Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3

Percentage Accurate: 94.0% → 99.9%

Time: 6.4s

Alternatives: 11

Speedup: 1.0×

• 26.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))

C

double code(double x, double y) {
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((1.0d0 - x) * (3.0d0 - x)) / (y * 3.0d0)
end function

Java

public static double code(double x, double y) {
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0);
}

Python

def code(x, y):
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0)

Julia

function code(x, y)
	return Float64(Float64(Float64(1.0 - x) * Float64(3.0 - x)) / Float64(y * 3.0))
end

MATLAB

function tmp = code(x, y)
	tmp = ((1.0 - x) * (3.0 - x)) / (y * 3.0);
end

Wolfram

code[x_, y_] := N[(N[(N[(1.0 - x), $MachinePrecision] * N[(3.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))

C

double code(double x, double y) {
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((1.0d0 - x) * (3.0d0 - x)) / (y * 3.0d0)
end function

Java

public static double code(double x, double y) {
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0);
}

Python

def code(x, y):
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0)

Julia

function code(x, y)
	return Float64(Float64(Float64(1.0 - x) * Float64(3.0 - x)) / Float64(y * 3.0))
end

MATLAB

function tmp = code(x, y)
	tmp = ((1.0 - x) * (3.0 - x)) / (y * 3.0);
end

Wolfram

code[x_, y_] := N[(N[(N[(1.0 - x), $MachinePrecision] * N[(3.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1 - x}{y} \cdot \frac{3 - x}{3} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0)))

C

double code(double x, double y) {
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((1.0d0 - x) / y) * ((3.0d0 - x) / 3.0d0)
end function

Java

public static double code(double x, double y) {
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0);
}

Python

def code(x, y):
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0)

Julia

function code(x, y)
	return Float64(Float64(Float64(1.0 - x) / y) * Float64(Float64(3.0 - x) / 3.0))
end

MATLAB

function tmp = code(x, y)
	tmp = ((1.0 - x) / y) * ((3.0 - x) / 3.0);
end

Wolfram

code[x_, y_] := N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] * N[(N[(3.0 - x), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.5%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
2. Step-by-step derivation

   1. times-frac 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\frac{1 - x}{y} \cdot \frac{3 - x}{3}} \]
4. Add Preprocessing

5. Final simplification 99.9%

   \[\leadsto \frac{1 - x}{y} \cdot \frac{3 - x}{3} \]
6. Add Preprocessing

Alternative 2: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{x}{\frac{y}{-0.3333333333333333}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-0.3333333333333333 + x \cdot 0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.9)
   (* (- 1.0 x) (/ x (/ y -0.3333333333333333)))
   (if (<= x 3.0)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (* (/ x y) (+ -0.3333333333333333 (* x 0.3333333333333333))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.9) {
		tmp = (1.0 - x) * (x / (y / -0.3333333333333333));
	} else if (x <= 3.0) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = (x / y) * (-0.3333333333333333 + (x * 0.3333333333333333));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.9d0)) then
        tmp = (1.0d0 - x) * (x / (y / (-0.3333333333333333d0)))
    else if (x <= 3.0d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = (x / y) * ((-0.3333333333333333d0) + (x * 0.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.9) {
		tmp = (1.0 - x) * (x / (y / -0.3333333333333333));
	} else if (x <= 3.0) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = (x / y) * (-0.3333333333333333 + (x * 0.3333333333333333));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.9:
		tmp = (1.0 - x) * (x / (y / -0.3333333333333333))
	elif x <= 3.0:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = (x / y) * (-0.3333333333333333 + (x * 0.3333333333333333))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.9)
		tmp = Float64(Float64(1.0 - x) * Float64(x / Float64(y / -0.3333333333333333)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(-0.3333333333333333 + Float64(x * 0.3333333333333333)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.9)
		tmp = (1.0 - x) * (x / (y / -0.3333333333333333));
	elseif (x <= 3.0)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = (x / y) * (-0.3333333333333333 + (x * 0.3333333333333333));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.9], N[(N[(1.0 - x), $MachinePrecision] * N[(x / N[(y / -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(-0.3333333333333333 + N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.89999999999999991

   1. Initial program 85.1%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 85.1%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. *-lft-identity 99.8%

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

      5. metadata-eval 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. metadata-eval 99.8%

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

      8. times-frac 99.8%

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

      9. *-commutative 99.8%

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

      10. neg-mul-1 99.8%

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

      11. distribute-rgt-neg-in 99.8%

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

      12. times-frac 99.6%

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

      13. metadata-eval 99.6%

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

      14. metadata-eval 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

      15. metadata-eval 99.6%

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

      16. distribute-lft-neg-in 99.6%

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

      17. distribute-frac-neg 99.6%

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

      18. sub-neg 99.6%

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

      19. +-commutative 99.6%

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

      20. distribute-neg-in 99.6%

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

      21. remove-double-neg 99.6%

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

      22. metadata-eval 99.6%

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

      23. metadata-eval 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 99.6%

      \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\frac{x}{y}} \cdot -0.3333333333333333\right) \]
   6. Step-by-step derivation

      1. associate-*l/ 99.5%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{x \cdot -0.3333333333333333}{y}} \]

      2. associate-/l* 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{x}{\frac{y}{-0.3333333333333333}}} \]

   7. Applied egg-rr 99.7%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{x}{\frac{y}{-0.3333333333333333}}} \]

   if -3.89999999999999991 < x < 3

   1. Initial program 98.4%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 98.4%

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

      2. associate-*l/ 98.4%

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

      3. *-commutative 98.4%

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

      4. *-lft-identity 98.4%

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

      5. metadata-eval 98.4%

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

      6. distribute-lft-neg-in 98.4%

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

      7. metadata-eval 98.4%

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

      8. times-frac 98.4%

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

      9. *-commutative 98.4%

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

      10. neg-mul-1 98.4%

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

      11. distribute-rgt-neg-in 98.4%

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

      12. times-frac 98.8%

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

      13. metadata-eval 98.8%

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

      14. metadata-eval 98.8%

          \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

      15. metadata-eval 98.8%

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

      16. distribute-lft-neg-in 98.8%

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

      17. distribute-frac-neg 98.8%

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

      18. sub-neg 98.8%

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

      19. +-commutative 98.8%

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

      20. distribute-neg-in 98.8%

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

      21. remove-double-neg 98.8%

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

      22. metadata-eval 98.8%

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

      23. metadata-eval 98.8%

          \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\left(x + -3\right) \cdot -0.3333333333333333}{y}} \]

