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

Percentage Accurate: 99.7% → 99.7%

Time: 7.6s

Alternatives: 10

Speedup: 1.4×

• 21.1% 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: 99.7% 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: 99.7% 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]

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z \cdot -4}{y}\\ t_1 := \frac{x \cdot 4}{y}\\ \mathbf{if}\;x \leq -4.7 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-306}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-252}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-235}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-203}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+50}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* z -4.0) y)) (t_1 (/ (* x 4.0) y)))
   (if (<= x -4.7e+97)
     t_1
     (if (<= x -2.6e-306)
       4.0
       (if (<= x 1.15e-252)
         t_0
         (if (<= x 9e-235)
           4.0
           (if (<= x 1.1e-203) t_0 (if (<= x 5.8e+50) 4.0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * -4.0) / y;
	double t_1 = (x * 4.0) / y;
	double tmp;
	if (x <= -4.7e+97) {
		tmp = t_1;
	} else if (x <= -2.6e-306) {
		tmp = 4.0;
	} else if (x <= 1.15e-252) {
		tmp = t_0;
	} else if (x <= 9e-235) {
		tmp = 4.0;
	} else if (x <= 1.1e-203) {
		tmp = t_0;
	} else if (x <= 5.8e+50) {
		tmp = 4.0;
	} 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 = (z * (-4.0d0)) / y
    t_1 = (x * 4.0d0) / y
    if (x <= (-4.7d+97)) then
        tmp = t_1
    else if (x <= (-2.6d-306)) then
        tmp = 4.0d0
    else if (x <= 1.15d-252) then
        tmp = t_0
    else if (x <= 9d-235) then
        tmp = 4.0d0
    else if (x <= 1.1d-203) then
        tmp = t_0
    else if (x <= 5.8d+50) then
        tmp = 4.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * -4.0) / y;
	double t_1 = (x * 4.0) / y;
	double tmp;
	if (x <= -4.7e+97) {
		tmp = t_1;
	} else if (x <= -2.6e-306) {
		tmp = 4.0;
	} else if (x <= 1.15e-252) {
		tmp = t_0;
	} else if (x <= 9e-235) {
		tmp = 4.0;
	} else if (x <= 1.1e-203) {
		tmp = t_0;
	} else if (x <= 5.8e+50) {
		tmp = 4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * -4.0) / y
	t_1 = (x * 4.0) / y
	tmp = 0
	if x <= -4.7e+97:
		tmp = t_1
	elif x <= -2.6e-306:
		tmp = 4.0
	elif x <= 1.15e-252:
		tmp = t_0
	elif x <= 9e-235:
		tmp = 4.0
	elif x <= 1.1e-203:
		tmp = t_0
	elif x <= 5.8e+50:
		tmp = 4.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * -4.0) / y)
	t_1 = Float64(Float64(x * 4.0) / y)
	tmp = 0.0
	if (x <= -4.7e+97)
		tmp = t_1;
	elseif (x <= -2.6e-306)
		tmp = 4.0;
	elseif (x <= 1.15e-252)
		tmp = t_0;
	elseif (x <= 9e-235)
		tmp = 4.0;
	elseif (x <= 1.1e-203)
		tmp = t_0;
	elseif (x <= 5.8e+50)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * -4.0) / y;
	t_1 = (x * 4.0) / y;
	tmp = 0.0;
	if (x <= -4.7e+97)
		tmp = t_1;
	elseif (x <= -2.6e-306)
		tmp = 4.0;
	elseif (x <= 1.15e-252)
		tmp = t_0;
	elseif (x <= 9e-235)
		tmp = 4.0;
	elseif (x <= 1.1e-203)
		tmp = t_0;
	elseif (x <= 5.8e+50)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * 4.0), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[x, -4.7e+97], t$95$1, If[LessEqual[x, -2.6e-306], 4.0, If[LessEqual[x, 1.15e-252], t$95$0, If[LessEqual[x, 9e-235], 4.0, If[LessEqual[x, 1.1e-203], t$95$0, If[LessEqual[x, 5.8e+50], 4.0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.6999999999999997e97 or 5.8e50 < x

