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

Percentage Accurate: 99.8% → 99.9%

Time: 7.9s

Alternatives: 9

Speedup: 1.2×

• 22.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (- x y) (* z 0.5))) z))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / 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 = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Python

def code(x, y, z):
	return (4.0 * ((x - y) - (z * 0.5))) / z

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) - (z * 0.5))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (- x y) (* z 0.5))) z))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / 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 = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

Python

def code(x, y, z):
	return (4.0 * ((x - y) - (z * 0.5))) / z

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) - (z * 0.5))) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 52.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-4 \cdot y}{z}\\ t_1 := \frac{4 \cdot x}{z}\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-46}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-158}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-286}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+124}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* -4.0 y) z)) (t_1 (/ (* 4.0 x) z)))
   (if (<= x -1.1e+91)
     t_1
     (if (<= x -3.7e-46)
       -2.0
       (if (<= x -1.75e-158)
         t_0
         (if (<= x 3.5e-286) -2.0 (if (<= x 1.08e+124) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = (-4.0 * y) / z;
	double t_1 = (4.0 * x) / z;
	double tmp;
	if (x <= -1.1e+91) {
		tmp = t_1;
	} else if (x <= -3.7e-46) {
		tmp = -2.0;
	} else if (x <= -1.75e-158) {
		tmp = t_0;
	} else if (x <= 3.5e-286) {
		tmp = -2.0;
	} else if (x <= 1.08e+124) {
		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 = ((-4.0d0) * y) / z
    t_1 = (4.0d0 * x) / z
    if (x <= (-1.1d+91)) then
        tmp = t_1
    else if (x <= (-3.7d-46)) then
        tmp = -2.0d0
    else if (x <= (-1.75d-158)) then
        tmp = t_0
    else if (x <= 3.5d-286) then
        tmp = -2.0d0
    else if (x <= 1.08d+124) 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 = (-4.0 * y) / z;
	double t_1 = (4.0 * x) / z;
	double tmp;
	if (x <= -1.1e+91) {
		tmp = t_1;
	} else if (x <= -3.7e-46) {
		tmp = -2.0;
	} else if (x <= -1.75e-158) {
		tmp = t_0;
	} else if (x <= 3.5e-286) {
		tmp = -2.0;
	} else if (x <= 1.08e+124) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-4.0 * y) / z
	t_1 = (4.0 * x) / z
	tmp = 0
	if x <= -1.1e+91:
		tmp = t_1
	elif x <= -3.7e-46:
		tmp = -2.0
	elif x <= -1.75e-158:
		tmp = t_0
	elif x <= 3.5e-286:
		tmp = -2.0
	elif x <= 1.08e+124:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-4.0 * y) / z)
	t_1 = Float64(Float64(4.0 * x) / z)
	tmp = 0.0
	if (x <= -1.1e+91)
		tmp = t_1;
	elseif (x <= -3.7e-46)
		tmp = -2.0;
	elseif (x <= -1.75e-158)
		tmp = t_0;
	elseif (x <= 3.5e-286)
		tmp = -2.0;
	elseif (x <= 1.08e+124)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-4.0 * y) / z;
	t_1 = (4.0 * x) / z;
	tmp = 0.0;
	if (x <= -1.1e+91)
		tmp = t_1;
	elseif (x <= -3.7e-46)
		tmp = -2.0;
	elseif (x <= -1.75e-158)
		tmp = t_0;
	elseif (x <= 3.5e-286)
		tmp = -2.0;
	elseif (x <= 1.08e+124)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-4.0 * y), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[x, -1.1e+91], t$95$1, If[LessEqual[x, -3.7e-46], -2.0, If[LessEqual[x, -1.75e-158], t$95$0, If[LessEqual[x, 3.5e-286], -2.0, If[LessEqual[x, 1.08e+124], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1e91 or 1.08000000000000005e124 < x

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.1e91 < x < -3.69999999999999983e-46 or -1.75000000000000006e-158 < x < 3.49999999999999988e-286

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -3.69999999999999983e-46 < x < -1.75000000000000006e-158 or 3.49999999999999988e-286 < x < 1.08000000000000005e124

