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

Percentage Accurate: 99.9% → 99.9%

Time: 6.0s

Alternatives: 9

Speedup: 1.0×

• 21.4% 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: 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]

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 58.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + z \cdot \frac{-4}{y}\\ t_1 := 1 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -9.4 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-199}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-278}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 3.85 \cdot 10^{+43}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 -9.4e+80)
     t_1
     (if (<= x -4.5e-199)
       t_0
       (if (<= x -3.9e-278) 2.0 (if (<= x 3.85e+43) 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 <= -9.4e+80) {
		tmp = t_1;
	} else if (x <= -4.5e-199) {
		tmp = t_0;
	} else if (x <= -3.9e-278) {
		tmp = 2.0;
	} else if (x <= 3.85e+43) {
		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 <= (-9.4d+80)) then
        tmp = t_1
    else if (x <= (-4.5d-199)) then
        tmp = t_0
    else if (x <= (-3.9d-278)) then
        tmp = 2.0d0
    else if (x <= 3.85d+43) 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 <= -9.4e+80) {
		tmp = t_1;
	} else if (x <= -4.5e-199) {
		tmp = t_0;
	} else if (x <= -3.9e-278) {
		tmp = 2.0;
	} else if (x <= 3.85e+43) {
		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 <= -9.4e+80:
		tmp = t_1
	elif x <= -4.5e-199:
		tmp = t_0
	elif x <= -3.9e-278:
		tmp = 2.0
	elif x <= 3.85e+43:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(z * Float64(-4.0 / y)))
	t_1 = Float64(1.0 + Float64(4.0 * Float64(x / y)))
	tmp = 0.0
	if (x <= -9.4e+80)
		tmp = t_1;
	elseif (x <= -4.5e-199)
		tmp = t_0;
	elseif (x <= -3.9e-278)
		tmp = 2.0;
	elseif (x <= 3.85e+43)
		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 <= -9.4e+80)
		tmp = t_1;
	elseif (x <= -4.5e-199)
		tmp = t_0;
	elseif (x <= -3.9e-278)
		tmp = 2.0;
	elseif (x <= 3.85e+43)
		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[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.4e+80], t$95$1, If[LessEqual[x, -4.5e-199], t$95$0, If[LessEqual[x, -3.9e-278], 2.0, If[LessEqual[x, 3.85e+43], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.40000000000000019e80 or 3.8499999999999998e43 < x

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 77.7%

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

   if -9.40000000000000019e80 < x < -4.49999999999999998e-199 or -3.9000000000000001e-278 < x < 3.8499999999999998e43

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 60.8%

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

      1. *-commutative 60.8%

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

   6. Simplified 60.8%

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

      1. *-commutative 60.8%

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

      2. clear-num 60.7%

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

      3. un-div-inv 60.7%

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

   8. Applied egg-rr 60.7%

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

      1. associate-/r/ 60.7%

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

   10. Applied egg-rr 60.7%

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

   if -4.49999999999999998e-199 < x < -3.9000000000000001e-278

   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/ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate--l+ 100.0%

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

      4. distribute-lft-in 100.0%

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

      5. associate-+r+ 100.0%

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

   3. Simplified 100.0%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 68.6%

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

      1. *-commutative 68.6%

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

      2. associate-*l/ 68.6%

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

      3. associate-*r/ 68.6%

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

   8. Simplified 68.6%

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

   9. Taylor expanded in x around 0 68.9%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{+80}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-199}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-278}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 3.85 \cdot 10^{+43}:\\ \;\;\;\;1 + z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 3: 58.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + -4 \cdot \frac{z}{y}\\ t_1 := 1 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-194}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-282}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+43}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* -4.0 (/ z y)))) (t_1 (+ 1.0 (* 4.0 (/ x y)))))
   (if (<= x -1.1e+82)
     t_1
     (if (<= x -2.5e-194)
       t_0
       (if (<= x -9e-282) 2.0 (if (<= x 2.75e+43) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + (-4.0 * (z / y));
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (x <= -1.1e+82) {
		tmp = t_1;
	} else if (x <= -2.5e-194) {
		tmp = t_0;
	} else if (x <= -9e-282) {
		tmp = 2.0;
	} else if (x <= 2.75e+43) {
		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) * (z / y))
    t_1 = 1.0d0 + (4.0d0 * (x / y))
    if (x <= (-1.1d+82)) then
        tmp = t_1
    else if (x <= (-2.5d-194)) then
        tmp = t_0
    else if (x <= (-9d-282)) then
        tmp = 2.0d0
    else if (x <= 2.75d+43) 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 * (z / y));
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (x <= -1.1e+82) {
		tmp = t_1;
	} else if (x <= -2.5e-194) {
		tmp = t_0;
	} else if (x <= -9e-282) {
		tmp = 2.0;
	} else if (x <= 2.75e+43) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + (-4.0 * (z / y))
	t_1 = 1.0 + (4.0 * (x / y))
	tmp = 0
	if x <= -1.1e+82:
		tmp = t_1
	elif x <= -2.5e-194:
		tmp = t_0
	elif x <= -9e-282:
		tmp = 2.0
	elif x <= 2.75e+43:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(-4.0 * Float64(z / y)))
	t_1 = Float64(1.0 + Float64(4.0 * Float64(x / y)))
	tmp = 0.0
	if (x <= -1.1e+82)
		tmp = t_1;
	elseif (x <= -2.5e-194)
		tmp = t_0;
	elseif (x <= -9e-282)
		tmp = 2.0;
	elseif (x <= 2.75e+43)
		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 * (z / y));
	t_1 = 1.0 + (4.0 * (x / y));
	tmp = 0.0;
	if (x <= -1.1e+82)
		tmp = t_1;
	elseif (x <= -2.5e-194)
		tmp = t_0;
	elseif (x <= -9e-282)
		tmp = 2.0;
	elseif (x <= 2.75e+43)
		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[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+82], t$95$1, If[LessEqual[x, -2.5e-194], t$95$0, If[LessEqual[x, -9e-282], 2.0, If[LessEqual[x, 2.75e+43], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1000000000000001e82 or 2.74999999999999995e43 < x

