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

Percentage Accurate: 99.8% → 100.0%

Time: 5.0s

Alternatives: 8

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: 100.0% accurate, 1.4× speedup

Math

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

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(4.0 * Float64(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[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
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. *-commutative 99.9%

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

   3. associate-*r/ 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. associate--l+ 99.3%

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

   6. --rgt-identity 99.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x - 0\right)} + \left(y \cdot 0.75 - z\right), \frac{4}{y}, 1\right) \]

   7. associate-+l- 99.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{x - \left(0 - \left(y \cdot 0.75 - z\right)\right)}, \frac{4}{y}, 1\right) \]

   8. sub-neg 99.3%

      \[\leadsto \mathsf{fma}\left(x - \left(0 - \color{blue}{\left(y \cdot 0.75 + \left(-z\right)\right)}\right), \frac{4}{y}, 1\right) \]

   9. associate--r+ 99.3%

      \[\leadsto \mathsf{fma}\left(x - \color{blue}{\left(\left(0 - y \cdot 0.75\right) - \left(-z\right)\right)}, \frac{4}{y}, 1\right) \]

   10. neg-sub0 99.3%

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

   11. distribute-rgt-neg-in 99.3%

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

   12. fma-neg 99.3%

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

   13. metadata-eval 99.3%

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

   14. 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. Taylor expanded in y around 0 100.0%

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

5. Final simplification 100.0%

   \[\leadsto 4 + 4 \cdot \frac{x - z}{y} \]

Alternative 2: 53.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{z \cdot -4}{y}\\ t_1 := 1 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -16200000:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-186}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-241}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* z -4.0) y))) (t_1 (+ 1.0 (* 4.0 (/ x y)))))
   (if (<= y -16200000.0)
     4.0
     (if (<= y -1.05e-168)
       t_1
       (if (<= y -3.7e-186)
         t_0
         (if (<= y -6.4e-281)
           t_1
           (if (<= y 2e-241) t_0 (if (<= y 2.4e+62) t_1 4.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + ((z * -4.0) / y);
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (y <= -16200000.0) {
		tmp = 4.0;
	} else if (y <= -1.05e-168) {
		tmp = t_1;
	} else if (y <= -3.7e-186) {
		tmp = t_0;
	} else if (y <= -6.4e-281) {
		tmp = t_1;
	} else if (y <= 2e-241) {
		tmp = t_0;
	} else if (y <= 2.4e+62) {
		tmp = t_1;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 + ((z * (-4.0d0)) / y)
    t_1 = 1.0d0 + (4.0d0 * (x / y))
    if (y <= (-16200000.0d0)) then
        tmp = 4.0d0
    else if (y <= (-1.05d-168)) then
        tmp = t_1
    else if (y <= (-3.7d-186)) then
        tmp = t_0
    else if (y <= (-6.4d-281)) then
        tmp = t_1
    else if (y <= 2d-241) then
        tmp = t_0
    else if (y <= 2.4d+62) then
        tmp = t_1
    else
        tmp = 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + ((z * -4.0) / y);
	double t_1 = 1.0 + (4.0 * (x / y));
	double tmp;
	if (y <= -16200000.0) {
		tmp = 4.0;
	} else if (y <= -1.05e-168) {
		tmp = t_1;
	} else if (y <= -3.7e-186) {
		tmp = t_0;
	} else if (y <= -6.4e-281) {
		tmp = t_1;
	} else if (y <= 2e-241) {
		tmp = t_0;
	} else if (y <= 2.4e+62) {
		tmp = t_1;
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + ((z * -4.0) / y)
	t_1 = 1.0 + (4.0 * (x / y))
	tmp = 0
	if y <= -16200000.0:
		tmp = 4.0
	elif y <= -1.05e-168:
		tmp = t_1
	elif y <= -3.7e-186:
		tmp = t_0
	elif y <= -6.4e-281:
		tmp = t_1
	elif y <= 2e-241:
		tmp = t_0
	elif y <= 2.4e+62:
		tmp = t_1
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(Float64(z * -4.0) / y))
	t_1 = Float64(1.0 + Float64(4.0 * Float64(x / y)))
	tmp = 0.0
	if (y <= -16200000.0)
		tmp = 4.0;
	elseif (y <= -1.05e-168)
		tmp = t_1;
	elseif (y <= -3.7e-186)
		tmp = t_0;
	elseif (y <= -6.4e-281)
		tmp = t_1;
	elseif (y <= 2e-241)
		tmp = t_0;
	elseif (y <= 2.4e+62)
		tmp = t_1;
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + ((z * -4.0) / y);
	t_1 = 1.0 + (4.0 * (x / y));
	tmp = 0.0;
	if (y <= -16200000.0)
		tmp = 4.0;
	elseif (y <= -1.05e-168)
		tmp = t_1;
	elseif (y <= -3.7e-186)
		tmp = t_0;
	elseif (y <= -6.4e-281)
		tmp = t_1;
	elseif (y <= 2e-241)
		tmp = t_0;
	elseif (y <= 2.4e+62)
		tmp = t_1;
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -16200000.0], 4.0, If[LessEqual[y, -1.05e-168], t$95$1, If[LessEqual[y, -3.7e-186], t$95$0, If[LessEqual[y, -6.4e-281], t$95$1, If[LessEqual[y, 2e-241], t$95$0, If[LessEqual[y, 2.4e+62], t$95$1, 4.0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.62e7 or 2.4e62 < y