      2. metadata-eval 100.0%

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

      3. div-inv 100.0%

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

      4. associate-*r/ 100.0%

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

      5. associate-/l* 100.0%

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

      6. frac-2neg 100.0%

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

      7. +-commutative 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. sub-neg 100.0%

          \[\leadsto \frac{1 - x}{\frac{y}{\frac{\color{blue}{3 - x}}{--3}}} \]

      11. metadata-eval 100.0%

          \[\leadsto \frac{1 - x}{\frac{y}{\frac{3 - x}{\color{blue}{3}}}} \]

      12. associate-/l* 100.0%

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

      13. div-sub 100.0%

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

      14. metadata-eval 100.0%

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

      15. div-inv 100.0%

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

      16. metadata-eval 100.0%

          \[\leadsto \frac{\left(1 - x\right) \cdot \left(1 - x \cdot \color{blue}{0.3333333333333333}\right)}{y} \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot \left(1 - x \cdot 0.3333333333333333\right)}{y}} \]

   7. Taylor expanded in x around 0 99.0%

      \[\leadsto \frac{\color{blue}{1 + -1.3333333333333333 \cdot x}}{y} \]

   if 3 < x

   1. Initial program 87.1%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.1%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. *-lft-identity 99.8%

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

      5. metadata-eval 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. metadata-eval 99.8%

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

      8. times-frac 99.8%

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

      9. *-commutative 99.8%

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

      10. neg-mul-1 99.8%

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

      11. distribute-rgt-neg-in 99.8%

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

      12. times-frac 99.8%

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

      13. metadata-eval 99.8%

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

      14. metadata-eval 99.8%

          \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

      15. metadata-eval 99.8%

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

      16. distribute-lft-neg-in 99.8%

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

      17. distribute-frac-neg 99.8%

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

      18. sub-neg 99.8%

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

      19. +-commutative 99.8%

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

      20. distribute-neg-in 99.8%

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

      21. remove-double-neg 99.8%

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

      22. metadata-eval 99.8%

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

      23. metadata-eval 99.8%

          \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 98.9%

      \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\frac{x}{y}} \cdot -0.3333333333333333\right) \]

   6. Taylor expanded in x around 0 52.8%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]
   7. Step-by-step derivation

      1. *-commutative 52.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot -0.3333333333333333} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      2. associate-*r/ 52.9%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \color{blue}{\frac{0.3333333333333333 \cdot {x}^{2}}{y}} \]

      3. unpow2 52.9%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{0.3333333333333333 \cdot \color{blue}{\left(x \cdot x\right)}}{y} \]

      4. associate-*r* 52.9%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(0.3333333333333333 \cdot x\right) \cdot x}}{y} \]

      5. *-commutative 52.9%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(x \cdot 0.3333333333333333\right)} \cdot x}{y} \]

      6. metadata-eval 52.9%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\left(x \cdot \color{blue}{\left(--0.3333333333333333\right)}\right) \cdot x}{y} \]

      7. distribute-rgt-neg-in 52.9%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(-x \cdot -0.3333333333333333\right)} \cdot x}{y} \]

      8. distribute-lft-neg-in 52.9%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(\left(-x\right) \cdot -0.3333333333333333\right)} \cdot x}{y} \]

      9. associate-*r* 52.9%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(-x\right) \cdot \left(-0.3333333333333333 \cdot x\right)}}{y} \]

      10. *-commutative 52.9%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\left(-x\right) \cdot \color{blue}{\left(x \cdot -0.3333333333333333\right)}}{y} \]

      11. associate-*r/ 65.6%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \color{blue}{\left(-x\right) \cdot \frac{x \cdot -0.3333333333333333}{y}} \]

      12. associate-*l/ 65.6%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \left(-x\right) \cdot \color{blue}{\left(\frac{x}{y} \cdot -0.3333333333333333\right)} \]

      13. *-commutative 65.6%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \color{blue}{\left(\frac{x}{y} \cdot -0.3333333333333333\right) \cdot \left(-x\right)} \]

      14. associate-*l* 65.6%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \color{blue}{\frac{x}{y} \cdot \left(-0.3333333333333333 \cdot \left(-x\right)\right)} \]

      15. *-commutative 65.6%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{x}{y} \cdot \color{blue}{\left(\left(-x\right) \cdot -0.3333333333333333\right)} \]

      16. distribute-lft-neg-in 65.6%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{x}{y} \cdot \color{blue}{\left(-x \cdot -0.3333333333333333\right)} \]

      17. distribute-rgt-neg-in 65.6%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{x}{y} \cdot \color{blue}{\left(x \cdot \left(--0.3333333333333333\right)\right)} \]

      18. metadata-eval 65.6%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{x}{y} \cdot \left(x \cdot \color{blue}{0.3333333333333333}\right) \]

      19. distribute-lft-out 99.0%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-0.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   8. Simplified 99.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-0.3333333333333333 + x \cdot 0.3333333333333333\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{x}{\frac{y}{-0.3333333333333333}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-0.3333333333333333 + x \cdot 0.3333333333333333\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{x}{\frac{y}{-0.3333333333333333}}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x - 3}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.9)
   (* (- 1.0 x) (/ x (/ y -0.3333333333333333)))
   (if (<= x 1.3)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (* (/ x y) (/ (- x 3.0) 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.9) {
		tmp = (1.0 - x) * (x / (y / -0.3333333333333333));
	} else if (x <= 1.3) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = (x / y) * ((x - 3.0) / 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.9d0)) then
        tmp = (1.0d0 - x) * (x / (y / (-0.3333333333333333d0)))
    else if (x <= 1.3d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = (x / y) * ((x - 3.0d0) / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.9) {
		tmp = (1.0 - x) * (x / (y / -0.3333333333333333));
	} else if (x <= 1.3) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = (x / y) * ((x - 3.0) / 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.9:
		tmp = (1.0 - x) * (x / (y / -0.3333333333333333))
	elif x <= 1.3:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = (x / y) * ((x - 3.0) / 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.9)
		tmp = Float64(Float64(1.0 - x) * Float64(x / Float64(y / -0.3333333333333333)));
	elseif (x <= 1.3)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(Float64(x - 3.0) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.9)
		tmp = (1.0 - x) * (x / (y / -0.3333333333333333));
	elseif (x <= 1.3)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = (x / y) * ((x - 3.0) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.9], N[(N[(1.0 - x), $MachinePrecision] * N[(x / N[(y / -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.89999999999999991

