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

Percentage Accurate: 94.0% → 99.8%

Time: 10.1s

Alternatives: 17

Speedup: 1.0×

• 24.8% 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: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	return ((1.0 - x) / y) * (1.0 - (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) * (1.0d0 - (x / 3.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

   1. times-frac 99.8%

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

   2. div-sub 99.8%

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

   3. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 97.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.0) || !(x <= 3.0)) {
		tmp = (1.0 - x) * (-0.3333333333333333 * (x / y));
	} 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 <= (-3.0d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = (1.0d0 - x) * ((-0.3333333333333333d0) * (x / y))
    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 <= -3.0) || !(x <= 3.0)) {
		tmp = (1.0 - x) * (-0.3333333333333333 * (x / y));
	} else {
		tmp = (1.0 - x) * (1.0 / y);
	}
	return tmp;
}

Python

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

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.0) || !(x <= 3.0))
		tmp = Float64(Float64(1.0 - x) * Float64(-0.3333333333333333 * Float64(x / y)));
	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 <= -3.0) || ~((x <= 3.0)))
		tmp = (1.0 - x) * (-0.3333333333333333 * (x / y));
	else
		tmp = (1.0 - x) * (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.0], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(N[(1.0 - x), $MachinePrecision] * N[(-0.3333333333333333 * N[(x / y), $MachinePrecision]), $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 or 3 < x

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

      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%

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

      5. associate-*l/ 99.8%

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

      6. *-commutative 99.8%

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

      7. *-commutative 99.8%

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

      8. associate-/r* 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 97.5%

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

   if -3 < x < 3

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*l/ 99.5%

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

      3. *-commutative 99.5%

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

      4. *-lft-identity 99.5%

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

      5. associate-*l/ 99.3%

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

      6. *-commutative 99.3%

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

      7. *-commutative 99.3%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 98.6%

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

4. Final simplification 98.0%

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

Alternative 3: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \lor \neg \left(x \leq 2.3\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-1.3333333333333333 - \frac{x}{-3}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.35) (not (<= x 2.3)))
   (* (/ x y) (- -1.3333333333333333 (/ x -3.0)))
   (* (- 1.0 x) (/ 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.35) || !(x <= 2.3)) {
		tmp = (x / y) * (-1.3333333333333333 - (x / -3.0));
	} 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 <= (-1.35d0)) .or. (.not. (x <= 2.3d0))) then
        tmp = (x / y) * ((-1.3333333333333333d0) - (x / (-3.0d0)))
    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 <= -1.35) || !(x <= 2.3)) {
		tmp = (x / y) * (-1.3333333333333333 - (x / -3.0));
	} else {
		tmp = (1.0 - x) * (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.35) or not (x <= 2.3):
		tmp = (x / y) * (-1.3333333333333333 - (x / -3.0))
	else:
		tmp = (1.0 - x) * (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.35) || !(x <= 2.3))
		tmp = Float64(Float64(x / y) * Float64(-1.3333333333333333 - Float64(x / -3.0)));
	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 <= -1.35) || ~((x <= 2.3)))
		tmp = (x / y) * (-1.3333333333333333 - (x / -3.0));
	else
		tmp = (1.0 - x) * (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.35], N[Not[LessEqual[x, 2.3]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(-1.3333333333333333 - N[(x / -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3500000000000001 or 2.2999999999999998 < x

   1. Initial program 89.1%

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

   2. Taylor expanded in x around inf 88.2%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 88.2%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 88.2%

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

      3. distribute-rgt-out 88.2%

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

   4. Simplified 88.2%

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

      1. associate-/l* 98.9%

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

      2. associate-/r/ 98.9%

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

   6. Applied egg-rr 98.9%

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

      1. *-commutative 98.9%

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

      2. clear-num 98.9%

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

      3. un-div-inv 98.9%

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

      4. *-commutative 98.9%

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

      5. associate-/l* 98.9%

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

   8. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\frac{x + -4}{\frac{3}{\frac{x}{y}}}} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 56.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x + -4}{\frac{3}{\frac{x}{y}}}\right)\right)} \]

      2. expm1-udef 45.7%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x + -4}{\frac{3}{\frac{x}{y}}}\right)} - 1} \]

      3. associate-/r/ 45.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x + -4}{3} \cdot \frac{x}{y}}\right)} - 1 \]

      4. *-commutative 45.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{y} \cdot \frac{x + -4}{3}}\right)} - 1 \]