   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. *-commutative 99.8%

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

      3. associate-*r/ 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. associate--l+ 99.7%

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

      6. --rgt-identity 99.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x - 0\right)} + \left(y \cdot 0.75 - z\right), \frac{4}{y}, 1\right) \]

      7. associate-+l- 99.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{x - \left(0 - \left(y \cdot 0.75 - z\right)\right)}, \frac{4}{y}, 1\right) \]

      8. sub-neg 99.7%

         \[\leadsto \mathsf{fma}\left(x - \left(0 - \color{blue}{\left(y \cdot 0.75 + \left(-z\right)\right)}\right), \frac{4}{y}, 1\right) \]

      9. associate--r+ 99.7%

         \[\leadsto \mathsf{fma}\left(x - \color{blue}{\left(\left(0 - y \cdot 0.75\right) - \left(-z\right)\right)}, \frac{4}{y}, 1\right) \]

      10. neg-sub0 99.7%

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

      11. distribute-rgt-neg-in 99.7%

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

      12. fma-neg 99.7%

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

      13. metadata-eval 99.7%

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

      14. remove-double-neg 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 68.0%

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

   if -1.62e7 < y < -1.04999999999999997e-168 or -3.7000000000000002e-186 < y < -6.4000000000000001e-281 or 1.9999999999999999e-241 < y < 2.4e62

   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/ 99.8%

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

      2. +-commutative 99.8%

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

      3. 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. Taylor expanded in x around inf 60.6%

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

   if -1.04999999999999997e-168 < y < -3.7000000000000002e-186 or -6.4000000000000001e-281 < y < 1.9999999999999999e-241

