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

Percentage Accurate: 99.8% → 99.9%

Time: 5.6s

Alternatives: 6

Speedup: 1.4×

• 20.6% 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: 99.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(4.0 + N[(N[(4.0 * N[(x - 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. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. associate-*l/ 99.3%

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

   3. *-commutative 99.3%

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

   4. fma-def 99.3%

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

   5. +-commutative 99.3%

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

   6. associate--l+ 99.3%

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

   7. +-commutative 99.3%

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

   8. associate-+l- 99.3%

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

   9. sub-neg 99.3%

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

   10. remove-double-neg 99.3%

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

   11. distribute-neg-in 99.3%

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

   12. +-commutative 99.3%

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

   13. distribute-neg-in 99.3%

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

   14. distribute-lft-neg-out 99.3%

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

   15. sub-neg 99.3%

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

   16. distribute-lft-neg-out 99.3%

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

   17. distribute-rgt-neg-in 99.3%

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

   18. fma-neg 99.3%

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

   19. metadata-eval 99.3%

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

   20. remove-double-neg 99.3%

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

3. Simplified 99.3%

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

5. Taylor expanded in y around 0 100.0%

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

   1. associate-*r/ 100.0%

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

7. Simplified 100.0%

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

8. Final simplification 100.0%

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

Alternative 2: 54.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{z}{y} \cdot -4\\ t_1 := 1 + x \cdot \frac{4}{y}\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-77}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-162}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-238}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-234}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-149}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-7}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* (/ z y) -4.0))) (t_1 (+ 1.0 (* x (/ 4.0 y)))))
   (if (<= x -3.9e-50)
     t_1
     (if (<= x -3.2e-77)
       t_0
       (if (<= x -2.1e-162)
         4.0
         (if (<= x -1.4e-238)
           t_0
           (if (<= x 6.6e-234)
             4.0
             (if (<= x 2.3e-149) t_0 (if (<= x 1.05e-7) 4.0 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((z / y) * -4.0);
	double t_1 = 1.0 + (x * (4.0 / y));
	double tmp;
	if (x <= -3.9e-50) {
		tmp = t_1;
	} else if (x <= -3.2e-77) {
		tmp = t_0;
	} else if (x <= -2.1e-162) {
		tmp = 4.0;
	} else if (x <= -1.4e-238) {
		tmp = t_0;
	} else if (x <= 6.6e-234) {
		tmp = 4.0;
	} else if (x <= 2.3e-149) {
		tmp = t_0;
	} else if (x <= 1.05e-7) {
		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 = 1.0d0 + ((z / y) * (-4.0d0))
    t_1 = 1.0d0 + (x * (4.0d0 / y))
    if (x <= (-3.9d-50)) then
        tmp = t_1
    else if (x <= (-3.2d-77)) then
        tmp = t_0
    else if (x <= (-2.1d-162)) then
        tmp = 4.0d0
    else if (x <= (-1.4d-238)) then
        tmp = t_0
    else if (x <= 6.6d-234) then
        tmp = 4.0d0
    else if (x <= 2.3d-149) then
        tmp = t_0
    else if (x <= 1.05d-7) 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 = 1.0 + ((z / y) * -4.0);
	double t_1 = 1.0 + (x * (4.0 / y));
	double tmp;
	if (x <= -3.9e-50) {
		tmp = t_1;
	} else if (x <= -3.2e-77) {
		tmp = t_0;
	} else if (x <= -2.1e-162) {
		tmp = 4.0;
	} else if (x <= -1.4e-238) {
		tmp = t_0;
	} else if (x <= 6.6e-234) {
		tmp = 4.0;
	} else if (x <= 2.3e-149) {
		tmp = t_0;
	} else if (x <= 1.05e-7) {
		tmp = 4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((z / y) * -4.0)
	t_1 = 1.0 + (x * (4.0 / y))
	tmp = 0
	if x <= -3.9e-50:
		tmp = t_1
	elif x <= -3.2e-77:
		tmp = t_0
	elif x <= -2.1e-162:
		tmp = 4.0
	elif x <= -1.4e-238:
		tmp = t_0
	elif x <= 6.6e-234:
		tmp = 4.0
	elif x <= 2.3e-149:
		tmp = t_0
	elif x <= 1.05e-7:
		tmp = 4.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(z / y) * -4.0))
	t_1 = Float64(1.0 + Float64(x * Float64(4.0 / y)))
	tmp = 0.0
	if (x <= -3.9e-50)
		tmp = t_1;
	elseif (x <= -3.2e-77)
		tmp = t_0;
	elseif (x <= -2.1e-162)
		tmp = 4.0;
	elseif (x <= -1.4e-238)
		tmp = t_0;
	elseif (x <= 6.6e-234)
		tmp = 4.0;
	elseif (x <= 2.3e-149)
		tmp = t_0;
	elseif (x <= 1.05e-7)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((z / y) * -4.0);
	t_1 = 1.0 + (x * (4.0 / y));
	tmp = 0.0;
	if (x <= -3.9e-50)
		tmp = t_1;
	elseif (x <= -3.2e-77)
		tmp = t_0;
	elseif (x <= -2.1e-162)
		tmp = 4.0;
	elseif (x <= -1.4e-238)
		tmp = t_0;
	elseif (x <= 6.6e-234)
		tmp = 4.0;
	elseif (x <= 2.3e-149)
		tmp = t_0;
	elseif (x <= 1.05e-7)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.9e-50], t$95$1, If[LessEqual[x, -3.2e-77], t$95$0, If[LessEqual[x, -2.1e-162], 4.0, If[LessEqual[x, -1.4e-238], t$95$0, If[LessEqual[x, 6.6e-234], 4.0, If[LessEqual[x, 2.3e-149], t$95$0, If[LessEqual[x, 1.05e-7], 4.0, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.90000000000000021e-50 or 1.05e-7 < x