   1. Initial program 85.1%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 85.1%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. *-lft-identity 99.8%

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

      5. metadata-eval 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. metadata-eval 99.8%

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

      8. times-frac 99.8%

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

      9. *-commutative 99.8%

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

      10. neg-mul-1 99.8%

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

      11. distribute-rgt-neg-in 99.8%

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

      12. times-frac 99.6%

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

      13. metadata-eval 99.6%

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

      14. metadata-eval 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

      15. metadata-eval 99.6%

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

      16. distribute-lft-neg-in 99.6%

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

      17. distribute-frac-neg 99.6%

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

      18. sub-neg 99.6%

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

      19. +-commutative 99.6%

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

      20. distribute-neg-in 99.6%

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

      21. remove-double-neg 99.6%

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

      22. metadata-eval 99.6%

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

      23. metadata-eval 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 99.6%

      \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\frac{x}{y}} \cdot -0.3333333333333333\right) \]
   6. Step-by-step derivation

      1. associate-*l/ 99.5%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{x \cdot -0.3333333333333333}{y}} \]

      2. associate-/l* 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{x}{\frac{y}{-0.3333333333333333}}} \]

   7. Applied egg-rr 99.7%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{x}{\frac{y}{-0.3333333333333333}}} \]

   if -3.89999999999999991 < x < 1.30000000000000004

   1. Initial program 98.4%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 98.4%

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

      2. associate-*l/ 98.4%

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

      3. *-commutative 98.4%

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

      4. *-lft-identity 98.4%

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

      5. metadata-eval 98.4%

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

      6. distribute-lft-neg-in 98.4%

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

      7. metadata-eval 98.4%

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

      8. times-frac 98.4%

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

      9. *-commutative 98.4%

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

      10. neg-mul-1 98.4%

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

      11. distribute-rgt-neg-in 98.4%

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

      12. times-frac 98.8%

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

      13. metadata-eval 98.8%

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

      14. metadata-eval 98.8%

          \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

      15. metadata-eval 98.8%

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

      16. distribute-lft-neg-in 98.8%

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

      17. distribute-frac-neg 98.8%

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

      18. sub-neg 98.8%

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

      19. +-commutative 98.8%

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

      20. distribute-neg-in 98.8%

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

      21. remove-double-neg 98.8%

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

      22. metadata-eval 98.8%

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

      23. metadata-eval 98.8%

          \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\left(x + -3\right) \cdot -0.3333333333333333}{y}} \]

      2. metadata-eval 100.0%

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

      3. div-inv 100.0%

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

      4. associate-*r/ 100.0%

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

      5. associate-/l* 100.0%

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

      6. frac-2neg 100.0%

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

      7. +-commutative 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. sub-neg 100.0%

          \[\leadsto \frac{1 - x}{\frac{y}{\frac{\color{blue}{3 - x}}{--3}}} \]

      11. metadata-eval 100.0%

          \[\leadsto \frac{1 - x}{\frac{y}{\frac{3 - x}{\color{blue}{3}}}} \]

      12. associate-/l* 100.0%

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

      13. div-sub 100.0%

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

      14. metadata-eval 100.0%

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

      15. div-inv 100.0%

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

      16. metadata-eval 100.0%

          \[\leadsto \frac{\left(1 - x\right) \cdot \left(1 - x \cdot \color{blue}{0.3333333333333333}\right)}{y} \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot \left(1 - x \cdot 0.3333333333333333\right)}{y}} \]

   7. Taylor expanded in x around 0 99.0%

      \[\leadsto \frac{\color{blue}{1 + -1.3333333333333333 \cdot x}}{y} \]

   if 1.30000000000000004 < x

   1. Initial program 87.1%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. times-frac 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{1 - x}{y} \cdot \frac{3 - x}{3}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 99.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{y}\right)} \cdot \frac{3 - x}{3} \]
   6. Step-by-step derivation

      1. neg-mul-1 99.1%

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

      2. distribute-neg-frac 99.1%

         \[\leadsto \color{blue}{\frac{-x}{y}} \cdot \frac{3 - x}{3} \]

   7. Simplified 99.1%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{x}{\frac{y}{-0.3333333333333333}}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x - 3}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.8) (not (<= x 3.0)))
   (* (/ x y) (* x 0.3333333333333333))
   (* (- 1.0 x) (/ 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = (x / y) * (x * 0.3333333333333333);
	} else {
		tmp = (1.0 - x) * (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-3.8d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = (x / y) * (x * 0.3333333333333333d0)
    else
        tmp = (1.0d0 - x) * (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = (x / y) * (x * 0.3333333333333333);
	} else {
		tmp = (1.0 - x) * (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.8) or not (x <= 3.0):
		tmp = (x / y) * (x * 0.3333333333333333)
	else:
		tmp = (1.0 - x) * (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.8) || !(x <= 3.0))
		tmp = Float64(Float64(x / y) * Float64(x * 0.3333333333333333));
	else
		tmp = Float64(Float64(1.0 - x) * Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -3.8) || ~((x <= 3.0)))
		tmp = (x / y) * (x * 0.3333333333333333);
	else
		tmp = (1.0 - x) * (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.8], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 86.2%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 86.2%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. *-lft-identity 99.8%

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

      5. metadata-eval 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. metadata-eval 99.8%

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

      8. times-frac 99.8%

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

      9. *-commutative 99.8%

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

      10. neg-mul-1 99.8%

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

      11. distribute-rgt-neg-in 99.8%

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

      12. times-frac 99.7%

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

      13. metadata-eval 99.7%

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

      14. metadata-eval 99.7%

          \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

      15. metadata-eval 99.7%

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

      16. distribute-lft-neg-in 99.7%

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

      17. distribute-frac-neg 99.7%

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

      18. sub-neg 99.7%

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

      19. +-commutative 99.7%

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

      20. distribute-neg-in 99.7%

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

      21. remove-double-neg 99.7%

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

      22. metadata-eval 99.7%

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

      23. metadata-eval 99.7%

          \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 99.2%

      \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\frac{x}{y}} \cdot -0.3333333333333333\right) \]

   6. Taylor expanded in x around 0 67.8%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]
   7. Step-by-step derivation

      1. *-commutative 67.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot -0.3333333333333333} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      2. associate-*r/ 67.8%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \color{blue}{\frac{0.3333333333333333 \cdot {x}^{2}}{y}} \]

