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

Percentage Accurate: 99.8% → 99.7%

Time: 10.0s

Alternatives: 11

Speedup: N/A×

• 21.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.75d0)) - z)) / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.75d0)) - z)) / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return fma((4.0 / y), (fma(y, 0.75, x) - z), 1.0);
}

Julia

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

   1. +-commutative N/A

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

   2. clear-num N/A

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

   3. associate-/r* N/A

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

   4. associate-/r/ N/A

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

   5. clear-num N/A

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

   6. accelerator-lowering-fma.f64 N/A

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

   7. /-lowering-/.f64 N/A

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

   8. --lowering--.f64 N/A

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

   9. +-commutative N/A

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

   10. accelerator-lowering-fma.f64 99.7

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

4. Applied egg-rr 99.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{4}{y}, \mathsf{fma}\left(y, 0.75, x\right) - z, 1\right)} \]
5. Add Preprocessing

Alternative 2: 98.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq -50:\\ \;\;\;\;\mathsf{fma}\left(\frac{4}{y}, x - z, 1\right)\\ \mathbf{elif}\;t\_0 \leq 2000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{4}{y}, x, 4\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{4 \cdot \left(x - z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))
   (if (<= t_0 -50.0)
     (fma (/ 4.0 y) (- x z) 1.0)
     (if (<= t_0 2000000000.0) (fma (/ 4.0 y) x 4.0) (/ (* 4.0 (- x z)) y)))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_0 <= -50.0) {
		tmp = fma((4.0 / y), (x - z), 1.0);
	} else if (t_0 <= 2000000000.0) {
		tmp = fma((4.0 / y), x, 4.0);
	} else {
		tmp = (4.0 * (x - z)) / y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y)
	tmp = 0.0
	if (t_0 <= -50.0)
		tmp = fma(Float64(4.0 / y), Float64(x - z), 1.0);
	elseif (t_0 <= 2000000000.0)
		tmp = fma(Float64(4.0 / y), x, 4.0);
	else
		tmp = Float64(Float64(4.0 * Float64(x - z)) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$0, -50.0], N[(N[(4.0 / y), $MachinePrecision] * N[(x - z), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[t$95$0, 2000000000.0], N[(N[(4.0 / y), $MachinePrecision] * x + 4.0), $MachinePrecision], N[(N[(4.0 * N[(x - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < -50

   1. Initial program 98.7%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. associate-/r* N/A

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

      4. associate-/r/ N/A

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

      5. clear-num N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. +-commutative N/A

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

      10. accelerator-lowering-fma.f64 99.7

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\frac{4}{y}, \color{blue}{x - z}, 1\right) \]
   6. Step-by-step derivation

      1. --lowering--.f64 98.4

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

   7. Simplified 98.4%

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

   if -50 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < 2e9

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 98.7%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(x, \frac{-4}{y}, -4\right)} \]
   6. Step-by-step derivation

      1. distribute-neg-in N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. distribute-frac-neg2 N/A

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

      5. metadata-eval N/A

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

      6. frac-2neg N/A

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{4}{y}, x, 4\right)} \]

      9. /-lowering-/.f64 98.7

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{4}{y}}, x, 4\right) \]

   7. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{4}{y}, x, 4\right)} \]

   if 2e9 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

   5. Simplified 98.8%

      \[\leadsto \color{blue}{\frac{4 \cdot \left(x - z\right)}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_0 \leq -50:\\ \;\;\;\;\frac{4}{y} \cdot \left(x - z\right)\\ \mathbf{elif}\;t\_0 \leq 2000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{4}{y}, x, 4\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{4 \cdot \left(x - z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))
   (if (<= t_0 -50.0)
     (* (/ 4.0 y) (- x z))
     (if (<= t_0 2000000000.0) (fma (/ 4.0 y) x 4.0) (/ (* 4.0 (- x z)) y)))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_0 <= -50.0) {
		tmp = (4.0 / y) * (x - z);
	} else if (t_0 <= 2000000000.0) {
		tmp = fma((4.0 / y), x, 4.0);
	} else {
		tmp = (4.0 * (x - z)) / y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y)
	tmp = 0.0
	if (t_0 <= -50.0)
		tmp = Float64(Float64(4.0 / y) * Float64(x - z));
	elseif (t_0 <= 2000000000.0)
		tmp = fma(Float64(4.0 / y), x, 4.0);
	else
		tmp = Float64(Float64(4.0 * Float64(x - z)) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$0, -50.0], N[(N[(4.0 / y), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2000000000.0], N[(N[(4.0 / y), $MachinePrecision] * x + 4.0), $MachinePrecision], N[(N[(4.0 * N[(x - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < -50