   1. Initial program 100.0%

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

      1. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-def 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 72.3%

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

   if -3.90000000000000021e-50 < x < -3.2e-77 or -2.1e-162 < x < -1.40000000000000002e-238 or 6.60000000000000028e-234 < x < 2.3e-149

   1. Initial program 99.9%

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

      1. associate-*l/ 97.4%

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

      2. sub-neg 97.4%

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

      3. sub-neg 97.4%

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

      4. +-commutative 97.4%

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

      5. fma-def 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in z around inf 71.8%

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

      1. *-commutative 71.8%

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

   7. Simplified 71.8%

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

   if -3.2e-77 < x < -2.1e-162 or -1.40000000000000002e-238 < x < 6.60000000000000028e-234 or 2.3e-149 < x < 1.05e-7

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. fma-def 99.7%

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

      5. +-commutative 99.7%

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

      6. associate--l+ 99.7%

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

      7. +-commutative 99.7%

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

      8. associate-+l- 99.7%

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

      9. sub-neg 99.7%

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

      10. remove-double-neg 99.7%

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

      11. distribute-neg-in 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-neg-in 99.7%

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

      14. distribute-lft-neg-out 99.7%

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

      15. sub-neg 99.7%

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

      16. distribute-lft-neg-out 99.7%

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

      17. distribute-rgt-neg-in 99.7%

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

      18. fma-neg 99.6%

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

      19. metadata-eval 99.6%

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

      20. remove-double-neg 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 66.5%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-50}:\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-77}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-162}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-238}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-234}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-149}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-7}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{z}{y} \cdot -4\\ t_1 := 1 + \frac{4}{\frac{y}{x}}\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-77}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-163}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-238}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-234}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{-149}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-8}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* (/ z y) -4.0))) (t_1 (+ 1.0 (/ 4.0 (/ y x)))))
   (if (<= x -3.9e-50)
     t_1
     (if (<= x -4.5e-77)
       t_0
       (if (<= x -3.5e-163)
         4.0
         (if (<= x -1.55e-238)
           t_0
           (if (<= x 2.25e-234)
             4.0
             (if (<= x 1.76e-149) t_0 (if (<= x 9.5e-8) 4.0 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((z / y) * -4.0);
	double t_1 = 1.0 + (4.0 / (y / x));
	double tmp;
	if (x <= -3.9e-50) {
		tmp = t_1;
	} else if (x <= -4.5e-77) {
		tmp = t_0;
	} else if (x <= -3.5e-163) {
		tmp = 4.0;
	} else if (x <= -1.55e-238) {
		tmp = t_0;
	} else if (x <= 2.25e-234) {
		tmp = 4.0;
	} else if (x <= 1.76e-149) {
		tmp = t_0;
	} else if (x <= 9.5e-8) {
		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 = 1.0d0 + ((z / y) * (-4.0d0))
    t_1 = 1.0d0 + (4.0d0 / (y / x))
    if (x <= (-3.9d-50)) then
        tmp = t_1
    else if (x <= (-4.5d-77)) then
        tmp = t_0
    else if (x <= (-3.5d-163)) then
        tmp = 4.0d0
    else if (x <= (-1.55d-238)) then
        tmp = t_0
    else if (x <= 2.25d-234) then
        tmp = 4.0d0
    else if (x <= 1.76d-149) then
        tmp = t_0
    else if (x <= 9.5d-8) 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 = 1.0 + ((z / y) * -4.0);
	double t_1 = 1.0 + (4.0 / (y / x));
	double tmp;
	if (x <= -3.9e-50) {
		tmp = t_1;
	} else if (x <= -4.5e-77) {
		tmp = t_0;
	} else if (x <= -3.5e-163) {
		tmp = 4.0;
	} else if (x <= -1.55e-238) {
		tmp = t_0;
	} else if (x <= 2.25e-234) {
		tmp = 4.0;
	} else if (x <= 1.76e-149) {
		tmp = t_0;
	} else if (x <= 9.5e-8) {
		tmp = 4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((z / y) * -4.0)
	t_1 = 1.0 + (4.0 / (y / x))
	tmp = 0
	if x <= -3.9e-50:
		tmp = t_1
	elif x <= -4.5e-77:
		tmp = t_0
	elif x <= -3.5e-163:
		tmp = 4.0
	elif x <= -1.55e-238:
		tmp = t_0
	elif x <= 2.25e-234:
		tmp = 4.0
	elif x <= 1.76e-149:
		tmp = t_0
	elif x <= 9.5e-8:
		tmp = 4.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(z / y) * -4.0))
	t_1 = Float64(1.0 + Float64(4.0 / Float64(y / x)))
	tmp = 0.0
	if (x <= -3.9e-50)
		tmp = t_1;
	elseif (x <= -4.5e-77)
		tmp = t_0;
	elseif (x <= -3.5e-163)
		tmp = 4.0;
	elseif (x <= -1.55e-238)
		tmp = t_0;
	elseif (x <= 2.25e-234)
		tmp = 4.0;
	elseif (x <= 1.76e-149)
		tmp = t_0;
	elseif (x <= 9.5e-8)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((z / y) * -4.0);
	t_1 = 1.0 + (4.0 / (y / x));
	tmp = 0.0;
	if (x <= -3.9e-50)
		tmp = t_1;
	elseif (x <= -4.5e-77)
		tmp = t_0;
	elseif (x <= -3.5e-163)
		tmp = 4.0;
	elseif (x <= -1.55e-238)
		tmp = t_0;
	elseif (x <= 2.25e-234)
		tmp = 4.0;
	elseif (x <= 1.76e-149)
		tmp = t_0;
	elseif (x <= 9.5e-8)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(4.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.9e-50], t$95$1, If[LessEqual[x, -4.5e-77], t$95$0, If[LessEqual[x, -3.5e-163], 4.0, If[LessEqual[x, -1.55e-238], t$95$0, If[LessEqual[x, 2.25e-234], 4.0, If[LessEqual[x, 1.76e-149], t$95$0, If[LessEqual[x, 9.5e-8], 4.0, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.90000000000000021e-50 or 9.50000000000000036e-8 < x