      5. frac-2neg 45.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \color{blue}{\frac{-\left(x + -4\right)}{-3}}\right)} - 1 \]

      6. neg-sub0 45.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{\color{blue}{0 - \left(x + -4\right)}}{-3}\right)} - 1 \]

      7. +-commutative 45.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{0 - \color{blue}{\left(-4 + x\right)}}{-3}\right)} - 1 \]

      8. associate--r+ 45.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{\color{blue}{\left(0 - -4\right) - x}}{-3}\right)} - 1 \]

      9. metadata-eval 45.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{\color{blue}{4} - x}{-3}\right)} - 1 \]

      10. metadata-eval 45.7%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{4 - x}{\color{blue}{-3}}\right)} - 1 \]

   10. Applied egg-rr 45.7%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{4 - x}{-3}\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 56.1%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{4 - x}{-3}\right)\right)} \]

       2. expm1-log1p 98.8%

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

       3. div-sub 98.8%

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

       4. metadata-eval 98.8%

          \[\leadsto \frac{x}{y} \cdot \left(\color{blue}{-1.3333333333333333} - \frac{x}{-3}\right) \]

   12. Simplified 98.8%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-1.3333333333333333 - \frac{x}{-3}\right)} \]

   if -1.3500000000000001 < x < 2.2999999999999998

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*l/ 99.5%

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

      3. *-commutative 99.5%

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

      4. *-lft-identity 99.5%

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

      5. associate-*l/ 99.3%

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

      6. *-commutative 99.3%

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

      7. *-commutative 99.3%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 98.6%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \lor \neg \left(x \leq 2.3\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-1.3333333333333333 - \frac{x}{-3}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \end{array} \]

Alternative 4: 97.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.0) {
		tmp = (1.0 - x) * (-0.3333333333333333 * (x / y));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = (1.0 - x) * (x / (y / -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 <= (-3.0d0)) then
        tmp = (1.0d0 - x) * ((-0.3333333333333333d0) * (x / y))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 - x) * (1.0d0 / y)
    else
        tmp = (1.0d0 - x) * (x / (y / (-0.3333333333333333d0)))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3

   1. Initial program 90.4%

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

      1. *-commutative 90.4%

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

      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%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-/r* 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 96.8%

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

   if -3 < x < 3

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*l/ 99.5%

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

      3. *-commutative 99.5%

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

      4. *-lft-identity 99.5%

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

      5. associate-*l/ 99.3%

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

      6. *-commutative 99.3%

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

      7. *-commutative 99.3%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 98.6%

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

   if 3 < x

   1. Initial program 87.3%

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

      1. *-commutative 87.3%

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

      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%

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

      5. associate-*l/ 99.8%

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

      6. *-commutative 99.8%

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

      7. *-commutative 99.8%

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

      8. associate-/r* 99.7%

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

      9. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 98.5%

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

      1. associate-*r/ 98.6%

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

      2. *-commutative 98.6%

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

      3. associate-/l* 98.5%

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

   6. Simplified 98.5%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{x}{\frac{y}{-0.3333333333333333}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.0%

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

Alternative 5: 97.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.0) {
		tmp = (1.0 - x) * (-0.3333333333333333 * (x / y));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = (1.0 - x) * ((x * -0.3333333333333333) / 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 <= (-3.0d0)) then
        tmp = (1.0d0 - x) * ((-0.3333333333333333d0) * (x / y))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 - x) * (1.0d0 / y)
    else
        tmp = (1.0d0 - x) * ((x * (-0.3333333333333333d0)) / y)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3

   1. Initial program 90.4%

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

      1. *-commutative 90.4%

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

      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%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-/r* 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 96.8%

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

   if -3 < x < 3

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*l/ 99.5%

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

      3. *-commutative 99.5%

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

      4. *-lft-identity 99.5%

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

      5. associate-*l/ 99.3%

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

      6. *-commutative 99.3%

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

      7. *-commutative 99.3%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 98.6%

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

   if 3 < x

   1. Initial program 87.3%

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

      1. *-commutative 87.3%

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

      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%

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

      5. associate-*l/ 99.8%

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

      6. *-commutative 99.8%

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

      7. *-commutative 99.8%

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

      8. associate-/r* 99.7%

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

      9. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 98.5%

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

      1. associate-*r/ 98.6%

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

      2. *-commutative 98.6%

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

   6. Applied egg-rr 98.6%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{x \cdot -0.3333333333333333}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.0%