   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/ 95.2%

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

      2. +-commutative 95.2%

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

      3. fma-def 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around inf 77.8%

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

      1. associate-*r/ 77.8%

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

      2. metadata-eval 77.8%

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

      3. associate-*r* 77.8%

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

      4. neg-mul-1 77.8%

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

      5. associate-*l/ 77.4%

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

      6. *-commutative 77.4%

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

      7. associate-*r/ 77.8%

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

      8. neg-mul-1 77.8%

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

      9. *-commutative 77.8%

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

      10. associate-*l* 77.8%

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

      11. metadata-eval 77.8%

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

   6. Simplified 77.8%

      \[\leadsto 1 + \color{blue}{\frac{z \cdot -4}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -16200000:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-168}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-186}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-281}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-241}:\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+62}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 3: 80.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+213} \lor \neg \left(z \leq 4.1 \cdot 10^{+81}\right):\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.7e+213) (not (<= z 4.1e+81)))
   (+ 1.0 (/ (* z -4.0) y))
   (+ 4.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.7e+213) || !(z <= 4.1e+81)) {
		tmp = 1.0 + ((z * -4.0) / y);
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.7d+213)) .or. (.not. (z <= 4.1d+81))) then
        tmp = 1.0d0 + ((z * (-4.0d0)) / y)
    else
        tmp = 4.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.7e+213) || !(z <= 4.1e+81)) {
		tmp = 1.0 + ((z * -4.0) / y);
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.7e+213) or not (z <= 4.1e+81):
		tmp = 1.0 + ((z * -4.0) / y)
	else:
		tmp = 4.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.7e+213) || !(z <= 4.1e+81))
		tmp = Float64(1.0 + Float64(Float64(z * -4.0) / y));
	else
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.7e+213) || ~((z <= 4.1e+81)))
		tmp = 1.0 + ((z * -4.0) / y);
	else
		tmp = 4.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.7e+213], N[Not[LessEqual[z, 4.1e+81]], $MachinePrecision]], N[(1.0 + N[(N[(z * -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.69999999999999993e213 or 4.10000000000000012e81 < z

   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/ 99.8%

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

      2. +-commutative 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 84.4%

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

      1. associate-*r/ 84.4%

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

      2. metadata-eval 84.4%

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

      3. associate-*r* 84.4%

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

      4. neg-mul-1 84.4%

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

      5. associate-*l/ 84.3%

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

      6. *-commutative 84.3%

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

      7. associate-*r/ 84.4%

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

      8. neg-mul-1 84.4%

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

      9. *-commutative 84.4%

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

      10. associate-*l* 84.4%

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

      11. metadata-eval 84.4%

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

   6. Simplified 84.4%

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

   if -3.69999999999999993e213 < z < 4.10000000000000012e81

   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. *-commutative 99.9%

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

      3. associate-*r/ 99.2%

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

      4. fma-def 99.2%

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

      5. associate--l+ 99.2%

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

      6. --rgt-identity 99.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x - 0\right)} + \left(y \cdot 0.75 - z\right), \frac{4}{y}, 1\right) \]

      7. associate-+l- 99.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{x - \left(0 - \left(y \cdot 0.75 - z\right)\right)}, \frac{4}{y}, 1\right) \]

      8. sub-neg 99.2%

         \[\leadsto \mathsf{fma}\left(x - \left(0 - \color{blue}{\left(y \cdot 0.75 + \left(-z\right)\right)}\right), \frac{4}{y}, 1\right) \]

      9. associate--r+ 99.2%

         \[\leadsto \mathsf{fma}\left(x - \color{blue}{\left(\left(0 - y \cdot 0.75\right) - \left(-z\right)\right)}, \frac{4}{y}, 1\right) \]

      10. neg-sub0 99.2%

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

      11. distribute-rgt-neg-in 99.2%

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

      12. fma-neg 99.2%

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

      13. metadata-eval 99.2%

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

      14. remove-double-neg 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around inf 88.1%

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

      1. *-commutative 88.1%

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

   7. Simplified 88.1%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+213} \lor \neg \left(z \leq 4.1 \cdot 10^{+81}\right):\\ \;\;\;\;1 + \frac{z \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 4: 82.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+213} \lor \neg \left(z \leq 4.1 \cdot 10^{+76}\right):\\ \;\;\;\;4 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.7e+213) (not (<= z 4.1e+76)))
   (+ 4.0 (* (/ z y) -4.0))
   (+ 4.0 (* 4.0 (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.7e+213) || !(z <= 4.1e+76)) {
		tmp = 4.0 + ((z / y) * -4.0);
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.7d+213)) .or. (.not. (z <= 4.1d+76))) then
        tmp = 4.0d0 + ((z / y) * (-4.0d0))
    else
        tmp = 4.0d0 + (4.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.7e+213) || !(z <= 4.1e+76)) {
		tmp = 4.0 + ((z / y) * -4.0);
	} else {
		tmp = 4.0 + (4.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.7e+213) or not (z <= 4.1e+76):
		tmp = 4.0 + ((z / y) * -4.0)
	else:
		tmp = 4.0 + (4.0 * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.7e+213) || !(z <= 4.1e+76))
		tmp = Float64(4.0 + Float64(Float64(z / y) * -4.0));
	else
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.7e+213) || ~((z <= 4.1e+76)))
		tmp = 4.0 + ((z / y) * -4.0);
	else
		tmp = 4.0 + (4.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.7e+213], N[Not[LessEqual[z, 4.1e+76]], $MachinePrecision]], N[(4.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.69999999999999993e213 or 4.0999999999999998e76 < z