   1. Initial program 100.0%

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

      1. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-def 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 72.3%

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

      1. associate-*l/ 72.5%

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

      2. associate-/l* 72.4%

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

   7. Applied egg-rr 72.4%

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

   if -3.90000000000000021e-50 < x < -4.5000000000000001e-77 or -3.50000000000000027e-163 < x < -1.5500000000000001e-238 or 2.25000000000000005e-234 < x < 1.7599999999999999e-149

   1. Initial program 99.9%

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

      1. associate-*l/ 97.4%

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

      2. sub-neg 97.4%

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

      3. sub-neg 97.4%

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

      4. +-commutative 97.4%

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

      5. fma-def 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in z around inf 71.8%

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

      1. *-commutative 71.8%

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

   7. Simplified 71.8%

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

   if -4.5000000000000001e-77 < x < -3.50000000000000027e-163 or -1.5500000000000001e-238 < x < 2.25000000000000005e-234 or 1.7599999999999999e-149 < x < 9.50000000000000036e-8

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. fma-def 99.7%

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

      5. +-commutative 99.7%

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

      6. associate--l+ 99.7%

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

      7. +-commutative 99.7%

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

      8. associate-+l- 99.7%

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

      9. sub-neg 99.7%

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

      10. remove-double-neg 99.7%

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

      11. distribute-neg-in 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-neg-in 99.7%