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 77.7%

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

   if -1.1000000000000001e82 < x < -2.5000000000000001e-194 or -9.00000000000000017e-282 < x < 2.74999999999999995e43

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 60.8%

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

      1. *-commutative 60.8%

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

   6. Simplified 60.8%

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

   if -2.5000000000000001e-194 < x < -9.00000000000000017e-282

   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/ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate--l+ 100.0%

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

      4. distribute-lft-in 100.0%

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

      5. associate-+r+ 100.0%

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

   3. Simplified 100.0%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 68.6%

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

      1. *-commutative 68.6%

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

      2. associate-*l/ 68.6%

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

      3. associate-*r/ 68.6%

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

   8. Simplified 68.6%

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

   9. Taylor expanded in x around 0 68.9%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+82}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-194}:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-282}:\\ \;\;\;\;2\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+43}:\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 4: 55.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{+76} \lor \neg \left(x \leq 2.2 \cdot 10^{+52}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.3e+76) (not (<= x 2.2e+52))) (+ 1.0 (* 4.0 (/ x y))) 2.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.3e+76) || !(x <= 2.2e+52)) {
		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 <= (-5.3d+76)) .or. (.not. (x <= 2.2d+52))) 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 <= -5.3e+76) || !(x <= 2.2e+52)) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.3e+76) or not (x <= 2.2e+52):
		tmp = 1.0 + (4.0 * (x / y))
	else:
		tmp = 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.3e+76) || !(x <= 2.2e+52))
		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 <= -5.3e+76) || ~((x <= 2.2e+52)))
		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, -5.3e+76], N[Not[LessEqual[x, 2.2e+52]], $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 < -5.30000000000000015e76 or 2.2e52 < x

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 78.8%

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

   if -5.30000000000000015e76 < x < 2.2e52

   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%

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

      2. +-commutative 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-lft-in 99.8%

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

      5. associate-+r+ 99.8%

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

   3. Simplified 99.8%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 50.5%

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

      1. *-commutative 50.5%

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

      2. associate-*l/ 50.5%

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

      3. associate-*r/ 50.4%

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

   8. Simplified 50.4%

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

   9. Taylor expanded in x around 0 42.6%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{+76} \lor \neg \left(x \leq 2.2 \cdot 10^{+52}\right):\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 5: 80.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+127} \lor \neg \left(z \leq 3 \cdot 10^{+194}\right):\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + x \cdot \frac{4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.4e+127) (not (<= z 3e+194)))
   (+ 1.0 (* -4.0 (/ z y)))
   (+ 2.0 (* x (/ 4.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e+127) || !(z <= 3e+194)) {
		tmp = 1.0 + (-4.0 * (z / y));
	} else {
		tmp = 2.0 + (x * (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 ((z <= (-1.4d+127)) .or. (.not. (z <= 3d+194))) then
        tmp = 1.0d0 + ((-4.0d0) * (z / y))
    else
        tmp = 2.0d0 + (x * (4.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e+127) || !(z <= 3e+194)) {
		tmp = 1.0 + (-4.0 * (z / y));
	} else {
		tmp = 2.0 + (x * (4.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.4e+127) or not (z <= 3e+194):
		tmp = 1.0 + (-4.0 * (z / y))
	else:
		tmp = 2.0 + (x * (4.0 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.4e+127) || !(z <= 3e+194))
		tmp = Float64(1.0 + Float64(-4.0 * Float64(z / y)));
	else
		tmp = Float64(2.0 + Float64(x * Float64(4.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.4e+127) || ~((z <= 3e+194)))
		tmp = 1.0 + (-4.0 * (z / y));
	else
		tmp = 2.0 + (x * (4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.4e+127], N[Not[LessEqual[z, 3e+194]], $MachinePrecision]], N[(1.0 + N[(-4.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4000000000000001e127 or 3.0000000000000003e194 < z