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

Alternative 6: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;\frac{x}{y} \cdot \left(-1.3333333333333333 - \frac{x}{-3}\right)\\ \mathbf{elif}\;x \leq 2.3:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \frac{x}{y \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.35)
   (* (/ x y) (- -1.3333333333333333 (/ x -3.0)))
   (if (<= x 2.3) (* (- 1.0 x) (/ 1.0 y)) (* (+ x -4.0) (/ x (* y 3.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.35) {
		tmp = (x / y) * (-1.3333333333333333 - (x / -3.0));
	} else if (x <= 2.3) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = (x + -4.0) * (x / (y * 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 <= (-1.35d0)) then
        tmp = (x / y) * ((-1.3333333333333333d0) - (x / (-3.0d0)))
    else if (x <= 2.3d0) then
        tmp = (1.0d0 - x) * (1.0d0 / y)
    else
        tmp = (x + (-4.0d0)) * (x / (y * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.35) {
		tmp = (x / y) * (-1.3333333333333333 - (x / -3.0));
	} else if (x <= 2.3) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = (x + -4.0) * (x / (y * 3.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.35:
		tmp = (x / y) * (-1.3333333333333333 - (x / -3.0))
	elif x <= 2.3:
		tmp = (1.0 - x) * (1.0 / y)
	else:
		tmp = (x + -4.0) * (x / (y * 3.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.35)
		tmp = Float64(Float64(x / y) * Float64(-1.3333333333333333 - Float64(x / -3.0)));
	elseif (x <= 2.3)
		tmp = Float64(Float64(1.0 - x) * Float64(1.0 / y));
	else
		tmp = Float64(Float64(x + -4.0) * Float64(x / Float64(y * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.35)
		tmp = (x / y) * (-1.3333333333333333 - (x / -3.0));
	elseif (x <= 2.3)
		tmp = (1.0 - x) * (1.0 / y);
	else
		tmp = (x + -4.0) * (x / (y * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.35], N[(N[(x / y), $MachinePrecision] * N[(-1.3333333333333333 - N[(x / -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3], N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(x + -4.0), $MachinePrecision] * N[(x / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3500000000000001

   1. Initial program 90.4%

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

   2. Taylor expanded in x around inf 89.3%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 89.3%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 89.3%

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

      3. distribute-rgt-out 89.3%

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

   4. Simplified 89.3%

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

      1. associate-/l* 98.7%

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

      2. associate-/r/ 98.7%

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

   6. Applied egg-rr 98.7%

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

      1. *-commutative 98.7%

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

      2. clear-num 98.7%

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

      3. un-div-inv 98.8%

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

      4. *-commutative 98.8%

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

      5. associate-/l* 98.7%

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

   8. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{\frac{x + -4}{\frac{3}{\frac{x}{y}}}} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 54.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x + -4}{\frac{3}{\frac{x}{y}}}\right)\right)} \]

      2. expm1-udef 41.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x + -4}{\frac{3}{\frac{x}{y}}}\right)} - 1} \]

      3. associate-/r/ 41.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x + -4}{3} \cdot \frac{x}{y}}\right)} - 1 \]

      4. *-commutative 41.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{y} \cdot \frac{x + -4}{3}}\right)} - 1 \]

      5. frac-2neg 41.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \color{blue}{\frac{-\left(x + -4\right)}{-3}}\right)} - 1 \]

      6. neg-sub0 41.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{\color{blue}{0 - \left(x + -4\right)}}{-3}\right)} - 1 \]

      7. +-commutative 41.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{0 - \color{blue}{\left(-4 + x\right)}}{-3}\right)} - 1 \]

      8. associate--r+ 41.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{\color{blue}{\left(0 - -4\right) - x}}{-3}\right)} - 1 \]

      9. metadata-eval 41.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{\color{blue}{4} - x}{-3}\right)} - 1 \]

      10. metadata-eval 41.4%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{4 - x}{\color{blue}{-3}}\right)} - 1 \]

   10. Applied egg-rr 41.4%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{4 - x}{-3}\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 54.8%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{4 - x}{-3}\right)\right)} \]

       2. expm1-log1p 98.7%

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

       3. div-sub 98.7%

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

       4. metadata-eval 98.7%

          \[\leadsto \frac{x}{y} \cdot \left(\color{blue}{-1.3333333333333333} - \frac{x}{-3}\right) \]

   12. Simplified 98.7%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-1.3333333333333333 - \frac{x}{-3}\right)} \]

   if -1.3500000000000001 < x < 2.2999999999999998

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*l/ 99.5%

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

      3. *-commutative 99.5%

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

      4. *-lft-identity 99.5%

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

      5. associate-*l/ 99.3%

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

      6. *-commutative 99.3%

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

      7. *-commutative 99.3%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 98.6%