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 52.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-4 \cdot y}{z}\\ t_1 := \frac{4}{\frac{z}{x}}\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-46}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-158}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-286}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+124}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* -4.0 y) z)) (t_1 (/ 4.0 (/ z x))))
   (if (<= x -8.5e+90)
     t_1
     (if (<= x -1.9e-46)
       -2.0
       (if (<= x -4.5e-158)
         t_0
         (if (<= x 1.3e-286) -2.0 (if (<= x 1.08e+124) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = (-4.0 * y) / z;
	double t_1 = 4.0 / (z / x);
	double tmp;
	if (x <= -8.5e+90) {
		tmp = t_1;
	} else if (x <= -1.9e-46) {
		tmp = -2.0;
	} else if (x <= -4.5e-158) {
		tmp = t_0;
	} else if (x <= 1.3e-286) {
		tmp = -2.0;
	} else if (x <= 1.08e+124) {
		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 = ((-4.0d0) * y) / z
    t_1 = 4.0d0 / (z / x)
    if (x <= (-8.5d+90)) then
        tmp = t_1
    else if (x <= (-1.9d-46)) then
        tmp = -2.0d0
    else if (x <= (-4.5d-158)) then
        tmp = t_0
    else if (x <= 1.3d-286) then
        tmp = -2.0d0
    else if (x <= 1.08d+124) 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 = (-4.0 * y) / z;
	double t_1 = 4.0 / (z / x);
	double tmp;
	if (x <= -8.5e+90) {
		tmp = t_1;
	} else if (x <= -1.9e-46) {
		tmp = -2.0;
	} else if (x <= -4.5e-158) {
		tmp = t_0;
	} else if (x <= 1.3e-286) {
		tmp = -2.0;
	} else if (x <= 1.08e+124) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-4.0 * y) / z
	t_1 = 4.0 / (z / x)
	tmp = 0
	if x <= -8.5e+90:
		tmp = t_1
	elif x <= -1.9e-46:
		tmp = -2.0
	elif x <= -4.5e-158:
		tmp = t_0
	elif x <= 1.3e-286:
		tmp = -2.0
	elif x <= 1.08e+124:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-4.0 * y) / z)
	t_1 = Float64(4.0 / Float64(z / x))
	tmp = 0.0
	if (x <= -8.5e+90)
		tmp = t_1;
	elseif (x <= -1.9e-46)
		tmp = -2.0;
	elseif (x <= -4.5e-158)
		tmp = t_0;
	elseif (x <= 1.3e-286)
		tmp = -2.0;
	elseif (x <= 1.08e+124)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-4.0 * y) / z;
	t_1 = 4.0 / (z / x);
	tmp = 0.0;
	if (x <= -8.5e+90)
		tmp = t_1;
	elseif (x <= -1.9e-46)
		tmp = -2.0;
	elseif (x <= -4.5e-158)
		tmp = t_0;
	elseif (x <= 1.3e-286)
		tmp = -2.0;
	elseif (x <= 1.08e+124)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-4.0 * y), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 / N[(z / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.5e+90], t$95$1, If[LessEqual[x, -1.9e-46], -2.0, If[LessEqual[x, -4.5e-158], t$95$0, If[LessEqual[x, 1.3e-286], -2.0, If[LessEqual[x, 1.08e+124], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.5000000000000002e90 or 1.08000000000000005e124 < x

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -8.5000000000000002e90 < x < -1.8999999999999998e-46 or -4.5e-158 < x < 1.3e-286

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.8999999999999998e-46 < x < -4.5e-158 or 1.3e-286 < x < 1.08000000000000005e124

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 52.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-4}{\frac{z}{y}}\\ t_1 := \frac{4}{\frac{z}{x}}\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-44}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-156}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-287}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+124}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ -4.0 (/ z y))) (t_1 (/ 4.0 (/ z x))))
   (if (<= x -1.5e+91)
     t_1
     (if (<= x -1.12e-44)
       -2.0
       (if (<= x -2.4e-156)
         t_0
         (if (<= x 7.5e-287) -2.0 (if (<= x 1.08e+124) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = -4.0 / (z / y);
	double t_1 = 4.0 / (z / x);
	double tmp;
	if (x <= -1.5e+91) {
		tmp = t_1;
	} else if (x <= -1.12e-44) {
		tmp = -2.0;
	} else if (x <= -2.4e-156) {
		tmp = t_0;
	} else if (x <= 7.5e-287) {
		tmp = -2.0;
	} else if (x <= 1.08e+124) {
		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 = (-4.0d0) / (z / y)
    t_1 = 4.0d0 / (z / x)
    if (x <= (-1.5d+91)) then
        tmp = t_1
    else if (x <= (-1.12d-44)) then
        tmp = -2.0d0
    else if (x <= (-2.4d-156)) then
        tmp = t_0
    else if (x <= 7.5d-287) then
        tmp = -2.0d0
    else if (x <= 1.08d+124) 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 = -4.0 / (z / y);
	double t_1 = 4.0 / (z / x);
	double tmp;
	if (x <= -1.5e+91) {
		tmp = t_1;
	} else if (x <= -1.12e-44) {
		tmp = -2.0;
	} else if (x <= -2.4e-156) {
		tmp = t_0;
	} else if (x <= 7.5e-287) {
		tmp = -2.0;
	} else if (x <= 1.08e+124) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -4.0 / (z / y)
	t_1 = 4.0 / (z / x)
	tmp = 0
	if x <= -1.5e+91:
		tmp = t_1
	elif x <= -1.12e-44:
		tmp = -2.0
	elif x <= -2.4e-156:
		tmp = t_0
	elif x <= 7.5e-287:
		tmp = -2.0
	elif x <= 1.08e+124:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-4.0 / Float64(z / y))
	t_1 = Float64(4.0 / Float64(z / x))
	tmp = 0.0
	if (x <= -1.5e+91)
		tmp = t_1;
	elseif (x <= -1.12e-44)
		tmp = -2.0;
	elseif (x <= -2.4e-156)
		tmp = t_0;
	elseif (x <= 7.5e-287)
		tmp = -2.0;
	elseif (x <= 1.08e+124)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -4.0 / (z / y);
	t_1 = 4.0 / (z / x);
	tmp = 0.0;
	if (x <= -1.5e+91)
		tmp = t_1;
	elseif (x <= -1.12e-44)
		tmp = -2.0;
	elseif (x <= -2.4e-156)
		tmp = t_0;
	elseif (x <= 7.5e-287)
		tmp = -2.0;
	elseif (x <= 1.08e+124)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-4.0 / N[(z / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(4.0 / N[(z / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e+91], t$95$1, If[LessEqual[x, -1.12e-44], -2.0, If[LessEqual[x, -2.4e-156], t$95$0, If[LessEqual[x, 7.5e-287], -2.0, If[LessEqual[x, 1.08e+124], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.50000000000000003e91 or 1.08000000000000005e124 < x