      3. unpow2 67.8%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{0.3333333333333333 \cdot \color{blue}{\left(x \cdot x\right)}}{y} \]

      4. associate-*r* 67.8%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(0.3333333333333333 \cdot x\right) \cdot x}}{y} \]

      5. *-commutative 67.8%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(x \cdot 0.3333333333333333\right)} \cdot x}{y} \]

      6. metadata-eval 67.8%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\left(x \cdot \color{blue}{\left(--0.3333333333333333\right)}\right) \cdot x}{y} \]

      7. distribute-rgt-neg-in 67.8%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(-x \cdot -0.3333333333333333\right)} \cdot x}{y} \]

      8. distribute-lft-neg-in 67.8%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(\left(-x\right) \cdot -0.3333333333333333\right)} \cdot x}{y} \]

      9. associate-*r* 67.8%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(-x\right) \cdot \left(-0.3333333333333333 \cdot x\right)}}{y} \]

      10. *-commutative 67.8%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\left(-x\right) \cdot \color{blue}{\left(x \cdot -0.3333333333333333\right)}}{y} \]

      11. associate-*r/ 81.3%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \color{blue}{\left(-x\right) \cdot \frac{x \cdot -0.3333333333333333}{y}} \]

      12. associate-*l/ 81.4%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \left(-x\right) \cdot \color{blue}{\left(\frac{x}{y} \cdot -0.3333333333333333\right)} \]

      13. *-commutative 81.4%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \color{blue}{\left(\frac{x}{y} \cdot -0.3333333333333333\right) \cdot \left(-x\right)} \]

      14. associate-*l* 81.4%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \color{blue}{\frac{x}{y} \cdot \left(-0.3333333333333333 \cdot \left(-x\right)\right)} \]

      15. *-commutative 81.4%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{x}{y} \cdot \color{blue}{\left(\left(-x\right) \cdot -0.3333333333333333\right)} \]

      16. distribute-lft-neg-in 81.4%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{x}{y} \cdot \color{blue}{\left(-x \cdot -0.3333333333333333\right)} \]

      17. distribute-rgt-neg-in 81.4%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{x}{y} \cdot \color{blue}{\left(x \cdot \left(--0.3333333333333333\right)\right)} \]

      18. metadata-eval 81.4%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{x}{y} \cdot \left(x \cdot \color{blue}{0.3333333333333333}\right) \]

      19. distribute-lft-out 99.3%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-0.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   8. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-0.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   9. Taylor expanded in x around inf 99.3%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(0.3333333333333333 \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 99.3%

          \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(x \cdot 0.3333333333333333\right)} \]

   11. Simplified 99.3%

       \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(x \cdot 0.3333333333333333\right)} \]

   if -3.7999999999999998 < x < 3

   1. Initial program 98.4%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 98.4%

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

      2. associate-*l/ 98.4%

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

      3. *-commutative 98.4%

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

      4. *-lft-identity 98.4%

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

      5. metadata-eval 98.4%

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

      6. distribute-lft-neg-in 98.4%

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

      7. metadata-eval 98.4%

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

      8. times-frac 98.4%

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

      9. *-commutative 98.4%

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

      10. neg-mul-1 98.4%

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

      11. distribute-rgt-neg-in 98.4%

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

      12. times-frac 98.8%

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

      13. metadata-eval 98.8%

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

      14. metadata-eval 98.8%

          \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

      15. metadata-eval 98.8%

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

      16. distribute-lft-neg-in 98.8%

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

      17. distribute-frac-neg 98.8%

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

      18. sub-neg 98.8%

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

      19. +-commutative 98.8%

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

      20. distribute-neg-in 98.8%

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

      21. remove-double-neg 98.8%

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

      22. metadata-eval 98.8%

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

      23. metadata-eval 98.8%

          \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 97.4%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.8) (not (<= x 3.0)))
   (* (/ x y) (* x 0.3333333333333333))
   (/ (+ (* x -1.3333333333333333) 1.0) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.8) || !(x <= 3.0)) {
		tmp = (x / y) * (x * 0.3333333333333333);
	} else {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-4.8d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = (x / y) * (x * 0.3333333333333333d0)
    else
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4.8) || !(x <= 3.0)) {
		tmp = (x / y) * (x * 0.3333333333333333);
	} else {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.8) or not (x <= 3.0):
		tmp = (x / y) * (x * 0.3333333333333333)
	else:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.8) || !(x <= 3.0))
		tmp = Float64(Float64(x / y) * Float64(x * 0.3333333333333333));
	else
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.8) || ~((x <= 3.0)))
		tmp = (x / y) * (x * 0.3333333333333333);
	else
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.8], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999982 or 3 < x

   1. Initial program 86.2%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 86.2%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. *-lft-identity 99.8%

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

      5. metadata-eval 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. metadata-eval 99.8%

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

      8. times-frac 99.8%

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

      9. *-commutative 99.8%

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

      10. neg-mul-1 99.8%

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

      11. distribute-rgt-neg-in 99.8%

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

      12. times-frac 99.7%

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

      13. metadata-eval 99.7%

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

      14. metadata-eval 99.7%

          \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

      15. metadata-eval 99.7%

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

      16. distribute-lft-neg-in 99.7%

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

      17. distribute-frac-neg 99.7%

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

      18. sub-neg 99.7%

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

      19. +-commutative 99.7%

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

      20. distribute-neg-in 99.7%

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

      21. remove-double-neg 99.7%

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

      22. metadata-eval 99.7%

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

      23. metadata-eval 99.7%

          \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 99.2%

      \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\frac{x}{y}} \cdot -0.3333333333333333\right) \]

   6. Taylor expanded in x around 0 67.8%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]
   7. Step-by-step derivation

      1. *-commutative 67.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot -0.3333333333333333} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      2. associate-*r/ 67.8%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \color{blue}{\frac{0.3333333333333333 \cdot {x}^{2}}{y}} \]

      3. unpow2 67.8%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{0.3333333333333333 \cdot \color{blue}{\left(x \cdot x\right)}}{y} \]

      4. associate-*r* 67.8%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(0.3333333333333333 \cdot x\right) \cdot x}}{y} \]

      5. *-commutative 67.8%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(x \cdot 0.3333333333333333\right)} \cdot x}{y} \]

      6. metadata-eval 67.8%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\left(x \cdot \color{blue}{\left(--0.3333333333333333\right)}\right) \cdot x}{y} \]

      7. distribute-rgt-neg-in 67.8%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(-x \cdot -0.3333333333333333\right)} \cdot x}{y} \]