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 80.5%

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

      1. *-commutative 80.5%

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

   6. Simplified 80.5%

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

   if -1.4000000000000001e127 < z < 3.0000000000000003e194

   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%

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

      2. +-commutative 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-lft-in 99.8%

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

      5. associate-+r+ 99.8%

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

   3. Simplified 99.8%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 82.5%

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

      1. *-commutative 82.5%

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

      2. associate-*l/ 82.5%

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

      3. associate-*r/ 82.4%

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

   8. Simplified 82.4%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+127} \lor \neg \left(z \leq 3 \cdot 10^{+194}\right):\\ \;\;\;\;1 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + x \cdot \frac{4}{y}\\ \end{array} \]

Alternative 6: 86.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+78} \lor \neg \left(x \leq 1.26 \cdot 10^{+44}\right):\\ \;\;\;\;2 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z}{\frac{y}{-4}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.25e+78) (not (<= x 1.26e+44)))
   (+ 2.0 (* x (/ 4.0 y)))
   (+ 2.0 (/ z (/ y -4.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.25e+78) || !(x <= 1.26e+44)) {
		tmp = 2.0 + (x * (4.0 / y));
	} else {
		tmp = 2.0 + (z / (y / -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 ((x <= (-1.25d+78)) .or. (.not. (x <= 1.26d+44))) then
        tmp = 2.0d0 + (x * (4.0d0 / y))
    else
        tmp = 2.0d0 + (z / (y / (-4.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.25e+78) || !(x <= 1.26e+44)) {
		tmp = 2.0 + (x * (4.0 / y));
	} else {
		tmp = 2.0 + (z / (y / -4.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.25e+78) or not (x <= 1.26e+44):
		tmp = 2.0 + (x * (4.0 / y))
	else:
		tmp = 2.0 + (z / (y / -4.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.25e+78) || !(x <= 1.26e+44))
		tmp = Float64(2.0 + Float64(x * Float64(4.0 / y)));
	else
		tmp = Float64(2.0 + Float64(z / Float64(y / -4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.25e+78) || ~((x <= 1.26e+44)))
		tmp = 2.0 + (x * (4.0 / y));
	else
		tmp = 2.0 + (z / (y / -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.25e+78], N[Not[LessEqual[x, 1.26e+44]], $MachinePrecision]], N[(2.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 + N[(z / N[(y / -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.24999999999999996e78 or 1.25999999999999996e44 < x

   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/ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate--l+ 99.7%

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

      4. distribute-lft-in 99.8%

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

      5. associate-+r+ 99.8%

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

   3. Simplified 99.8%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 91.6%

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

      1. *-commutative 91.6%

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

      2. associate-*l/ 91.6%

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

      3. associate-*r/ 91.5%

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

   8. Simplified 91.5%

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

   if -1.24999999999999996e78 < x < 1.25999999999999996e44

   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%

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

      2. +-commutative 99.8%

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

      3. associate--l+ 99.8%

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

      4. distribute-lft-in 99.8%

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

      5. associate-+r+ 99.8%

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

   3. Simplified 99.8%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-/r/ 91.7%

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

   8. Simplified 91.7%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+78} \lor \neg \left(x \leq 1.26 \cdot 10^{+44}\right):\\ \;\;\;\;2 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + \frac{z}{\frac{y}{-4}}\\ \end{array} \]

Alternative 7: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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%

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

   2. +-commutative 99.8%

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

   3. associate--l+ 99.8%

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

   4. distribute-lft-in 99.8%

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

   5. associate-+r+ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 8: 8.2% 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 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%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around inf 43.3%

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

5. Taylor expanded in x around 0 7.6%

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

6. Final simplification 7.6%

   \[\leadsto 1 \]

Alternative 9: 34.6% 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 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%

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

   2. +-commutative 99.8%

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

   3. associate--l+ 99.8%

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

   4. distribute-lft-in 99.8%

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

   5. associate-+r+ 99.8%

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

3. Simplified 99.8%

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

   1. associate-*l/ 100.0%

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

   2. associate-/l* 99.8%

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

5. Applied egg-rr 99.8%

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

6. Taylor expanded in x around inf 67.9%

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

   1. *-commutative 67.9%

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

   2. associate-*l/ 67.9%

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

   3. associate-*r/ 67.8%

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

8. Simplified 67.8%

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

9. Taylor expanded in x around 0 31.4%

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

10. Final simplification 31.4%

    \[\leadsto 2 \]

Reproduce

herbie shell --seed 2023274 
(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)))