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

Percentage Accurate: 99.8% → 100.0%

Time: 5.9s

Alternatives: 9

Speedup: 1.2×

• 21.3% 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, 1.2× speedup

Math

\[\begin{array}{l} \\ 1 + \left(4 \cdot \frac{x - z}{y} + 3\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 1.0 (+ (* 4.0 (/ (- x z) y)) 3.0)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x - z) / y)) + 3.0);
}

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 + ((4.0d0 * ((x - z) / y)) + 3.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x - z) / y)) + 3.0);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x - z) / y)) + 3.0)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x - z) / y)) + 3.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x - z) / y)) + 3.0);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + 3.0), $MachinePrecision]), $MachinePrecision]

Derivation

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/ 99.7%

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

   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%

   \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
5. Step-by-step derivation

   1. +-commutative 100.0%

      \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

6. Simplified 100.0%

   \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

7. Final simplification 100.0%

   \[\leadsto 1 + \left(4 \cdot \frac{x - z}{y} + 3\right) \]

Alternative 2: 57.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{z \cdot -4}{y}\\ t_1 := 1 + \frac{4 \cdot x}{y}\\ \mathbf{if}\;x \leq -6 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-271}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-181}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 210:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* z -4.0) y))) (t_1 (+ 1.0 (/ (* 4.0 x) y))))
   (if (<= x -6e-5)
     t_1
     (if (<= x 5.6e-271)
       t_0
       (if (<= x 5.8e-181) 4.0 (if (<= x 210.0) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((z * -4.0) / y);
	double t_1 = 1.0 + ((4.0 * x) / y);
	double tmp;
	if (x <= -6e-5) {
		tmp = t_1;
	} else if (x <= 5.6e-271) {
		tmp = t_0;
	} else if (x <= 5.8e-181) {
		tmp = 4.0;
	} else if (x <= 210.0) {
		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 + ((z * (-4.0d0)) / y)
    t_1 = 1.0d0 + ((4.0d0 * x) / y)
    if (x <= (-6d-5)) then
        tmp = t_1
    else if (x <= 5.6d-271) then
        tmp = t_0
    else if (x <= 5.8d-181) then
        tmp = 4.0d0
    else if (x <= 210.0d0) 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 + ((z * -4.0) / y);
	double t_1 = 1.0 + ((4.0 * x) / y);
	double tmp;
	if (x <= -6e-5) {
		tmp = t_1;
	} else if (x <= 5.6e-271) {
		tmp = t_0;
	} else if (x <= 5.8e-181) {
		tmp = 4.0;
	} else if (x <= 210.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((z * -4.0) / y)
	t_1 = 1.0 + ((4.0 * x) / y)
	tmp = 0
	if x <= -6e-5:
		tmp = t_1
	elif x <= 5.6e-271:
		tmp = t_0
	elif x <= 5.8e-181:
		tmp = 4.0
	elif x <= 210.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(z * -4.0) / y))
	t_1 = Float64(1.0 + Float64(Float64(4.0 * x) / y))
	tmp = 0.0
	if (x <= -6e-5)
		tmp = t_1;
	elseif (x <= 5.6e-271)
		tmp = t_0;
	elseif (x <= 5.8e-181)
		tmp = 4.0;
	elseif (x <= 210.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((z * -4.0) / y);
	t_1 = 1.0 + ((4.0 * x) / y);
	tmp = 0.0;
	if (x <= -6e-5)
		tmp = t_1;
	elseif (x <= 5.6e-271)
		tmp = t_0;
	elseif (x <= 5.8e-181)
		tmp = 4.0;
	elseif (x <= 210.0)
		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[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e-5], t$95$1, If[LessEqual[x, 5.6e-271], t$95$0, If[LessEqual[x, 5.8e-181], 4.0, If[LessEqual[x, 210.0], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.00000000000000015e-5 or 210 < x

   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 x around inf 65.5%

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

      1. associate-*r/ 65.5%

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

   6. Simplified 65.5%

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

   if -6.00000000000000015e-5 < x < 5.5999999999999995e-271 or 5.7999999999999996e-181 < x < 210

   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/ 99.7%

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

      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 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 62.6%

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

      1. *-commutative 62.6%

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

      2. associate-*l/ 62.6%

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

   6. Simplified 62.6%

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

   if 5.5999999999999995e-271 < x < 5.7999999999999996e-181

   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/ 99.8%

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

      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%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   5. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   6. Simplified 100.0%

      \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   7. Taylor expanded in x around inf 78.9%

      \[\leadsto 1 + \left(\color{blue}{4 \cdot \frac{x}{y}} + 3\right) \]

   8. Taylor expanded in x around 0 78.6%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-5}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-271}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-181}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 210:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \end{array} \]