      8. distribute-lft-neg-in 67.8%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(\left(-x\right) \cdot -0.3333333333333333\right)} \cdot x}{y} \]

      9. associate-*r* 67.8%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(-x\right) \cdot \left(-0.3333333333333333 \cdot x\right)}}{y} \]

      10. *-commutative 67.8%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\left(-x\right) \cdot \color{blue}{\left(x \cdot -0.3333333333333333\right)}}{y} \]

      11. associate-*r/ 81.3%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \color{blue}{\left(-x\right) \cdot \frac{x \cdot -0.3333333333333333}{y}} \]

      12. associate-*l/ 81.4%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \left(-x\right) \cdot \color{blue}{\left(\frac{x}{y} \cdot -0.3333333333333333\right)} \]

      13. *-commutative 81.4%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \color{blue}{\left(\frac{x}{y} \cdot -0.3333333333333333\right) \cdot \left(-x\right)} \]

      14. associate-*l* 81.4%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \color{blue}{\frac{x}{y} \cdot \left(-0.3333333333333333 \cdot \left(-x\right)\right)} \]

      15. *-commutative 81.4%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{x}{y} \cdot \color{blue}{\left(\left(-x\right) \cdot -0.3333333333333333\right)} \]

      16. distribute-lft-neg-in 81.4%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{x}{y} \cdot \color{blue}{\left(-x \cdot -0.3333333333333333\right)} \]

      17. distribute-rgt-neg-in 81.4%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{x}{y} \cdot \color{blue}{\left(x \cdot \left(--0.3333333333333333\right)\right)} \]

      18. metadata-eval 81.4%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{x}{y} \cdot \left(x \cdot \color{blue}{0.3333333333333333}\right) \]

      19. distribute-lft-out 99.3%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-0.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   8. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-0.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   9. Taylor expanded in x around inf 99.3%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(0.3333333333333333 \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 99.3%

          \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(x \cdot 0.3333333333333333\right)} \]

   11. Simplified 99.3%

       \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(x \cdot 0.3333333333333333\right)} \]

   if -4.79999999999999982 < x < 3

   1. Initial program 98.4%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 98.4%

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

      2. associate-*l/ 98.4%

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

      3. *-commutative 98.4%

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

      4. *-lft-identity 98.4%

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

      5. metadata-eval 98.4%

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

      6. distribute-lft-neg-in 98.4%

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

      7. metadata-eval 98.4%

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

      8. times-frac 98.4%

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

      9. *-commutative 98.4%

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

      10. neg-mul-1 98.4%

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

      11. distribute-rgt-neg-in 98.4%

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

      12. times-frac 98.8%

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

      13. metadata-eval 98.8%

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

      14. metadata-eval 98.8%

          \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

      15. metadata-eval 98.8%

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

      16. distribute-lft-neg-in 98.8%

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

      17. distribute-frac-neg 98.8%

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

      18. sub-neg 98.8%

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

      19. +-commutative 98.8%

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

      20. distribute-neg-in 98.8%

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

      21. remove-double-neg 98.8%

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

      22. metadata-eval 98.8%

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

      23. metadata-eval 98.8%

          \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\left(x + -3\right) \cdot -0.3333333333333333}{y}} \]

      2. metadata-eval 100.0%

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

      3. div-inv 100.0%

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

      4. associate-*r/ 100.0%

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

      5. associate-/l* 100.0%

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

      6. frac-2neg 100.0%

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

      7. +-commutative 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. sub-neg 100.0%

          \[\leadsto \frac{1 - x}{\frac{y}{\frac{\color{blue}{3 - x}}{--3}}} \]

      11. metadata-eval 100.0%

          \[\leadsto \frac{1 - x}{\frac{y}{\frac{3 - x}{\color{blue}{3}}}} \]

      12. associate-/l* 100.0%

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

      13. div-sub 100.0%

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

      14. metadata-eval 100.0%

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

      15. div-inv 100.0%

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

      16. metadata-eval 100.0%

          \[\leadsto \frac{\left(1 - x\right) \cdot \left(1 - x \cdot \color{blue}{0.3333333333333333}\right)}{y} \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot \left(1 - x \cdot 0.3333333333333333\right)}{y}} \]

   7. Taylor expanded in x around 0 99.0%

      \[\leadsto \frac{\color{blue}{1 + -1.3333333333333333 \cdot x}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{x}{\frac{y}{-0.3333333333333333}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.9)
   (* (- 1.0 x) (/ x (/ y -0.3333333333333333)))
   (if (<= x 3.0)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (* (/ x y) (* x 0.3333333333333333)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.9) {
		tmp = (1.0 - x) * (x / (y / -0.3333333333333333));
	} else if (x <= 3.0) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = (x / y) * (x * 0.3333333333333333);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.9d0)) then
        tmp = (1.0d0 - x) * (x / (y / (-0.3333333333333333d0)))
    else if (x <= 3.0d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = (x / y) * (x * 0.3333333333333333d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.9) {
		tmp = (1.0 - x) * (x / (y / -0.3333333333333333));
	} else if (x <= 3.0) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = (x / y) * (x * 0.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.9:
		tmp = (1.0 - x) * (x / (y / -0.3333333333333333))
	elif x <= 3.0:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = (x / y) * (x * 0.3333333333333333)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.9)
		tmp = Float64(Float64(1.0 - x) * Float64(x / Float64(y / -0.3333333333333333)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(x * 0.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.9)
		tmp = (1.0 - x) * (x / (y / -0.3333333333333333));
	elseif (x <= 3.0)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = (x / y) * (x * 0.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.9], N[(N[(1.0 - x), $MachinePrecision] * N[(x / N[(y / -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.89999999999999991

   1. Initial program 85.1%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 85.1%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. *-lft-identity 99.8%

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

      5. metadata-eval 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. metadata-eval 99.8%

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

      8. times-frac 99.8%

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

      9. *-commutative 99.8%

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

      10. neg-mul-1 99.8%

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

      11. distribute-rgt-neg-in 99.8%

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

      12. times-frac 99.6%

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

      13. metadata-eval 99.6%

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

      14. metadata-eval 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

      15. metadata-eval 99.6%

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

      16. distribute-lft-neg-in 99.6%

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

      17. distribute-frac-neg 99.6%

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

      18. sub-neg 99.6%

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

      19. +-commutative 99.6%

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

      20. distribute-neg-in 99.6%

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

      21. remove-double-neg 99.6%

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

      22. metadata-eval 99.6%

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

      23. metadata-eval 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 99.6%

      \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\frac{x}{y}} \cdot -0.3333333333333333\right) \]
   6. Step-by-step derivation