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -1.50000000000000003e91 < x < -1.1200000000000001e-44 or -2.4e-156 < x < 7.5000000000000001e-287

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.1200000000000001e-44 < x < -2.4e-156 or 7.5000000000000001e-287 < x < 1.08000000000000005e124

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-82}:\\ \;\;\;\;\frac{4 \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 0.135:\\ \;\;\;\;\frac{4 \cdot x}{z} + -2\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{-4 \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6e-82)
   (/ (* 4.0 (- x y)) z)
   (if (<= y 0.135) (+ (/ (* 4.0 x) z) -2.0) (+ -2.0 (/ (* -4.0 y) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e-82) {
		tmp = (4.0 * (x - y)) / z;
	} else if (y <= 0.135) {
		tmp = ((4.0 * x) / z) + -2.0;
	} else {
		tmp = -2.0 + ((-4.0 * y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6d-82)) then
        tmp = (4.0d0 * (x - y)) / z
    else if (y <= 0.135d0) then
        tmp = ((4.0d0 * x) / z) + (-2.0d0)
    else
        tmp = (-2.0d0) + (((-4.0d0) * y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e-82) {
		tmp = (4.0 * (x - y)) / z;
	} else if (y <= 0.135) {
		tmp = ((4.0 * x) / z) + -2.0;
	} else {
		tmp = -2.0 + ((-4.0 * y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6e-82:
		tmp = (4.0 * (x - y)) / z
	elif y <= 0.135:
		tmp = ((4.0 * x) / z) + -2.0
	else:
		tmp = -2.0 + ((-4.0 * y) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6e-82)
		tmp = Float64(Float64(4.0 * Float64(x - y)) / z);
	elseif (y <= 0.135)
		tmp = Float64(Float64(Float64(4.0 * x) / z) + -2.0);
	else
		tmp = Float64(-2.0 + Float64(Float64(-4.0 * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6e-82)
		tmp = (4.0 * (x - y)) / z;
	elseif (y <= 0.135)
		tmp = ((4.0 * x) / z) + -2.0;
	else
		tmp = -2.0 + ((-4.0 * y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6e-82], N[(N[(4.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 0.135], N[(N[(N[(4.0 * x), $MachinePrecision] / z), $MachinePrecision] + -2.0), $MachinePrecision], N[(-2.0 + N[(N[(-4.0 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.9999999999999998e-82

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -5.9999999999999998e-82 < y < 0.13500000000000001