   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. *-commutative 99.9%

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

      3. associate-*r/ 99.8%

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

      4. fma-def 99.8%

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

      5. associate--l+ 99.8%

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

      6. --rgt-identity 99.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x - 0\right)} + \left(y \cdot 0.75 - z\right), \frac{4}{y}, 1\right) \]

      7. associate-+l- 99.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{x - \left(0 - \left(y \cdot 0.75 - z\right)\right)}, \frac{4}{y}, 1\right) \]

      8. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - \left(0 - \color{blue}{\left(y \cdot 0.75 + \left(-z\right)\right)}\right), \frac{4}{y}, 1\right) \]

      9. associate--r+ 99.8%

         \[\leadsto \mathsf{fma}\left(x - \color{blue}{\left(\left(0 - y \cdot 0.75\right) - \left(-z\right)\right)}, \frac{4}{y}, 1\right) \]

      10. neg-sub0 99.8%

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

      11. distribute-rgt-neg-in 99.8%

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

      12. fma-neg 99.8%

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

      13. metadata-eval 99.8%

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

      14. remove-double-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around 0 98.5%

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

      1. *-commutative 98.5%

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

   7. Simplified 98.5%

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

   if -3.69999999999999993e213 < z < 4.0999999999999998e76

   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. *-commutative 99.9%

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

      3. associate-*r/ 99.2%

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

      4. fma-def 99.2%

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

      5. associate--l+ 99.2%

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

      6. --rgt-identity 99.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x - 0\right)} + \left(y \cdot 0.75 - z\right), \frac{4}{y}, 1\right) \]

      7. associate-+l- 99.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{x - \left(0 - \left(y \cdot 0.75 - z\right)\right)}, \frac{4}{y}, 1\right) \]

      8. sub-neg 99.2%

         \[\leadsto \mathsf{fma}\left(x - \left(0 - \color{blue}{\left(y \cdot 0.75 + \left(-z\right)\right)}\right), \frac{4}{y}, 1\right) \]

      9. associate--r+ 99.2%

         \[\leadsto \mathsf{fma}\left(x - \color{blue}{\left(\left(0 - y \cdot 0.75\right) - \left(-z\right)\right)}, \frac{4}{y}, 1\right) \]

      10. neg-sub0 99.2%

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

      11. distribute-rgt-neg-in 99.2%

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

      12. fma-neg 99.2%

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

      13. metadata-eval 99.2%

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

      14. remove-double-neg 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around inf 88.1%

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

      1. *-commutative 88.1%

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

   7. Simplified 88.1%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+213} \lor \neg \left(z \leq 4.1 \cdot 10^{+76}\right):\\ \;\;\;\;4 + \frac{z}{y} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 53.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -12500000:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+61}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -12500000.0) 4.0 (if (<= y 4.4e+61) (+ 1.0 (* 4.0 (/ x y))) 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -12500000.0) {
		tmp = 4.0;
	} else if (y <= 4.4e+61) {
		tmp = 1.0 + (4.0 * (x / 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 (y <= (-12500000.0d0)) then
        tmp = 4.0d0
    else if (y <= 4.4d+61) then
        tmp = 1.0d0 + (4.0d0 * (x / 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 (y <= -12500000.0) {
		tmp = 4.0;
	} else if (y <= 4.4e+61) {
		tmp = 1.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -12500000.0:
		tmp = 4.0
	elif y <= 4.4e+61:
		tmp = 1.0 + (4.0 * (x / y))
	else:
		tmp = 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -12500000.0)
		tmp = 4.0;
	elseif (y <= 4.4e+61)
		tmp = Float64(1.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = 4.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -12500000.0)
		tmp = 4.0;
	elseif (y <= 4.4e+61)
		tmp = 1.0 + (4.0 * (x / y));
	else
		tmp = 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -12500000.0], 4.0, If[LessEqual[y, 4.4e+61], N[(1.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e7 or 4.4000000000000001e61 < y

   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. *-commutative 99.8%

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

      3. associate-*r/ 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. associate--l+ 99.7%