      1. associate-*l/ 99.5%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{x \cdot -0.3333333333333333}{y}} \]

      2. associate-/l* 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{x}{\frac{y}{-0.3333333333333333}}} \]

   7. Applied egg-rr 99.7%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{x}{\frac{y}{-0.3333333333333333}}} \]

   if -3.89999999999999991 < x < 3

   1. Initial program 98.4%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 98.4%

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

      2. associate-*l/ 98.4%

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

      3. *-commutative 98.4%

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

      4. *-lft-identity 98.4%

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

      5. metadata-eval 98.4%

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

      6. distribute-lft-neg-in 98.4%

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

      7. metadata-eval 98.4%

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

      8. times-frac 98.4%

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

      9. *-commutative 98.4%

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

      10. neg-mul-1 98.4%

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

      11. distribute-rgt-neg-in 98.4%

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

      12. times-frac 98.8%

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

      13. metadata-eval 98.8%

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

      14. metadata-eval 98.8%

          \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

      15. metadata-eval 98.8%

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

      16. distribute-lft-neg-in 98.8%

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

      17. distribute-frac-neg 98.8%

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

      18. sub-neg 98.8%

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

      19. +-commutative 98.8%

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

      20. distribute-neg-in 98.8%

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

      21. remove-double-neg 98.8%

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

      22. metadata-eval 98.8%

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

      23. metadata-eval 98.8%

          \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\left(x + -3\right) \cdot -0.3333333333333333}{y}} \]

      2. metadata-eval 100.0%

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

      3. div-inv 100.0%

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

      4. associate-*r/ 100.0%

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

      5. associate-/l* 100.0%

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

      6. frac-2neg 100.0%

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

      7. +-commutative 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. sub-neg 100.0%

          \[\leadsto \frac{1 - x}{\frac{y}{\frac{\color{blue}{3 - x}}{--3}}} \]

      11. metadata-eval 100.0%

          \[\leadsto \frac{1 - x}{\frac{y}{\frac{3 - x}{\color{blue}{3}}}} \]

      12. associate-/l* 100.0%

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

      13. div-sub 100.0%

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

      14. metadata-eval 100.0%

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

      15. div-inv 100.0%

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

      16. metadata-eval 100.0%

          \[\leadsto \frac{\left(1 - x\right) \cdot \left(1 - x \cdot \color{blue}{0.3333333333333333}\right)}{y} \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot \left(1 - x \cdot 0.3333333333333333\right)}{y}} \]

   7. Taylor expanded in x around 0 99.0%

      \[\leadsto \frac{\color{blue}{1 + -1.3333333333333333 \cdot x}}{y} \]

   if 3 < x

   1. Initial program 87.1%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.1%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. *-lft-identity 99.8%

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

      5. metadata-eval 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. metadata-eval 99.8%

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

      8. times-frac 99.8%

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

      9. *-commutative 99.8%

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

      10. neg-mul-1 99.8%

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

      11. distribute-rgt-neg-in 99.8%

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

      12. times-frac 99.8%

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

      13. metadata-eval 99.8%

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

      14. metadata-eval 99.8%

          \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

      15. metadata-eval 99.8%

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

      16. distribute-lft-neg-in 99.8%

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

      17. distribute-frac-neg 99.8%

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

      18. sub-neg 99.8%

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

      19. +-commutative 99.8%

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

      20. distribute-neg-in 99.8%

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

      21. remove-double-neg 99.8%

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

      22. metadata-eval 99.8%

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

      23. metadata-eval 99.8%

          \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 98.9%

      \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\frac{x}{y}} \cdot -0.3333333333333333\right) \]

   6. Taylor expanded in x around 0 52.8%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]
   7. Step-by-step derivation

      1. *-commutative 52.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot -0.3333333333333333} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      2. associate-*r/ 52.9%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \color{blue}{\frac{0.3333333333333333 \cdot {x}^{2}}{y}} \]

      3. unpow2 52.9%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{0.3333333333333333 \cdot \color{blue}{\left(x \cdot x\right)}}{y} \]

      4. associate-*r* 52.9%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(0.3333333333333333 \cdot x\right) \cdot x}}{y} \]

      5. *-commutative 52.9%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(x \cdot 0.3333333333333333\right)} \cdot x}{y} \]

      6. metadata-eval 52.9%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\left(x \cdot \color{blue}{\left(--0.3333333333333333\right)}\right) \cdot x}{y} \]

      7. distribute-rgt-neg-in 52.9%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(-x \cdot -0.3333333333333333\right)} \cdot x}{y} \]

      8. distribute-lft-neg-in 52.9%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(\left(-x\right) \cdot -0.3333333333333333\right)} \cdot x}{y} \]

      9. associate-*r* 52.9%

         \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\color{blue}{\left(-x\right) \cdot \left(-0.3333333333333333 \cdot x\right)}}{y} \]

      10. *-commutative 52.9%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{\left(-x\right) \cdot \color{blue}{\left(x \cdot -0.3333333333333333\right)}}{y} \]

      11. associate-*r/ 65.6%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \color{blue}{\left(-x\right) \cdot \frac{x \cdot -0.3333333333333333}{y}} \]

      12. associate-*l/ 65.6%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \left(-x\right) \cdot \color{blue}{\left(\frac{x}{y} \cdot -0.3333333333333333\right)} \]

      13. *-commutative 65.6%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \color{blue}{\left(\frac{x}{y} \cdot -0.3333333333333333\right) \cdot \left(-x\right)} \]

      14. associate-*l* 65.6%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \color{blue}{\frac{x}{y} \cdot \left(-0.3333333333333333 \cdot \left(-x\right)\right)} \]

      15. *-commutative 65.6%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{x}{y} \cdot \color{blue}{\left(\left(-x\right) \cdot -0.3333333333333333\right)} \]

      16. distribute-lft-neg-in 65.6%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{x}{y} \cdot \color{blue}{\left(-x \cdot -0.3333333333333333\right)} \]

      17. distribute-rgt-neg-in 65.6%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{x}{y} \cdot \color{blue}{\left(x \cdot \left(--0.3333333333333333\right)\right)} \]

      18. metadata-eval 65.6%

          \[\leadsto \frac{x}{y} \cdot -0.3333333333333333 + \frac{x}{y} \cdot \left(x \cdot \color{blue}{0.3333333333333333}\right) \]