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.6999999999999997e97 < x < -2.6e-306 or 1.1499999999999999e-252 < x < 8.9999999999999996e-235 or 1.1e-203 < x < 5.8e50

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.6e-306 < x < 1.1499999999999999e-252 or 8.9999999999999996e-235 < x < 1.1e-203

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 3: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-4}{y} \cdot z\\ t_1 := \frac{x \cdot 4}{y}\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-304}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-252}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-234}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-203}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+51}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ -4.0 y) z)) (t_1 (/ (* x 4.0) y)))
   (if (<= x -2.6e+96)
     t_1
     (if (<= x 3.5e-304)
       4.0
       (if (<= x 1.6e-252)
         t_0
         (if (<= x 2e-234)
           4.0
           (if (<= x 7e-203) t_0 (if (<= x 1.08e+51) 4.0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = (-4.0 / y) * z;
	double t_1 = (x * 4.0) / y;
	double tmp;
	if (x <= -2.6e+96) {
		tmp = t_1;
	} else if (x <= 3.5e-304) {
		tmp = 4.0;
	} else if (x <= 1.6e-252) {
		tmp = t_0;
	} else if (x <= 2e-234) {
		tmp = 4.0;
	} else if (x <= 7e-203) {
		tmp = t_0;
	} else if (x <= 1.08e+51) {
		tmp = 4.0;
	} 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 = (x * 4.0d0) / y
    if (x <= (-2.6d+96)) then
        tmp = t_1
    else if (x <= 3.5d-304) then
        tmp = 4.0d0
    else if (x <= 1.6d-252) then
        tmp = t_0
    else if (x <= 2d-234) then
        tmp = 4.0d0
    else if (x <= 7d-203) then
        tmp = t_0
    else if (x <= 1.08d+51) then
        tmp = 4.0d0
    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 = (x * 4.0) / y;
	double tmp;
	if (x <= -2.6e+96) {
		tmp = t_1;
	} else if (x <= 3.5e-304) {
		tmp = 4.0;
	} else if (x <= 1.6e-252) {
		tmp = t_0;
	} else if (x <= 2e-234) {
		tmp = 4.0;
	} else if (x <= 7e-203) {
		tmp = t_0;
	} else if (x <= 1.08e+51) {
		tmp = 4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-4.0 / y) * z
	t_1 = (x * 4.0) / y
	tmp = 0
	if x <= -2.6e+96:
		tmp = t_1
	elif x <= 3.5e-304:
		tmp = 4.0
	elif x <= 1.6e-252:
		tmp = t_0
	elif x <= 2e-234:
		tmp = 4.0
	elif x <= 7e-203:
		tmp = t_0
	elif x <= 1.08e+51:
		tmp = 4.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-4.0 / y) * z)
	t_1 = Float64(Float64(x * 4.0) / y)
	tmp = 0.0
	if (x <= -2.6e+96)
		tmp = t_1;
	elseif (x <= 3.5e-304)
		tmp = 4.0;
	elseif (x <= 1.6e-252)
		tmp = t_0;
	elseif (x <= 2e-234)
		tmp = 4.0;
	elseif (x <= 7e-203)
		tmp = t_0;
	elseif (x <= 1.08e+51)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-4.0 / y) * z;
	t_1 = (x * 4.0) / y;
	tmp = 0.0;
	if (x <= -2.6e+96)
		tmp = t_1;
	elseif (x <= 3.5e-304)
		tmp = 4.0;
	elseif (x <= 1.6e-252)
		tmp = t_0;
	elseif (x <= 2e-234)
		tmp = 4.0;
	elseif (x <= 7e-203)
		tmp = t_0;
	elseif (x <= 1.08e+51)
		tmp = 4.0;
	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[(x * 4.0), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[x, -2.6e+96], t$95$1, If[LessEqual[x, 3.5e-304], 4.0, If[LessEqual[x, 1.6e-252], t$95$0, If[LessEqual[x, 2e-234], 4.0, If[LessEqual[x, 7e-203], t$95$0, If[LessEqual[x, 1.08e+51], 4.0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.6e96 or 1.08e51 < x

