\right) \]

      3. fma-def 99.7%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.75, x\right)} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.75, x\right) - z\right)} \]

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in y around 0 83.6%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+165}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+94}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 6: 52.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -92000000000000:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-55}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -92000000000000.0) 4.0 (if (<= y 5e-55) (* -4.0 (/ z y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -92000000000000.0) {
		tmp = 4.0;
	} else if (y <= 5e-55) {
		tmp = -4.0 * (z / y);
	} else {
		tmp = 4.0;
	}
	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 <= (-92000000000000.0d0)) then
        tmp = 4.0d0
    else if (y <= 5d-55) then
        tmp = (-4.0d0) * (z / y)
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -92000000000000.0) {
		tmp = 4.0;
	} else if (y <= 5e-55) {
		tmp = -4.0 * (z / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -92000000000000.0:
		tmp = 4.0
	elif y <= 5e-55:
		tmp = -4.0 * (z / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -92000000000000.0)
		tmp = 4.0;
	elseif (y <= 5e-55)
		tmp = Float64(-4.0 * Float64(z / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -92000000000000.0)
		tmp = 4.0;
	elseif (y <= 5e-55)
		tmp = -4.0 * (z / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -92000000000000.0], 4.0, If[LessEqual[y, 5e-55], N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -9.2e13 or 5.0000000000000002e-55 < y

   1. Initial program 99.1%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.75\right) - z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.75 + x\right)} - z\right) \]

      3. fma-def 99.7%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.75, x\right)} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.75, x\right) - z\right)} \]

   4. Taylor expanded in y around inf 57.5%

      \[\leadsto \color{blue}{4} \]

   if -9.2e13 < y < 5.0000000000000002e-55

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.75\right) - z\right)} \]

      2. +-commutative 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.75 + x\right)} - z\right) \]

      3. fma-def 99.8%

         \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.75, x\right)} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.75, x\right) - z\right)} \]

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in y around 0 92.6%

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

   6. Taylor expanded in x around 0 45.2%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -92000000000000:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-55}:\\ \;\;\;\;-4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 7: 7.7% accurate, 13.0× 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 99.5%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 99.7%

      \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.75\right) - z\right)} \]

   2. +-commutative 99.7%

      \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.75 + x\right)} - z\right) \]

   3. fma-def 99.7%

      \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.75, x\right)} - z\right) \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.75, x\right) - z\right)} \]

4. Taylor expanded in x around inf 45.5%

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

5. Taylor expanded in x around 0 7.2%

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

6. Final simplification 7.2%

   \[\leadsto 1 \]

Alternative 8: 34.0% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 4 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 4.0)

C

double code(double x, double y, double z) {
	return 4.0;
}

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
end function

Java

public static double code(double x, double y, double z) {
	return 4.0;
}

Python

def code(x, y, z):
	return 4.0

Julia

function code(x, y, z)
	return 4.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 4.0;
end

Wolfram

code[x_, y_, z_] := 4.0

Derivation

1. Initial program 99.5%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 99.7%

      \[\leadsto 1 + \color{blue}{\frac{4}{y} \cdot \left(\left(x + y \cdot 0.75\right) - z\right)} \]

   2. +-commutative 99.7%

      \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\left(y \cdot 0.75 + x\right)} - z\right) \]

   3. fma-def 99.7%

      \[\leadsto 1 + \frac{4}{y} \cdot \left(\color{blue}{\mathsf{fma}\left(y, 0.75, x\right)} - z\right) \]

3. Simplified 99.7%

   \[\leadsto \color{blue}{1 + \frac{4}{y} \cdot \left(\mathsf{fma}\left(y, 0.75, x\right) - z\right)} \]

4. Taylor expanded in y around inf 32.6%

   \[\leadsto \color{blue}{4} \]

5. Final simplification 32.6%

   \[\leadsto 4 \]

Reproduce

herbie shell --seed 2023310 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))