      19. distribute-lft-out 99.0%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-0.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   8. Simplified 99.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-0.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   9. Taylor expanded in x around inf 99.0%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(0.3333333333333333 \cdot x\right)} \]
   10. Step-by-step derivation

       1. *-commutative 99.0%

          \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(x \cdot 0.3333333333333333\right)} \]

   11. Simplified 99.0%

       \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(x \cdot 0.3333333333333333\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{x}{\frac{y}{-0.3333333333333333}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* (- 1.0 x) (* (/ (+ x -3.0) y) -0.3333333333333333)))

C

double code(double x, double y) {
	return (1.0 - x) * (((x + -3.0) / y) * -0.3333333333333333);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - x) * (((x + (-3.0d0)) / y) * (-0.3333333333333333d0))
end function

Java

public static double code(double x, double y) {
	return (1.0 - x) * (((x + -3.0) / y) * -0.3333333333333333);
}

Python

def code(x, y):
	return (1.0 - x) * (((x + -3.0) / y) * -0.3333333333333333)

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) * Float64(Float64(Float64(x + -3.0) / y) * -0.3333333333333333))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) * (((x + -3.0) / y) * -0.3333333333333333);
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] * N[(N[(N[(x + -3.0), $MachinePrecision] / y), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.5%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
2. Step-by-step derivation

   1. *-commutative 92.5%

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

   2. associate-*l/ 99.1%

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

   3. *-commutative 99.1%

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

   4. *-lft-identity 99.1%

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

   5. metadata-eval 99.1%

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

   6. distribute-lft-neg-in 99.1%

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

   7. metadata-eval 99.1%

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

   8. times-frac 99.1%

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

   9. *-commutative 99.1%

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

   10. neg-mul-1 99.1%

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

   11. distribute-rgt-neg-in 99.1%

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

   12. times-frac 99.2%

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

   13. metadata-eval 99.2%

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

   14. metadata-eval 99.2%

       \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   15. metadata-eval 99.2%

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

   16. distribute-lft-neg-in 99.2%

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

   17. distribute-frac-neg 99.2%

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

   18. sub-neg 99.2%

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

   19. +-commutative 99.2%

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

   20. distribute-neg-in 99.2%

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

   21. remove-double-neg 99.2%

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

   22. metadata-eval 99.2%

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

   23. metadata-eval 99.2%

       \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

3. Simplified 99.2%

   \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
4. Add Preprocessing

5. Final simplification 99.2%

   \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right) \]
6. Add Preprocessing

Alternative 8: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (- 1.0 x) (/ (/ (+ x -3.0) -3.0) y)))

C

double code(double x, double y) {
	return (1.0 - x) * (((x + -3.0) / -3.0) / y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - x) * (((x + (-3.0d0)) / (-3.0d0)) / y)
end function

Java

public static double code(double x, double y) {
	return (1.0 - x) * (((x + -3.0) / -3.0) / y);
}

Python

def code(x, y):
	return (1.0 - x) * (((x + -3.0) / -3.0) / y)

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) * Float64(Float64(Float64(x + -3.0) / -3.0) / y))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) * (((x + -3.0) / -3.0) / y);
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] * N[(N[(N[(x + -3.0), $MachinePrecision] / -3.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.5%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
2. Step-by-step derivation

   1. *-commutative 92.5%

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

   2. associate-*l/ 99.1%

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

   3. *-commutative 99.1%

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

   4. associate-/l/ 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

   \[\leadsto \left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y} \]
6. Add Preprocessing

Alternative 9: 58.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75) (* -1.3333333333333333 (/ x y)) (/ 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = -1.3333333333333333 * (x / y);
	} else {
		tmp = 1.0 / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.75d0)) then
        tmp = (-1.3333333333333333d0) * (x / y)
    else
        tmp = 1.0d0 / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = -1.3333333333333333 * (x / y);
	} else {
		tmp = 1.0 / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = -1.3333333333333333 * (x / y)
	else:
		tmp = 1.0 / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(-1.3333333333333333 * Float64(x / y));
	else
		tmp = Float64(1.0 / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.75)
		tmp = -1.3333333333333333 * (x / y);
	else
		tmp = 1.0 / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(-1.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(1.0 / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.75

   1. Initial program 85.1%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 85.1%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. *-lft-identity 99.8%

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

      5. metadata-eval 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. metadata-eval 99.8%

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

      8. times-frac 99.8%

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

      9. *-commutative 99.8%

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

      10. neg-mul-1 99.8%

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

      11. distribute-rgt-neg-in 99.8%

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

      12. times-frac 99.6%

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

      13. metadata-eval 99.6%

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

      14. metadata-eval 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

      15. metadata-eval 99.6%

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

      16. distribute-lft-neg-in 99.6%

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

      17. distribute-frac-neg 99.6%

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

      18. sub-neg 99.6%

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

      19. +-commutative 99.6%

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

      20. distribute-neg-in 99.6%

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

      21. remove-double-neg 99.6%

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

      22. metadata-eval 99.6%

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

      23. metadata-eval 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 24.5%

      \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}} \]

   6. Taylor expanded in x around inf 24.5%

      \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y}} \]

   if -0.75 < x

   1. Initial program 94.6%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 94.6%

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

      2. associate-*l/ 98.9%

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

      3. *-commutative 98.9%

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

      4. *-lft-identity 98.9%

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

      5. metadata-eval 98.9%

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

      6. distribute-lft-neg-in 98.9%

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

      7. metadata-eval 98.9%

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

      8. times-frac 98.9%

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

      9. *-commutative 98.9%

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

      10. neg-mul-1 98.9%

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

      11. distribute-rgt-neg-in 98.9%

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

      12. times-frac 99.1%

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

      13. metadata-eval 99.1%

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

      14. metadata-eval 99.1%

          \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

      15. metadata-eval 99.1%

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

      16. distribute-lft-neg-in 99.1%

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

      17. distribute-frac-neg 99.1%

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

      18. sub-neg 99.1%

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

      19. +-commutative 99.1%

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

      20. distribute-neg-in 99.1%

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

      21. remove-double-neg 99.1%

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

      22. metadata-eval 99.1%

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

      23. metadata-eval 99.1%

          \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   3. Simplified 99.1%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*l/ 99.9%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\left(x + -3\right) \cdot -0.3333333333333333}{y}} \]