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

   5. Simplified 97.4%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. /-lowering-/.f64 98.4

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

   7. Applied egg-rr 98.4%

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

   if -50 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < 2e9

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 98.7%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(x, \frac{-4}{y}, -4\right)} \]
   6. Step-by-step derivation

      1. distribute-neg-in N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. distribute-frac-neg2 N/A

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

      5. metadata-eval N/A

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

      6. frac-2neg N/A

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{4}{y}, x, 4\right)} \]

      9. /-lowering-/.f64 98.7

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{4}{y}}, x, 4\right) \]

   7. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{4}{y}, x, 4\right)} \]

   if 2e9 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

   5. Simplified 98.8%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \leq -50:\\ \;\;\;\;\frac{4}{y} \cdot \left(x - z\right)\\ \mathbf{elif}\;\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \leq 2000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{4}{y}, x, 4\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{4 \cdot \left(x - z\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4}{y} \cdot \left(x - z\right)\\ t_1 := \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_1 \leq -50:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 2000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{4}{y}, x, 4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ 4.0 y) (- x z))) (t_1 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))
   (if (<= t_1 -50.0)
     t_0
     (if (<= t_1 2000000000.0) (fma (/ 4.0 y) x 4.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 / y) * (x - z);
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_0;
	} else if (t_1 <= 2000000000.0) {
		tmp = fma((4.0 / y), x, 4.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 / y) * Float64(x - z))
	t_1 = Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y)
	tmp = 0.0
	if (t_1 <= -50.0)
		tmp = t_0;
	elseif (t_1 <= 2000000000.0)
		tmp = fma(Float64(4.0 / y), x, 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 / y), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -50.0], t$95$0, If[LessEqual[t$95$1, 2000000000.0], N[(N[(4.0 / y), $MachinePrecision] * x + 4.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < -50 or 2e9 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

   5. Simplified 98.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. /-lowering-/.f64 98.5

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

   7. Applied egg-rr 98.5%

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

   if -50 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < 2e9

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 98.7%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(x, \frac{-4}{y}, -4\right)} \]
   6. Step-by-step derivation

      1. distribute-neg-in N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. distribute-frac-neg2 N/A

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

      5. metadata-eval N/A

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

      6. frac-2neg N/A

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{4}{y}, x, 4\right)} \]

      9. /-lowering-/.f64 98.7

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{4}{y}}, x, 4\right) \]

   7. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{4}{y}, x, 4\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \leq -50:\\ \;\;\;\;\frac{4}{y} \cdot \left(x - z\right)\\ \mathbf{elif}\;\frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \leq 2000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{4}{y}, x, 4\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{4}{y} \cdot \left(x - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4 \cdot x}{y}\\ t_1 := \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_1 \leq -50:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* 4.0 x) y)) (t_1 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))
   (if (<= t_1 -50.0) t_0 (if (<= t_1 5.0) 4.0 t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * x) / y;
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_0;
	} else if (t_1 <= 5.0) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (4.0d0 * x) / y
    t_1 = (4.0d0 * ((x + (y * 0.75d0)) - z)) / y
    if (t_1 <= (-50.0d0)) then
        tmp = t_0
    else if (t_1 <= 5.0d0) then
        tmp = 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.0 * x) / y;
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_0;
	} else if (t_1 <= 5.0) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 * x) / y
	t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y
	tmp = 0
	if t_1 <= -50.0:
		tmp = t_0
	elif t_1 <= 5.0:
		tmp = 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * x) / y)
	t_1 = Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y)
	tmp = 0.0
	if (t_1 <= -50.0)
		tmp = t_0;
	elseif (t_1 <= 5.0)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 * x) / y;
	t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	tmp = 0.0;
	if (t_1 <= -50.0)
		tmp = t_0;
	elseif (t_1 <= 5.0)
		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 * x), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -50.0], t$95$0, If[LessEqual[t$95$1, 5.0], 4.0, t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < -50 or 5 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 56.7

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

   5. Simplified 56.7%

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

   if -50 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < 5

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{4} \]
   4. Step-by-step derivation