Alternative 3: 84.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \left(3 + -4 \cdot \frac{z}{y}\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+235}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+105}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+166}:\\ \;\;\;\;1 + 4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (+ 3.0 (* -4.0 (/ z y))))))
   (if (<= y -4.8e+235)
     t_0
     (if (<= y -1.3e+105)
       (+ 4.0 (* 4.0 (/ x y)))
       (if (<= y 2.85e+166) (+ 1.0 (* 4.0 (/ (- x z) y))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + (3.0 + (-4.0 * (z / y)));
	double tmp;
	if (y <= -4.8e+235) {
		tmp = t_0;
	} else if (y <= -1.3e+105) {
		tmp = 4.0 + (4.0 * (x / y));
	} else if (y <= 2.85e+166) {
		tmp = 1.0 + (4.0 * ((x - z) / y));
	} 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) :: tmp
    t_0 = 1.0d0 + (3.0d0 + ((-4.0d0) * (z / y)))
    if (y <= (-4.8d+235)) then
        tmp = t_0
    else if (y <= (-1.3d+105)) then
        tmp = 4.0d0 + (4.0d0 * (x / y))
    else if (y <= 2.85d+166) then
        tmp = 1.0d0 + (4.0d0 * ((x - z) / y))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + (3.0 + (-4.0 * (z / y)));
	double tmp;
	if (y <= -4.8e+235) {
		tmp = t_0;
	} else if (y <= -1.3e+105) {
		tmp = 4.0 + (4.0 * (x / y));
	} else if (y <= 2.85e+166) {
		tmp = 1.0 + (4.0 * ((x - z) / y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + (3.0 + (-4.0 * (z / y)))
	tmp = 0
	if y <= -4.8e+235:
		tmp = t_0
	elif y <= -1.3e+105:
		tmp = 4.0 + (4.0 * (x / y))
	elif y <= 2.85e+166:
		tmp = 1.0 + (4.0 * ((x - z) / y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(3.0 + Float64(-4.0 * Float64(z / y))))
	tmp = 0.0
	if (y <= -4.8e+235)
		tmp = t_0;
	elseif (y <= -1.3e+105)
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	elseif (y <= 2.85e+166)
		tmp = Float64(1.0 + Float64(4.0 * Float64(Float64(x - z) / y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + (3.0 + (-4.0 * (z / y)));
	tmp = 0.0;
	if (y <= -4.8e+235)
		tmp = t_0;
	elseif (y <= -1.3e+105)
		tmp = 4.0 + (4.0 * (x / y));
	elseif (y <= 2.85e+166)
		tmp = 1.0 + (4.0 * ((x - z) / y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(3.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+235], t$95$0, If[LessEqual[y, -1.3e+105], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.85e+166], N[(1.0 + N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7999999999999998e235 or 2.84999999999999989e166 < y

   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%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   5. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   6. Simplified 100.0%

      \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   7. Taylor expanded in x around 0 99.1%

      \[\leadsto 1 + \left(\color{blue}{-4 \cdot \frac{z}{y}} + 3\right) \]

   if -4.7999999999999998e235 < y < -1.3000000000000001e105

   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/ 99.8%

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

      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 99.9%

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

   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 0 100.0%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   5. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   6. Simplified 100.0%

      \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   7. Taylor expanded in x around inf 89.8%

      \[\leadsto 1 + \left(\color{blue}{4 \cdot \frac{x}{y}} + 3\right) \]

   8. Taylor expanded in x around 0 89.8%

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

   if -1.3000000000000001e105 < y < 2.84999999999999989e166

   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/ 99.7%

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

      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 89.2%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+235}:\\ \;\;\;\;1 + \left(3 + -4 \cdot \frac{z}{y}\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+105}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+166}:\\ \;\;\;\;1 + 4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(3 + -4 \cdot \frac{z}{y}\right)\\ \end{array} \]

Alternative 4: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-14} \lor \neg \left(z \leq 25500000\right):\\ \;\;\;\;1 + 4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.5e-14) (not (<= z 25500000.0)))
   (+ 1.0 (* 4.0 (/ (- x z) y)))
   (+ 4.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e-14) || !(z <= 25500000.0)) {
		tmp = 1.0 + (4.0 * ((x - z) / y));
	} else {
		tmp = 4.0 + (4.0 * (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) :: tmp
    if ((z <= (-4.5d-14)) .or. (.not. (z <= 25500000.0d0))) then
        tmp = 1.0d0 + (4.0d0 * ((x - z) / y))
    else
        tmp = 4.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e-14) || !(z <= 25500000.0)) {
		tmp = 1.0 + (4.0 * ((x - z) / y));
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.5e-14) or not (z <= 25500000.0):
		tmp = 1.0 + (4.0 * ((x - z) / y))
	else:
		tmp = 4.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.5e-14) || !(z <= 25500000.0))
		tmp = Float64(1.0 + Float64(4.0 * Float64(Float64(x - z) / y)));
	else
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.5e-14) || ~((z <= 25500000.0)))
		tmp = 1.0 + (4.0 * ((x - z) / y));
	else
		tmp = 4.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.5e-14], N[Not[LessEqual[z, 25500000.0]], $MachinePrecision]], N[(1.0 + N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999998e-14 or 2.55e7 < z