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.6e96 < x < 3.5e-304 or 1.6000000000000001e-252 < x < 1.9999999999999999e-234 or 7.0000000000000003e-203 < x < 1.08e51

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 3.5e-304 < x < 1.6000000000000001e-252 or 1.9999999999999999e-234 < x < 7.0000000000000003e-203

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

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

Alternative 4: 53.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-4}{y} \cdot z\\ t_1 := \frac{4}{y} \cdot x\\ \mathbf{if}\;x \leq -9 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-304}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-251}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-234}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-204}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+50}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ -4.0 y) z)) (t_1 (* (/ 4.0 y) x)))
   (if (<= x -9e+94)
     t_1
     (if (<= x -2.7e-304)
       4.0
       (if (<= x 2.2e-251)
         t_0
         (if (<= x 2.2e-234)
           4.0
           (if (<= x 3.7e-204) t_0 (if (<= x 5.4e+50) 4.0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = (-4.0 / y) * z;
	double t_1 = (4.0 / y) * x;
	double tmp;
	if (x <= -9e+94) {
		tmp = t_1;
	} else if (x <= -2.7e-304) {
		tmp = 4.0;
	} else if (x <= 2.2e-251) {
		tmp = t_0;
	} else if (x <= 2.2e-234) {
		tmp = 4.0;
	} else if (x <= 3.7e-204) {
		tmp = t_0;
	} else if (x <= 5.4e+50) {
		tmp = 4.0;
	} 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 / y) * x
    if (x <= (-9d+94)) then
        tmp = t_1
    else if (x <= (-2.7d-304)) then
        tmp = 4.0d0
    else if (x <= 2.2d-251) then
        tmp = t_0
    else if (x <= 2.2d-234) then
        tmp = 4.0d0
    else if (x <= 3.7d-204) then
        tmp = t_0
    else if (x <= 5.4d+50) then
        tmp = 4.0d0
    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 / y) * x;
	double tmp;
	if (x <= -9e+94) {
		tmp = t_1;
	} else if (x <= -2.7e-304) {
		tmp = 4.0;
	} else if (x <= 2.2e-251) {
		tmp = t_0;
	} else if (x <= 2.2e-234) {
		tmp = 4.0;
	} else if (x <= 3.7e-204) {
		tmp = t_0;
	} else if (x <= 5.4e+50) {
		tmp = 4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-4.0 / y) * z
	t_1 = (4.0 / y) * x
	tmp = 0
	if x <= -9e+94:
		tmp = t_1
	elif x <= -2.7e-304:
		tmp = 4.0
	elif x <= 2.2e-251:
		tmp = t_0
	elif x <= 2.2e-234:
		tmp = 4.0
	elif x <= 3.7e-204:
		tmp = t_0
	elif x <= 5.4e+50:
		tmp = 4.0
	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 / y) * x)
	tmp = 0.0
	if (x <= -9e+94)
		tmp = t_1;
	elseif (x <= -2.7e-304)
		tmp = 4.0;
	elseif (x <= 2.2e-251)
		tmp = t_0;
	elseif (x <= 2.2e-234)
		tmp = 4.0;
	elseif (x <= 3.7e-204)
		tmp = t_0;
	elseif (x <= 5.4e+50)
		tmp = 4.0;
	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 / y) * x;
	tmp = 0.0;
	if (x <= -9e+94)
		tmp = t_1;
	elseif (x <= -2.7e-304)
		tmp = 4.0;
	elseif (x <= 2.2e-251)
		tmp = t_0;
	elseif (x <= 2.2e-234)
		tmp = 4.0;
	elseif (x <= 3.7e-204)
		tmp = t_0;
	elseif (x <= 5.4e+50)
		tmp = 4.0;
	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 / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -9e+94], t$95$1, If[LessEqual[x, -2.7e-304], 4.0, If[LessEqual[x, 2.2e-251], t$95$0, If[LessEqual[x, 2.2e-234], 4.0, If[LessEqual[x, 3.7e-204], t$95$0, If[LessEqual[x, 5.4e+50], 4.0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.99999999999999944e94 or 5.4e50 < x