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

      6. --rgt-identity 99.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x - 0\right)} + \left(y \cdot 0.75 - z\right), \frac{4}{y}, 1\right) \]

      7. associate-+l- 99.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{x - \left(0 - \left(y \cdot 0.75 - z\right)\right)}, \frac{4}{y}, 1\right) \]

      8. sub-neg 99.7%

         \[\leadsto \mathsf{fma}\left(x - \left(0 - \color{blue}{\left(y \cdot 0.75 + \left(-z\right)\right)}\right), \frac{4}{y}, 1\right) \]

      9. associate--r+ 99.7%

         \[\leadsto \mathsf{fma}\left(x - \color{blue}{\left(\left(0 - y \cdot 0.75\right) - \left(-z\right)\right)}, \frac{4}{y}, 1\right) \]

      10. neg-sub0 99.7%

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

      11. distribute-rgt-neg-in 99.7%

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

      12. fma-neg 99.7%

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

      13. metadata-eval 99.7%

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

      14. remove-double-neg 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 68.0%

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

   if -1.25e7 < y < 4.4000000000000001e61

   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/ 98.9%

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

      2. +-commutative 98.9%

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

      3. fma-def 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in x around inf 55.6%

      \[\leadsto 1 + \color{blue}{4 \cdot \frac{x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12500000:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+61}:\\ \;\;\;\;1 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 6: 84.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.22 \cdot 10^{+161}:\\ \;\;\;\;1 + \left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+76}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + \frac{z}{y} \cdot -4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.22e+161)
   (+ 1.0 (* (- x z) (/ 4.0 y)))
   (if (<= z 6.2e+76) (+ 4.0 (* 4.0 (/ x y))) (+ 4.0 (* (/ z y) -4.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.22e+161) {
		tmp = 1.0 + ((x - z) * (4.0 / y));
	} else if (z <= 6.2e+76) {
		tmp = 4.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 + ((z / y) * -4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.22d+161)) then
        tmp = 1.0d0 + ((x - z) * (4.0d0 / y))
    else if (z <= 6.2d+76) then
        tmp = 4.0d0 + (4.0d0 * (x / y))
    else
        tmp = 4.0d0 + ((z / y) * (-4.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.22e+161) {
		tmp = 1.0 + ((x - z) * (4.0 / y));
	} else if (z <= 6.2e+76) {
		tmp = 4.0 + (4.0 * (x / y));
	} else {
		tmp = 4.0 + ((z / y) * -4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.22e+161:
		tmp = 1.0 + ((x - z) * (4.0 / y))
	elif z <= 6.2e+76:
		tmp = 4.0 + (4.0 * (x / y))
	else:
		tmp = 4.0 + ((z / y) * -4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.22e+161)
		tmp = Float64(1.0 + Float64(Float64(x - z) * Float64(4.0 / y)));
	elseif (z <= 6.2e+76)
		tmp = Float64(4.0 + Float64(4.0 * Float64(x / y)));
	else
		tmp = Float64(4.0 + Float64(Float64(z / y) * -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.22e+161)
		tmp = 1.0 + ((x - z) * (4.0 / y));
	elseif (z <= 6.2e+76)
		tmp = 4.0 + (4.0 * (x / y));
	else
		tmp = 4.0 + ((z / y) * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.22e+161], N[(1.0 + N[(N[(x - z), $MachinePrecision] * N[(4.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+76], N[(4.0 + N[(4.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.0 + N[(N[(z / y), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.22e161

   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/ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 92.1%

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

   if -2.22e161 < z < 6.20000000000000023e76

   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. *-commutative 99.9%

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

      3. associate-*r/ 99.2%

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

      4. fma-def 99.1%

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

      5. associate--l+ 99.1%

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

      6. --rgt-identity 99.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x - 0\right)} + \left(y \cdot 0.75 - z\right), \frac{4}{y}, 1\right) \]

      7. associate-+l- 99.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{x - \left(0 - \left(y \cdot 0.75 - z\right)\right)}, \frac{4}{y}, 1\right) \]

      8. sub-neg 99.1%

         \[\leadsto \mathsf{fma}\left(x - \left(0 - \color{blue}{\left(y \cdot 0.75 + \left(-z\right)\right)}\right), \frac{4}{y}, 1\right) \]