   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 99.7%

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

   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 86.7%

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

   if -4.4999999999999998e-14 < z < 2.55e7

   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/ 99.7%

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

      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%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   5. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   6. Simplified 100.0%

      \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   7. Taylor expanded in x around inf 91.6%

      \[\leadsto 1 + \left(\color{blue}{4 \cdot \frac{x}{y}} + 3\right) \]

   8. Taylor expanded in x around 0 91.6%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-14} \lor \neg \left(z \leq 25500000\right):\\ \;\;\;\;1 + 4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 81.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+96} \lor \neg \left(z \leq 3.4 \cdot 10^{+137}\right):\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.05e+96) (not (<= z 3.4e+137)))
   (+ 1.0 (/ (* z -4.0) y))
   (+ 4.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05e+96) || !(z <= 3.4e+137)) {
		tmp = 1.0 + ((z * -4.0) / y);
	} else {
		tmp = 4.0 + (4.0 * (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) :: tmp
    if ((z <= (-1.05d+96)) .or. (.not. (z <= 3.4d+137))) then
        tmp = 1.0d0 + ((z * (-4.0d0)) / y)
    else
        tmp = 4.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05e+96) || !(z <= 3.4e+137)) {
		tmp = 1.0 + ((z * -4.0) / y);
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.05e+96) or not (z <= 3.4e+137):
		tmp = 1.0 + ((z * -4.0) / y)
	else:
		tmp = 4.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.05e+96) || !(z <= 3.4e+137))
		tmp = Float64(1.0 + Float64(Float64(z * -4.0) / y));
	else
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.05e+96) || ~((z <= 3.4e+137)))
		tmp = 1.0 + ((z * -4.0) / y);
	else
		tmp = 4.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.05e+96], N[Not[LessEqual[z, 3.4e+137]], $MachinePrecision]], N[(1.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0500000000000001e96 or 3.39999999999999986e137 < z

   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 z around inf 75.4%

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

      1. *-commutative 75.4%

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

      2. associate-*l/ 75.4%

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

   6. Simplified 75.4%

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

   if -1.0500000000000001e96 < z < 3.39999999999999986e137

   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/ 99.7%

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

      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%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   5. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   6. Simplified 100.0%

      \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   7. Taylor expanded in x around inf 86.8%

      \[\leadsto 1 + \left(\color{blue}{4 \cdot \frac{x}{y}} + 3\right) \]

   8. Taylor expanded in x around 0 86.8%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+96} \lor \neg \left(z \leq 3.4 \cdot 10^{+137}\right):\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 6: 52.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+103}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+166}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.6e+103) 4.0 (if (<= y 2.15e+166) (+ 1.0 (/ 4.0 (/ y x))) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.6e+103) {
		tmp = 4.0;
	} else if (y <= 2.15e+166) {
		tmp = 1.0 + (4.0 / (y / x));
	} 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 <= (-2.6d+103)) then
        tmp = 4.0d0
    else if (y <= 2.15d+166) then
        tmp = 1.0d0 + (4.0d0 / (y / x))
    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 <= -2.6e+103) {
		tmp = 4.0;
	} else if (y <= 2.15e+166) {
		tmp = 1.0 + (4.0 / (y / x));
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.6e+103:
		tmp = 4.0
	elif y <= 2.15e+166:
		tmp = 1.0 + (4.0 / (y / x))
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.6e+103)
		tmp = 4.0;
	elseif (y <= 2.15e+166)
		tmp = Float64(1.0 + Float64(4.0 / Float64(y / x)));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.6e+103)
		tmp = 4.0;
	elseif (y <= 2.15e+166)
		tmp = 1.0 + (4.0 / (y / x));
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.6e+103], 4.0, If[LessEqual[y, 2.15e+166], N[(1.0 + N[(4.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6000000000000002e103 or 2.15e166 < y

   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/ 99.8%

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

      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%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   5. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   6. Simplified 100.0%

      \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   7. Taylor expanded in x around inf 80.5%

      \[\leadsto 1 + \left(\color{blue}{4 \cdot \frac{x}{y}} + 3\right) \]