      2. metadata-eval 99.9%

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

      3. div-inv 99.9%

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

      4. associate-*r/ 95.7%

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

      5. associate-/l* 99.9%

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

      6. frac-2neg 99.9%

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

      7. +-commutative 99.9%

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

      8. distribute-neg-in 99.9%

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

      9. metadata-eval 99.9%

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

      10. sub-neg 99.9%

          \[\leadsto \frac{1 - x}{\frac{y}{\frac{\color{blue}{3 - x}}{--3}}} \]

      11. metadata-eval 99.9%

          \[\leadsto \frac{1 - x}{\frac{y}{\frac{3 - x}{\color{blue}{3}}}} \]

      12. associate-/l* 95.7%

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

      13. div-sub 95.7%

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

      14. metadata-eval 95.7%

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

      15. div-inv 95.7%

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

      16. metadata-eval 95.7%

          \[\leadsto \frac{\left(1 - x\right) \cdot \left(1 - x \cdot \color{blue}{0.3333333333333333}\right)}{y} \]

   6. Applied egg-rr 95.7%

      \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot \left(1 - x \cdot 0.3333333333333333\right)}{y}} \]

   7. Taylor expanded in x around 0 66.6%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.0% accurate, 1.6× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (* (- 1.0 x) (/ 1.0 y)))

C

double code(double x, double y) {
	return (1.0 - x) * (1.0 / y);
}

Fortran

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

Java

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

Python

def code(x, y):
	return (1.0 - x) * (1.0 / y)

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) * Float64(1.0 / y))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) * (1.0 / y);
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.5%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
2. Step-by-step derivation

   1. *-commutative 92.5%

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

   2. associate-*l/ 99.1%

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

   3. *-commutative 99.1%

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

   4. *-lft-identity 99.1%

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

   5. metadata-eval 99.1%

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

   6. distribute-lft-neg-in 99.1%

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

   7. metadata-eval 99.1%

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

   8. times-frac 99.1%

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

   9. *-commutative 99.1%

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

   10. neg-mul-1 99.1%

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

   11. distribute-rgt-neg-in 99.1%

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

   12. times-frac 99.2%

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

   13. metadata-eval 99.2%

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

   14. metadata-eval 99.2%

       \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   15. metadata-eval 99.2%

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

   16. distribute-lft-neg-in 99.2%

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

   17. distribute-frac-neg 99.2%

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

   18. sub-neg 99.2%

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

   19. +-commutative 99.2%

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

   20. distribute-neg-in 99.2%

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

   21. remove-double-neg 99.2%

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

   22. metadata-eval 99.2%

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

   23. metadata-eval 99.2%

       \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

3. Simplified 99.2%

   \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 56.2%

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

6. Final simplification 56.2%

   \[\leadsto \left(1 - x\right) \cdot \frac{1}{y} \]
7. Add Preprocessing

Alternative 11: 51.4% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y)
	return Float64(1.0 / y)
end

MATLAB

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

Wolfram

code[x_, y_] := N[(1.0 / y), $MachinePrecision]

Derivation

1. Initial program 92.5%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
2. Step-by-step derivation

   1. *-commutative 92.5%

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

   2. associate-*l/ 99.1%

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

   3. *-commutative 99.1%

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

   4. *-lft-identity 99.1%

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

   5. metadata-eval 99.1%

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

   6. distribute-lft-neg-in 99.1%

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

   7. metadata-eval 99.1%

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

   8. times-frac 99.1%

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

   9. *-commutative 99.1%

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

   10. neg-mul-1 99.1%

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

   11. distribute-rgt-neg-in 99.1%

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

   12. times-frac 99.2%

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

   13. metadata-eval 99.2%

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

   14. metadata-eval 99.2%

       \[\leadsto \left(1 - x\right) \cdot \left(-\frac{3 - x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

   15. metadata-eval 99.2%

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

   16. distribute-lft-neg-in 99.2%

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

   17. distribute-frac-neg 99.2%

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

   18. sub-neg 99.2%

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

   19. +-commutative 99.2%

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

   20. distribute-neg-in 99.2%

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

   21. remove-double-neg 99.2%

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

   22. metadata-eval 99.2%

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

   23. metadata-eval 99.2%

       \[\leadsto \left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot \color{blue}{-0.3333333333333333}\right) \]

3. Simplified 99.2%

   \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\frac{x + -3}{y} \cdot -0.3333333333333333\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. associate-*l/ 99.8%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\left(x + -3\right) \cdot -0.3333333333333333}{y}} \]

   2. metadata-eval 99.8%

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

   3. div-inv 99.8%

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

   4. associate-*r/ 93.4%

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

   5. associate-/l* 99.9%

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

   6. frac-2neg 99.9%

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

   7. +-commutative 99.9%

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

   8. distribute-neg-in 99.9%

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

   9. metadata-eval 99.9%

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

   10. sub-neg 99.9%

       \[\leadsto \frac{1 - x}{\frac{y}{\frac{\color{blue}{3 - x}}{--3}}} \]

   11. metadata-eval 99.9%

       \[\leadsto \frac{1 - x}{\frac{y}{\frac{3 - x}{\color{blue}{3}}}} \]

   12. associate-/l* 93.4%

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

   13. div-sub 93.4%

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

   14. metadata-eval 93.4%

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

   15. div-inv 93.3%

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

   16. metadata-eval 93.3%

       \[\leadsto \frac{\left(1 - x\right) \cdot \left(1 - x \cdot \color{blue}{0.3333333333333333}\right)}{y} \]

6. Applied egg-rr 93.3%

   \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot \left(1 - x \cdot 0.3333333333333333\right)}{y}} \]

7. Taylor expanded in x around 0 52.8%

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

8. Final simplification 52.8%

   \[\leadsto \frac{1}{y} \]
9. Add Preprocessing

Developer target: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1 - x}{y} \cdot \frac{3 - x}{3} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0)))

C

double code(double x, double y) {
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((1.0d0 - x) / y) * ((3.0d0 - x) / 3.0d0)
end function

Java

public static double code(double x, double y) {
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0);
}

Python

def code(x, y):
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0)

Julia

function code(x, y)
	return Float64(Float64(Float64(1.0 - x) / y) * Float64(Float64(3.0 - x) / 3.0))
end

MATLAB

function tmp = code(x, y)
	tmp = ((1.0 - x) / y) * ((3.0 - x) / 3.0);
end

Wolfram

code[x_, y_] := N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] * N[(N[(3.0 - x), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024010 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0))

  (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))