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -8.99999999999999944e94 < x < -2.7000000000000001e-304 or 2.2e-251 < x < 2.1999999999999999e-234 or 3.6999999999999997e-204 < x < 5.4e50

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.7000000000000001e-304 < x < 2.2e-251 or 2.1999999999999999e-234 < x < 3.6999999999999997e-204

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

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

Alternative 5: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4 \cdot \left(x - z\right)}{y}\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{+94}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+50}:\\ \;\;\;\;4 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* 4.0 (- x z)) y)))
   (if (<= x -4.6e+94) t_0 (if (<= x 6.5e+50) (+ 4.0 (/ (* z -4.0) y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * (x - z)) / y;
	double tmp;
	if (x <= -4.6e+94) {
		tmp = t_0;
	} else if (x <= 6.5e+50) {
		tmp = 4.0 + ((z * -4.0) / 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 = (4.0d0 * (x - z)) / y
    if (x <= (-4.6d+94)) then
        tmp = t_0
    else if (x <= 6.5d+50) then
        tmp = 4.0d0 + ((z * (-4.0d0)) / 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 = (4.0 * (x - z)) / y;
	double tmp;
	if (x <= -4.6e+94) {
		tmp = t_0;
	} else if (x <= 6.5e+50) {
		tmp = 4.0 + ((z * -4.0) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 * (x - z)) / y
	tmp = 0
	if x <= -4.6e+94:
		tmp = t_0
	elif x <= 6.5e+50:
		tmp = 4.0 + ((z * -4.0) / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * Float64(x - z)) / y)
	tmp = 0.0
	if (x <= -4.6e+94)
		tmp = t_0;
	elseif (x <= 6.5e+50)
		tmp = Float64(4.0 + Float64(Float64(z * -4.0) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 * (x - z)) / y;
	tmp = 0.0;
	if (x <= -4.6e+94)
		tmp = t_0;
	elseif (x <= 6.5e+50)
		tmp = 4.0 + ((z * -4.0) / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * N[(x - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[x, -4.6e+94], t$95$0, If[LessEqual[x, 6.5e+50], N[(4.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5999999999999999e94 or 6.5000000000000003e50 < x

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.5999999999999999e94 < x < 6.5000000000000003e50

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 6: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 + \frac{z \cdot -4}{y}\\ \mathbf{if}\;z \leq -1 \cdot 10^{-26}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2200:\\ \;\;\;\;4 + \frac{x \cdot 4}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 4.0 (/ (* z -4.0) y))))
   (if (<= z -1e-26) t_0 (if (<= z 2200.0) (+ 4.0 (/ (* x 4.0) y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 4.0 + ((z * -4.0) / y);
	double tmp;
	if (z <= -1e-26) {
		tmp = t_0;
	} else if (z <= 2200.0) {
		tmp = 4.0 + ((x * 4.0) / 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 = 4.0d0 + ((z * (-4.0d0)) / y)
    if (z <= (-1d-26)) then
        tmp = t_0
    else if (z <= 2200.0d0) then
        tmp = 4.0d0 + ((x * 4.0d0) / 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 = 4.0 + ((z * -4.0) / y);
	double tmp;
	if (z <= -1e-26) {
		tmp = t_0;
	} else if (z <= 2200.0) {
		tmp = 4.0 + ((x * 4.0) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.0 + ((z * -4.0) / y)
	tmp = 0
	if z <= -1e-26:
		tmp = t_0
	elif z <= 2200.0:
		tmp = 4.0 + ((x * 4.0) / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.0 + Float64(Float64(z * -4.0) / y))
	tmp = 0.0
	if (z <= -1e-26)
		tmp = t_0;
	elseif (z <= 2200.0)
		tmp = Float64(4.0 + Float64(Float64(x * 4.0) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.0 + ((z * -4.0) / y);
	tmp = 0.0;
	if (z <= -1e-26)
		tmp = t_0;
	elseif (z <= 2200.0)
		tmp = 4.0 + ((x * 4.0) / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e-26], t$95$0, If[LessEqual[z, 2200.0], N[(4.0 + N[(N[(x * 4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e-26 or 2200 < z