   5. Simplified 95.7%

      \[\leadsto \color{blue}{4} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 66.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4}{y} \cdot x\\ t_1 := \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_1 \leq -50:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ 4.0 y) x)) (t_1 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))
   (if (<= t_1 -50.0) t_0 (if (<= t_1 5.0) 4.0 t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 / y) * x;
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_0;
	} else if (t_1 <= 5.0) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (4.0d0 / y) * x
    t_1 = (4.0d0 * ((x + (y * 0.75d0)) - z)) / y
    if (t_1 <= (-50.0d0)) then
        tmp = t_0
    else if (t_1 <= 5.0d0) 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) * x;
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_0;
	} else if (t_1 <= 5.0) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.0 / y) * x
	t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y
	tmp = 0
	if t_1 <= -50.0:
		tmp = t_0
	elif t_1 <= 5.0:
		tmp = 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 / y) * x)
	t_1 = Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y)
	tmp = 0.0
	if (t_1 <= -50.0)
		tmp = t_0;
	elseif (t_1 <= 5.0)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.0 / y) * x;
	t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	tmp = 0.0;
	if (t_1 <= -50.0)
		tmp = t_0;
	elseif (t_1 <= 5.0)
		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] * x), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -50.0], t$95$0, If[LessEqual[t$95$1, 5.0], 4.0, t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < -50 or 5 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 56.7

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

   5. Simplified 56.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. frac-2neg N/A

         \[\leadsto x \cdot \color{blue}{\frac{\mathsf{neg}\left(4\right)}{\mathsf{neg}\left(y\right)}} \]

      4. metadata-eval N/A

         \[\leadsto x \cdot \frac{\color{blue}{-4}}{\mathsf{neg}\left(y\right)} \]

      5. distribute-frac-neg2 N/A

         \[\leadsto x \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{-4}{y}\right)\right)} \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(x \cdot \frac{-4}{y}\right)} \]

      7. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\frac{-4}{y} \cdot x}\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{-4}{y}\right)\right) \cdot x} \]

      9. distribute-frac-neg2 N/A

         \[\leadsto \color{blue}{\frac{-4}{\mathsf{neg}\left(y\right)}} \cdot x \]

      10. metadata-eval N/A

          \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(4\right)}}{\mathsf{neg}\left(y\right)} \cdot x \]

      11. frac-2neg N/A

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

      12. *-lowering-*.f64 N/A

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

      13. /-lowering-/.f64 56.6

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

   7. Applied egg-rr 56.6%

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

   if -50 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < 5

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{4} \]
   4. Step-by-step derivation

   5. Simplified 95.7%

      \[\leadsto \color{blue}{4} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 65.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{-4}{y}\\ t_1 := \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\\ \mathbf{if}\;t\_1 \leq -50:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+32}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ -4.0 y))) (t_1 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))
   (if (<= t_1 -50.0) t_0 (if (<= t_1 5e+32) 4.0 t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-4.0 / y);
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_0;
	} else if (t_1 <= 5e+32) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z * ((-4.0d0) / y)
    t_1 = (4.0d0 * ((x + (y * 0.75d0)) - z)) / y
    if (t_1 <= (-50.0d0)) then
        tmp = t_0
    else if (t_1 <= 5d+32) 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 = z * (-4.0 / y);
	double t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_0;
	} else if (t_1 <= 5e+32) {
		tmp = 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-4.0 / y)
	t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y
	tmp = 0
	if t_1 <= -50.0:
		tmp = t_0
	elif t_1 <= 5e+32:
		tmp = 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-4.0 / y))
	t_1 = Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y)
	tmp = 0.0
	if (t_1 <= -50.0)
		tmp = t_0;
	elseif (t_1 <= 5e+32)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-4.0 / y);
	t_1 = (4.0 * ((x + (y * 0.75)) - z)) / y;
	tmp = 0.0;
	if (t_1 <= -50.0)
		tmp = t_0;
	elseif (t_1 <= 5e+32)
		tmp = 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-4.0 / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -50.0], t$95$0, If[LessEqual[t$95$1, 5e+32], 4.0, t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < -50 or 4.9999999999999997e32 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y)

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf

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

      1. *-lft-identity N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(4\right)\right)} \cdot \frac{1}{y}\right) \cdot z \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(4 \cdot \frac{1}{y}\right)\right)} \cdot z \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\mathsf{neg}\left(4 \cdot \frac{1}{y}\right)\right)} \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(\mathsf{neg}\left(4 \cdot \frac{1}{y}\right)\right)} \]

      8. associate-*r/ N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\color{blue}{\frac{4 \cdot 1}{y}}\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto z \cdot \left(\mathsf{neg}\left(\frac{\color{blue}{4}}{y}\right)\right) \]

      10. distribute-neg-frac N/A

          \[\leadsto z \cdot \color{blue}{\frac{\mathsf{neg}\left(4\right)}{y}} \]

      11. metadata-eval N/A

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

      12. /-lowering-/.f64 46.3

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

   5. Simplified 46.3%

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

   if -50 < (/.f64 (*.f64 #s(literal 4 binary64) (-.f64 (+.f64 x (*.f64 y #s(literal 3/4 binary64))) z)) y) < 4.9999999999999997e32