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

      14. distribute-lft-neg-out 99.7%

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

      15. sub-neg 99.7%

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

      16. distribute-lft-neg-out 99.7%

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

      17. distribute-rgt-neg-in 99.7%

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

      18. fma-neg 99.6%

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

      19. metadata-eval 99.6%

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

      20. remove-double-neg 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 66.5%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-50}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-77}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-163}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-238}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-234}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{-149}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-8}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{4}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{z}{y} \cdot -4\\ t_1 := 1 + \frac{4 \cdot x}{y}\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-82}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-157}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-238}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.12 \cdot 10^{-234}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-150}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* (/ z y) -4.0))) (t_1 (+ 1.0 (/ (* 4.0 x) y))))
   (if (<= x -2.4e-50)
     t_1
     (if (<= x -3.2e-82)
       t_0
       (if (<= x -1.7e-157)
         4.0
         (if (<= x -1.9e-238)
           t_0
           (if (<= x 2.12e-234)
             4.0
             (if (<= x 9.5e-150) t_0 (if (<= x 7.5e-6) 4.0 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((z / y) * -4.0);
	double t_1 = 1.0 + ((4.0 * x) / y);
	double tmp;
	if (x <= -2.4e-50) {
		tmp = t_1;
	} else if (x <= -3.2e-82) {
		tmp = t_0;
	} else if (x <= -1.7e-157) {
		tmp = 4.0;
	} else if (x <= -1.9e-238) {
		tmp = t_0;
	} else if (x <= 2.12e-234) {
		tmp = 4.0;
	} else if (x <= 9.5e-150) {
		tmp = t_0;
	} else if (x <= 7.5e-6) {
		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 = 1.0d0 + ((z / y) * (-4.0d0))
    t_1 = 1.0d0 + ((4.0d0 * x) / y)
    if (x <= (-2.4d-50)) then
        tmp = t_1
    else if (x <= (-3.2d-82)) then
        tmp = t_0
    else if (x <= (-1.7d-157)) then
        tmp = 4.0d0
    else if (x <= (-1.9d-238)) then
        tmp = t_0
    else if (x <= 2.12d-234) then
        tmp = 4.0d0
    else if (x <= 9.5d-150) then
        tmp = t_0
    else if (x <= 7.5d-6) 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 = 1.0 + ((z / y) * -4.0);
	double t_1 = 1.0 + ((4.0 * x) / y);
	double tmp;
	if (x <= -2.4e-50) {
		tmp = t_1;
	} else if (x <= -3.2e-82) {
		tmp = t_0;
	} else if (x <= -1.7e-157) {
		tmp = 4.0;
	} else if (x <= -1.9e-238) {
		tmp = t_0;
	} else if (x <= 2.12e-234) {
		tmp = 4.0;
	} else if (x <= 9.5e-150) {
		tmp = t_0;
	} else if (x <= 7.5e-6) {
		tmp = 4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((z / y) * -4.0)
	t_1 = 1.0 + ((4.0 * x) / y)
	tmp = 0
	if x <= -2.4e-50:
		tmp = t_1
	elif x <= -3.2e-82:
		tmp = t_0
	elif x <= -1.7e-157:
		tmp = 4.0
	elif x <= -1.9e-238:
		tmp = t_0
	elif x <= 2.12e-234:
		tmp = 4.0
	elif x <= 9.5e-150:
		tmp = t_0
	elif x <= 7.5e-6:
		tmp = 4.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(z / y) * -4.0))
	t_1 = Float64(1.0 + Float64(Float64(4.0 * x) / y))
	tmp = 0.0
	if (x <= -2.4e-50)
		tmp = t_1;
	elseif (x <= -3.2e-82)
		tmp = t_0;
	elseif (x <= -1.7e-157)
		tmp = 4.0;
	elseif (x <= -1.9e-238)
		tmp = t_0;
	elseif (x <= 2.12e-234)
		tmp = 4.0;
	elseif (x <= 9.5e-150)
		tmp = t_0;
	elseif (x <= 7.5e-6)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((z / y) * -4.0);
	t_1 = 1.0 + ((4.0 * x) / y);
	tmp = 0.0;
	if (x <= -2.4e-50)
		tmp = t_1;
	elseif (x <= -3.2e-82)
		tmp = t_0;
	elseif (x <= -1.7e-157)
		tmp = 4.0;
	elseif (x <= -1.9e-238)
		tmp = t_0;
	elseif (x <= 2.12e-234)
		tmp = 4.0;
	elseif (x <= 9.5e-150)
		tmp = t_0;
	elseif (x <= 7.5e-6)
		tmp = 4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(N[(4.0 * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e-50], t$95$1, If[LessEqual[x, -3.2e-82], t$95$0, If[LessEqual[x, -1.7e-157], 4.0, If[LessEqual[x, -1.9e-238], t$95$0, If[LessEqual[x, 2.12e-234], 4.0, If[LessEqual[x, 9.5e-150], t$95$0, If[LessEqual[x, 7.5e-6], 4.0, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.40000000000000002e-50 or 7.50000000000000019e-6 < x

   1. Initial program 100.0%

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

      1. associate-*l/ 99.7%

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

      2. sub-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. fma-def 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 72.5%

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

      1. associate-*r/ 72.5%

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

   7. Simplified 72.5%

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

   if -2.40000000000000002e-50 < x < -3.2000000000000001e-82 or -1.69999999999999989e-157 < x < -1.8999999999999998e-238 or 2.12000000000000008e-234 < x < 9.50000000000000013e-150

   1. Initial program 99.9%

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

      1. associate-*l/ 97.4%

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

      2. sub-neg 97.4%

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

      3. sub-neg 97.4%

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

      4. +-commutative 97.4%

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

      5. fma-def 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in z around inf 71.8%

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

      1. *-commutative 71.8%

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

   7. Simplified 71.8%

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

   if -3.2000000000000001e-82 < x < -1.69999999999999989e-157 or -1.8999999999999998e-238 < x < 2.12000000000000008e-234 or 9.50000000000000013e-150 < x < 7.50000000000000019e-6

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. fma-def 99.7%

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

      5. +-commutative 99.7%

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

      6. associate--l+ 99.7%

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

      7. +-commutative 99.7%

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

      8. associate-+l- 99.7%

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

      9. sub-neg 99.7%

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

      10. remove-double-neg 99.7%

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

      11. distribute-neg-in 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-neg-in 99.7%