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1e-26 < z < 2200

   1. Initial program 99.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 7: 80.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z \cdot -4}{y}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+150}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+195}:\\ \;\;\;\;4 + \frac{x \cdot 4}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* z -4.0) y)))
   (if (<= z -9e+150) t_0 (if (<= z 6e+195) (+ 4.0 (/ (* x 4.0) y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z * -4.0) / y;
	double tmp;
	if (z <= -9e+150) {
		tmp = t_0;
	} else if (z <= 6e+195) {
		tmp = 4.0 + ((x * 4.0) / 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 = (z * (-4.0d0)) / y
    if (z <= (-9d+150)) then
        tmp = t_0
    else if (z <= 6d+195) then
        tmp = 4.0d0 + ((x * 4.0d0) / 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 = (z * -4.0) / y;
	double tmp;
	if (z <= -9e+150) {
		tmp = t_0;
	} else if (z <= 6e+195) {
		tmp = 4.0 + ((x * 4.0) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * -4.0) / y
	tmp = 0
	if z <= -9e+150:
		tmp = t_0
	elif z <= 6e+195:
		tmp = 4.0 + ((x * 4.0) / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * -4.0) / y)
	tmp = 0.0
	if (z <= -9e+150)
		tmp = t_0;
	elseif (z <= 6e+195)
		tmp = Float64(4.0 + Float64(Float64(x * 4.0) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * -4.0) / y;
	tmp = 0.0;
	if (z <= -9e+150)
		tmp = t_0;
	elseif (z <= 6e+195)
		tmp = 4.0 + ((x * 4.0) / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -9e+150], t$95$0, If[LessEqual[z, 6e+195], N[(4.0 + N[(N[(x * 4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.00000000000000001e150 or 6.0000000000000001e195 < z

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -9.00000000000000001e150 < z < 6.0000000000000001e195

   1. Initial program 99.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 8: 54.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-4}{y} \cdot z\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+70}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+74}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ -4.0 y) z)))
   (if (<= z -1.35e+70) t_0 (if (<= z 6.6e+74) 4.0 t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (-4.0 / y) * z;
	double tmp;
	if (z <= -1.35e+70) {
		tmp = t_0;
	} else if (z <= 6.6e+74) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((-4.0d0) / y) * z
    if (z <= (-1.35d+70)) then
        tmp = t_0
    else if (z <= 6.6d+74) then
        tmp = 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (-4.0 / y) * z;
	double tmp;
	if (z <= -1.35e+70) {
		tmp = t_0;
	} else if (z <= 6.6e+74) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-4.0 / y) * z
	tmp = 0
	if z <= -1.35e+70:
		tmp = t_0
	elif z <= 6.6e+74:
		tmp = 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-4.0 / y) * z)
	tmp = 0.0
	if (z <= -1.35e+70)
		tmp = t_0;
	elseif (z <= 6.6e+74)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-4.0 / y) * z;
	tmp = 0.0;
	if (z <= -1.35e+70)
		tmp = t_0;
	elseif (z <= 6.6e+74)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-4.0 / y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -1.35e+70], t$95$0, If[LessEqual[z, 6.6e+74], 4.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e70 or 6.6000000000000004e74 < z

   1. Initial program 100.0%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -1.35e70 < z < 6.6000000000000004e74

   1. Initial program 99.9%

      \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 9: 99.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Simplified 0

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

Alternative 10: 34.5% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 4.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 4.0

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(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)))