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 0.13500000000000001 < y

   1. Initial program 99.9%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 85.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -2 + \frac{-4 \cdot y}{z}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+76}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{4 \cdot x}{z} + -2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ -2.0 (/ (* -4.0 y) z))))
   (if (<= y -1.2e+76) t_0 (if (<= y 1.3e-6) (+ (/ (* 4.0 x) z) -2.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -2.0 + ((-4.0 * y) / z);
	double tmp;
	if (y <= -1.2e+76) {
		tmp = t_0;
	} else if (y <= 1.3e-6) {
		tmp = ((4.0 * x) / z) + -2.0;
	} 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) :: tmp
    t_0 = (-2.0d0) + (((-4.0d0) * y) / z)
    if (y <= (-1.2d+76)) then
        tmp = t_0
    else if (y <= 1.3d-6) then
        tmp = ((4.0d0 * x) / z) + (-2.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -2.0 + ((-4.0 * y) / z);
	double tmp;
	if (y <= -1.2e+76) {
		tmp = t_0;
	} else if (y <= 1.3e-6) {
		tmp = ((4.0 * x) / z) + -2.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -2.0 + ((-4.0 * y) / z)
	tmp = 0
	if y <= -1.2e+76:
		tmp = t_0
	elif y <= 1.3e-6:
		tmp = ((4.0 * x) / z) + -2.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-2.0 + Float64(Float64(-4.0 * y) / z))
	tmp = 0.0
	if (y <= -1.2e+76)
		tmp = t_0;
	elseif (y <= 1.3e-6)
		tmp = Float64(Float64(Float64(4.0 * x) / z) + -2.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -2.0 + ((-4.0 * y) / z);
	tmp = 0.0;
	if (y <= -1.2e+76)
		tmp = t_0;
	elseif (y <= 1.3e-6)
		tmp = ((4.0 * x) / z) + -2.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-2.0 + N[(N[(-4.0 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+76], t$95$0, If[LessEqual[y, 1.3e-6], N[(N[(N[(4.0 * x), $MachinePrecision] / z), $MachinePrecision] + -2.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e76 or 1.30000000000000005e-6 < y

   1. Initial program 99.9%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.2e76 < y < 1.30000000000000005e-6

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 80.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4 \cdot x}{z}\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+109}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+164}:\\ \;\;\;\;-2 + \frac{-4 \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* 4.0 x) z)))
   (if (<= x -2.2e+109)
     t_0
     (if (<= x 1.3e+164) (+ -2.0 (/ (* -4.0 y) z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * x) / z;
	double tmp;
	if (x <= -2.2e+109) {
		tmp = t_0;
	} else if (x <= 1.3e+164) {
		tmp = -2.0 + ((-4.0 * y) / z);
	} 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 = (4.0d0 * x) / z
    if (x <= (-2.2d+109)) then
        tmp = t_0
    else if (x <= 1.3d+164) then
        tmp = (-2.0d0) + (((-4.0d0) * y) / z)
    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) / z;
	double tmp;
	if (x <= -2.2e+109) {
		tmp = t_0;
	} else if (x <= 1.3e+164) {
		tmp = -2.0 + ((-4.0 * y) / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 * x) / z
	tmp = 0
	if x <= -2.2e+109:
		tmp = t_0
	elif x <= 1.3e+164:
		tmp = -2.0 + ((-4.0 * y) / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * x) / z)
	tmp = 0.0
	if (x <= -2.2e+109)
		tmp = t_0;
	elseif (x <= 1.3e+164)
		tmp = Float64(-2.0 + Float64(Float64(-4.0 * y) / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 * x) / z;
	tmp = 0.0;
	if (x <= -2.2e+109)
		tmp = t_0;
	elseif (x <= 1.3e+164)
		tmp = -2.0 + ((-4.0 * y) / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[x, -2.2e+109], t$95$0, If[LessEqual[x, 1.3e+164], N[(-2.0 + N[(N[(-4.0 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1999999999999999e109 or 1.3e164 < x

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -2.1999999999999999e109 < x < 1.3e164

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 53.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+110}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+72}:\\ \;\;\;\;\frac{-4}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.2e+110) -2.0 (if (<= z 1.55e+72) (/ -4.0 (/ z y)) -2.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.2e+110) {
		tmp = -2.0;
	} else if (z <= 1.55e+72) {
		tmp = -4.0 / (z / 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 (z <= (-7.2d+110)) then
        tmp = -2.0d0
    else if (z <= 1.55d+72) then
        tmp = (-4.0d0) / (z / 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 (z <= -7.2e+110) {
		tmp = -2.0;
	} else if (z <= 1.55e+72) {
		tmp = -4.0 / (z / y);
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.2e+110:
		tmp = -2.0
	elif z <= 1.55e+72:
		tmp = -4.0 / (z / y)
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.2e+110)
		tmp = -2.0;
	elseif (z <= 1.55e+72)
		tmp = Float64(-4.0 / Float64(z / y));
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.2e+110)
		tmp = -2.0;
	elseif (z <= 1.55e+72)
		tmp = -4.0 / (z / y);
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.2e+110], -2.0, If[LessEqual[z, 1.55e+72], N[(-4.0 / N[(z / y), $MachinePrecision]), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if z < -7.1999999999999994e110 or 1.54999999999999994e72 < z

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -7.1999999999999994e110 < z < 1.54999999999999994e72

   1. Initial program 100.0%

      \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 33.5% accurate, 11.0× 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%

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in z around inf 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. Add Preprocessing

Developer target: 97.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (4.0 * (x / z)) - (2.0 + (4.0 * (y / 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 = (4.0d0 * (x / z)) - (2.0d0 + (4.0d0 * (y / z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :alt
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))