      9. associate--r+ 99.1%

         \[\leadsto \mathsf{fma}\left(x - \color{blue}{\left(\left(0 - y \cdot 0.75\right) - \left(-z\right)\right)}, \frac{4}{y}, 1\right) \]

      10. neg-sub0 99.1%

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

      11. distribute-rgt-neg-in 99.1%

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

      12. fma-neg 99.1%

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

      13. metadata-eval 99.1%

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

      14. remove-double-neg 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around inf 89.0%

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

      1. *-commutative 89.0%

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

   7. Simplified 89.0%

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

   if 6.20000000000000023e76 < z

   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. *-commutative 99.9%

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

      3. associate-*r/ 99.8%

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

      4. fma-def 99.8%

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

      5. associate--l+ 99.8%

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

      6. --rgt-identity 99.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x - 0\right)} + \left(y \cdot 0.75 - z\right), \frac{4}{y}, 1\right) \]

      7. associate-+l- 99.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{x - \left(0 - \left(y \cdot 0.75 - z\right)\right)}, \frac{4}{y}, 1\right) \]

      8. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(x - \left(0 - \color{blue}{\left(y \cdot 0.75 + \left(-z\right)\right)}\right), \frac{4}{y}, 1\right) \]

      9. associate--r+ 99.8%

         \[\leadsto \mathsf{fma}\left(x - \color{blue}{\left(\left(0 - y \cdot 0.75\right) - \left(-z\right)\right)}, \frac{4}{y}, 1\right) \]

      10. neg-sub0 99.8%

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

      11. distribute-rgt-neg-in 99.8%

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

      12. fma-neg 99.8%

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

      13. metadata-eval 99.8%

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

      14. remove-double-neg 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.22 \cdot 10^{+161}:\\ \;\;\;\;1 + \left(x - z\right) \cdot \frac{4}{y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+76}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + \frac{z}{y} \cdot -4\\ \end{array} \]

Alternative 7: 7.5% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 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/ 99.3%

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

   2. +-commutative 99.3%

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

   3. fma-def 99.3%

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

3. Simplified 99.3%

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

4. Taylor expanded in z around inf 35.3%

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

   1. associate-*r/ 35.3%

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

   2. metadata-eval 35.3%

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

   3. associate-*r* 35.3%

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

   4. neg-mul-1 35.3%

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

   5. associate-*l/ 35.2%

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

   6. *-commutative 35.2%

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

   7. associate-*r/ 35.3%

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

   8. neg-mul-1 35.3%

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

   9. *-commutative 35.3%

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

   10. associate-*l* 35.3%

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

   11. metadata-eval 35.3%

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

6. Simplified 35.3%

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

7. Taylor expanded in z around 0 8.2%

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

8. Final simplification 8.2%

   \[\leadsto 1 \]

Alternative 8: 33.5% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 4.0

Derivation

1. Initial program 99.9%

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]
2. 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. *-commutative 99.9%

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

   3. associate-*r/ 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. associate--l+ 99.3%

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

   6. --rgt-identity 99.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x - 0\right)} + \left(y \cdot 0.75 - z\right), \frac{4}{y}, 1\right) \]

   7. associate-+l- 99.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{x - \left(0 - \left(y \cdot 0.75 - z\right)\right)}, \frac{4}{y}, 1\right) \]

   8. sub-neg 99.3%

      \[\leadsto \mathsf{fma}\left(x - \left(0 - \color{blue}{\left(y \cdot 0.75 + \left(-z\right)\right)}\right), \frac{4}{y}, 1\right) \]

   9. associate--r+ 99.3%

      \[\leadsto \mathsf{fma}\left(x - \color{blue}{\left(\left(0 - y \cdot 0.75\right) - \left(-z\right)\right)}, \frac{4}{y}, 1\right) \]

   10. neg-sub0 99.3%

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

   11. distribute-rgt-neg-in 99.3%

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

   12. fma-neg 99.3%

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

   13. metadata-eval 99.3%

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

   14. 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. Taylor expanded in y around inf 39.2%

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

5. Final simplification 39.2%

   \[\leadsto 4 \]

Reproduce

herbie shell --seed 2023290 
(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)))