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{4} \]
   4. Step-by-step derivation

   5. Simplified 94.0%

      \[\leadsto \color{blue}{4} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(z, \frac{-4}{y}, 4\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{-10}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+57}:\\ \;\;\;\;\mathsf{fma}\left(\frac{4}{y}, x, 4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma z (/ -4.0 y) 4.0)))
   (if (<= z -3.3e-10) t_0 (if (<= z 7.2e+57) (fma (/ 4.0 y) x 4.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(z, (-4.0 / y), 4.0);
	double tmp;
	if (z <= -3.3e-10) {
		tmp = t_0;
	} else if (z <= 7.2e+57) {
		tmp = fma((4.0 / y), x, 4.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(z, Float64(-4.0 / y), 4.0)
	tmp = 0.0
	if (z <= -3.3e-10)
		tmp = t_0;
	elseif (z <= 7.2e+57)
		tmp = fma(Float64(4.0 / y), x, 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(-4.0 / y), $MachinePrecision] + 4.0), $MachinePrecision]}, If[LessEqual[z, -3.3e-10], t$95$0, If[LessEqual[z, 7.2e+57], N[(N[(4.0 / y), $MachinePrecision] * x + 4.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e-10 or 7.2000000000000005e57 < z

   1. Initial program 98.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. div-sub N/A

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

      4. associate-/l* N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

      7. *-commutative N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. *-lft-identity N/A

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

      13. associate-*l/ N/A

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

      14. distribute-rgt-neg-in N/A

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

      15. associate-*l* N/A

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

      16. metadata-eval N/A

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

      17. associate-+l+ N/A

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

   5. Simplified 85.7%

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

   if -3.3e-10 < z < 7.2000000000000005e57

   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 z around 0

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

   5. Simplified 94.1%

      \[\leadsto \color{blue}{-\mathsf{fma}\left(x, \frac{-4}{y}, -4\right)} \]
   6. Step-by-step derivation

      1. distribute-neg-in N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

      4. distribute-frac-neg2 N/A

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

      5. metadata-eval N/A

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

      6. frac-2neg N/A

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

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{4}{y}, x, 4\right)} \]

      9. /-lowering-/.f64 94.1

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{4}{y}}, x, 4\right) \]

   7. Applied egg-rr 94.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{4}{y}, x, 4\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{4 \cdot x}{y}\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+38}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+132}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{-4}{y}, 4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* 4.0 x) y)))
   (if (<= x -2.9e+38) t_0 (if (<= x 5.3e+132) (fma z (/ -4.0 y) 4.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.0 * x) / y;
	double tmp;
	if (x <= -2.9e+38) {
		tmp = t_0;
	} else if (x <= 5.3e+132) {
		tmp = fma(z, (-4.0 / y), 4.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.0 * x) / y)
	tmp = 0.0
	if (x <= -2.9e+38)
		tmp = t_0;
	elseif (x <= 5.3e+132)
		tmp = fma(z, Float64(-4.0 / y), 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[x, -2.9e+38], t$95$0, If[LessEqual[x, 5.3e+132], N[(z * N[(-4.0 / y), $MachinePrecision] + 4.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.90000000000000007e38 or 5.3e132 < x

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 71.4

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

   5. Simplified 71.4%

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

   if -2.90000000000000007e38 < x < 5.3e132

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 + 4 \cdot \frac{\frac{3}{4} \cdot y - z}{y}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. div-sub N/A

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

      4. associate-/l* N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

      7. *-commutative N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. *-lft-identity N/A

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

      13. associate-*l/ N/A

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

      14. distribute-rgt-neg-in N/A

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

      15. associate-*l* N/A

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

      16. metadata-eval N/A

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

      17. associate-+l+ N/A

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

   5. Simplified 86.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \frac{-4}{y}, 4\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 33.9% accurate, 31.0× 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 99.1%

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

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{4} \]
4. Step-by-step derivation

5. Simplified 37.6%

   \[\leadsto \color{blue}{4} \]
6. Add Preprocessing

Alternative 11: 7.6% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.1%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

   4. /-lowering-/.f64 N/A

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

   5. /-lowering-/.f64 N/A

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

   6. --lowering--.f64 N/A

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

   7. +-commutative N/A

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

   8. accelerator-lowering-fma.f64 99.6

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

4. Applied egg-rr 99.6%

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

5. Taylor expanded in x around inf

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

7. Simplified 42.0%

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

8. Taylor expanded in y around inf

   \[\leadsto \color{blue}{1} \]
9. Step-by-step derivation

10. Simplified 8.2%

    \[\leadsto \color{blue}{1} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024198 
(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)))