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

      14. distribute-lft-neg-out 99.7%

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

      15. sub-neg 99.7%

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

      16. distribute-lft-neg-out 99.7%

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

      17. distribute-rgt-neg-in 99.7%

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

      18. fma-neg 99.6%

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

      19. metadata-eval 99.6%

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

      20. remove-double-neg 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 66.5%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-50}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-82}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-157}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-238}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 2.12 \cdot 10^{-234}:\\ \;\;\;\;4\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-150}:\\ \;\;\;\;1 + \frac{z}{y} \cdot -4\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{4 \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -29000000 \lor \neg \left(x \leq 7 \cdot 10^{-6}\right):\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -29000000.0) (not (<= x 7e-6))) (+ 1.0 (* x (/ 4.0 y))) 4.0))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -29000000.0) || !(x <= 7e-6)) {
		tmp = 1.0 + (x * (4.0 / y));
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-29000000.0d0)) .or. (.not. (x <= 7d-6))) then
        tmp = 1.0d0 + (x * (4.0d0 / y))
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -29000000.0) || !(x <= 7e-6)) {
		tmp = 1.0 + (x * (4.0 / y));
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -29000000.0) or not (x <= 7e-6):
		tmp = 1.0 + (x * (4.0 / y))
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -29000000.0) || !(x <= 7e-6))
		tmp = Float64(1.0 + Float64(x * Float64(4.0 / y)));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -29000000.0) || ~((x <= 7e-6)))
		tmp = 1.0 + (x * (4.0 / y));
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -29000000.0], N[Not[LessEqual[x, 7e-6]], $MachinePrecision]], N[(1.0 + N[(x * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4.0]

Derivation

1. Split input into 2 regimes

2. if x < -2.9e7 or 6.99999999999999989e-6 < x

   1. Initial program 100.0%

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

      1. associate-*l/ 99.6%

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

      2. sub-neg 99.6%

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

      3. sub-neg 99.6%

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

      4. +-commutative 99.6%

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

      5. fma-def 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 76.5%

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

   if -2.9e7 < x < 6.99999999999999989e-6

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l/ 99.0%

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

      3. *-commutative 99.0%

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

      4. fma-def 99.0%

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

      5. +-commutative 99.0%

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

      6. associate--l+ 99.0%

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

      7. +-commutative 99.0%

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

      8. associate-+l- 99.0%

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

      9. sub-neg 99.0%

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

      10. remove-double-neg 99.0%

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

      11. distribute-neg-in 99.0%

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

      12. +-commutative 99.0%

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

      13. distribute-neg-in 99.0%

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

      14. distribute-lft-neg-out 99.0%

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

      15. sub-neg 99.0%

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

      16. distribute-lft-neg-out 99.0%

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

      17. distribute-rgt-neg-in 99.0%

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

      18. fma-neg 99.0%

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

      19. metadata-eval 99.0%

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

      20. remove-double-neg 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in y around inf 53.2%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -29000000 \lor \neg \left(x \leq 7 \cdot 10^{-6}\right):\\ \;\;\;\;1 + x \cdot \frac{4}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 34.7% 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. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. associate-*l/ 99.3%

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

   3. *-commutative 99.3%

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

   4. fma-def 99.3%

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

   5. +-commutative 99.3%

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

   6. associate--l+ 99.3%

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

   7. +-commutative 99.3%

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

   8. associate-+l- 99.3%

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

   9. sub-neg 99.3%

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

   10. remove-double-neg 99.3%

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

   11. distribute-neg-in 99.3%

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

   12. +-commutative 99.3%

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

   13. distribute-neg-in 99.3%

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

   14. distribute-lft-neg-out 99.3%

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

   15. sub-neg 99.3%

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

   16. distribute-lft-neg-out 99.3%

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

   17. distribute-rgt-neg-in 99.3%

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

   18. fma-neg 99.3%

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

   19. metadata-eval 99.3%

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

   20. remove-double-neg 99.3%

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

3. Simplified 99.3%

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

5. Taylor expanded in y around inf 34.5%

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

6. Final simplification 34.5%

   \[\leadsto 4 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024021 
(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)))