   8. Taylor expanded in x around 0 70.9%

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

   if -2.6000000000000002e103 < y < 2.15e166

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 50.2%

      \[\leadsto 1 + \frac{4}{\color{blue}{\frac{y}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+103}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+166}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 7: 52.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+103}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+166}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e+103) 4.0 (if (<= y 2.15e+166) (+ 1.0 (/ (* 4.0 x) y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e+103) {
		tmp = 4.0;
	} else if (y <= 2.15e+166) {
		tmp = 1.0 + ((4.0 * x) / 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 <= (-6.5d+103)) then
        tmp = 4.0d0
    else if (y <= 2.15d+166) then
        tmp = 1.0d0 + ((4.0d0 * x) / 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 <= -6.5e+103) {
		tmp = 4.0;
	} else if (y <= 2.15e+166) {
		tmp = 1.0 + ((4.0 * x) / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.5e+103:
		tmp = 4.0
	elif y <= 2.15e+166:
		tmp = 1.0 + ((4.0 * x) / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e+103)
		tmp = 4.0;
	elseif (y <= 2.15e+166)
		tmp = Float64(1.0 + Float64(Float64(4.0 * x) / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.5e+103)
		tmp = 4.0;
	elseif (y <= 2.15e+166)
		tmp = 1.0 + ((4.0 * x) / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e+103], 4.0, If[LessEqual[y, 2.15e+166], N[(1.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -6.50000000000000001e103 or 2.15e166 < y

   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/ 99.8%

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

      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%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   5. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   6. Simplified 100.0%

      \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   7. Taylor expanded in x around inf 80.5%

      \[\leadsto 1 + \left(\color{blue}{4 \cdot \frac{x}{y}} + 3\right) \]

   8. Taylor expanded in x around 0 70.9%

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

   if -6.50000000000000001e103 < y < 2.15e166

   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/ 99.7%

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

      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 50.4%

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

      1. associate-*r/ 50.4%

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

   6. Simplified 50.4%

      \[\leadsto 1 + \color{blue}{\frac{4 \cdot x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+103}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+166}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 8: 52.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+49}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.9e+61) 4.0 (if (<= y 1.95e+49) (* 4.0 (/ x y)) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.9e+61) {
		tmp = 4.0;
	} else if (y <= 1.95e+49) {
		tmp = 4.0 * (x / 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 <= (-4.9d+61)) then
        tmp = 4.0d0
    else if (y <= 1.95d+49) then
        tmp = 4.0d0 * (x / 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 <= -4.9e+61) {
		tmp = 4.0;
	} else if (y <= 1.95e+49) {
		tmp = 4.0 * (x / y);
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.9e+61:
		tmp = 4.0
	elif y <= 1.95e+49:
		tmp = 4.0 * (x / y)
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.9e+61)
		tmp = 4.0;
	elseif (y <= 1.95e+49)
		tmp = Float64(4.0 * Float64(x / y));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.9e+61)
		tmp = 4.0;
	elseif (y <= 1.95e+49)
		tmp = 4.0 * (x / y);
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.9e+61], 4.0, If[LessEqual[y, 1.95e+49], N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.90000000000000025e61 or 1.95e49 < y

   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/ 99.8%

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

      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%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   5. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   6. Simplified 100.0%

      \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   7. Taylor expanded in x around inf 76.1%

      \[\leadsto 1 + \left(\color{blue}{4 \cdot \frac{x}{y}} + 3\right) \]

   8. Taylor expanded in x around 0 59.7%

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

   if -4.90000000000000025e61 < y < 1.95e49

   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/ 99.7%

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

      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%

      \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
   5. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   6. Simplified 100.0%

      \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

   7. Taylor expanded in x around inf 59.0%

      \[\leadsto 1 + \left(\color{blue}{4 \cdot \frac{x}{y}} + 3\right) \]

   8. Taylor expanded in x around inf 51.7%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+61}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+49}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 9: 33.1% 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 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/ 99.7%

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

   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%

   \[\leadsto 1 + \color{blue}{\left(3 + 4 \cdot \frac{x - z}{y}\right)} \]
5. Step-by-step derivation

   1. +-commutative 100.0%

      \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

6. Simplified 100.0%

   \[\leadsto 1 + \color{blue}{\left(4 \cdot \frac{x - z}{y} + 3\right)} \]

7. Taylor expanded in x around inf 66.0%

   \[\leadsto 1 + \left(\color{blue}{4 \cdot \frac{x}{y}} + 3\right) \]

8. Taylor expanded in x around 0 30.4%

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

9. Final simplification 30.4%

   \[\leadsto 4 \]

Reproduce

herbie shell --seed 2023297 
(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)))