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

   if 2.2999999999999998 < x

   1. Initial program 87.3%

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

   2. Taylor expanded in x around inf 86.7%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 86.7%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 86.7%

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

      3. distribute-rgt-out 86.7%

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

   4. Simplified 86.7%

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

      1. associate-/l* 99.1%

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

      2. associate-/r/ 99.2%

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

   6. Applied egg-rr 99.2%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;\frac{x}{y} \cdot \left(-1.3333333333333333 - \frac{x}{-3}\right)\\ \mathbf{elif}\;x \leq 2.3:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \frac{x}{y \cdot 3}\\ \end{array} \]

Alternative 7: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{x}{y} \cdot \left(-1.3333333333333333 - \frac{x}{-3}\right)\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \frac{x}{y \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.75)
   (* (/ x y) (- -1.3333333333333333 (/ x -3.0)))
   (if (<= x 1.7)
     (/ (+ 3.0 (* x -4.0)) (* y 3.0))
     (* (+ x -4.0) (/ x (* y 3.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = (x / y) * (-1.3333333333333333 - (x / -3.0));
	} else if (x <= 1.7) {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	} else {
		tmp = (x + -4.0) * (x / (y * 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 <= (-1.75d0)) then
        tmp = (x / y) * ((-1.3333333333333333d0) - (x / (-3.0d0)))
    else if (x <= 1.7d0) then
        tmp = (3.0d0 + (x * (-4.0d0))) / (y * 3.0d0)
    else
        tmp = (x + (-4.0d0)) * (x / (y * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = (x / y) * (-1.3333333333333333 - (x / -3.0));
	} else if (x <= 1.7) {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	} else {
		tmp = (x + -4.0) * (x / (y * 3.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.75:
		tmp = (x / y) * (-1.3333333333333333 - (x / -3.0))
	elif x <= 1.7:
		tmp = (3.0 + (x * -4.0)) / (y * 3.0)
	else:
		tmp = (x + -4.0) * (x / (y * 3.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.75)
		tmp = Float64(Float64(x / y) * Float64(-1.3333333333333333 - Float64(x / -3.0)));
	elseif (x <= 1.7)
		tmp = Float64(Float64(3.0 + Float64(x * -4.0)) / Float64(y * 3.0));
	else
		tmp = Float64(Float64(x + -4.0) * Float64(x / Float64(y * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.75)
		tmp = (x / y) * (-1.3333333333333333 - (x / -3.0));
	elseif (x <= 1.7)
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	else
		tmp = (x + -4.0) * (x / (y * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.75], N[(N[(x / y), $MachinePrecision] * N[(-1.3333333333333333 - N[(x / -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7], N[(N[(3.0 + N[(x * -4.0), $MachinePrecision]), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + -4.0), $MachinePrecision] * N[(x / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75

   1. Initial program 90.4%

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

   2. Taylor expanded in x around inf 89.3%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 89.3%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 89.3%

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

      3. distribute-rgt-out 89.3%

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

   4. Simplified 89.3%

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

      1. associate-/l* 98.7%

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

      2. associate-/r/ 98.7%

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

   6. Applied egg-rr 98.7%

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

      1. *-commutative 98.7%

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

      2. clear-num 98.7%

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

      3. un-div-inv 98.8%

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

      4. *-commutative 98.8%

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

      5. associate-/l* 98.7%

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

   8. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{\frac{x + -4}{\frac{3}{\frac{x}{y}}}} \]
   9. Step-by-step derivation

      1. expm1-log1p-u 54.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x + -4}{\frac{3}{\frac{x}{y}}}\right)\right)} \]

      2. expm1-udef 41.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x + -4}{\frac{3}{\frac{x}{y}}}\right)} - 1} \]

      3. associate-/r/ 41.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x + -4}{3} \cdot \frac{x}{y}}\right)} - 1 \]

      4. *-commutative 41.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{y} \cdot \frac{x + -4}{3}}\right)} - 1 \]

      5. frac-2neg 41.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \color{blue}{\frac{-\left(x + -4\right)}{-3}}\right)} - 1 \]

      6. neg-sub0 41.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{\color{blue}{0 - \left(x + -4\right)}}{-3}\right)} - 1 \]

      7. +-commutative 41.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{0 - \color{blue}{\left(-4 + x\right)}}{-3}\right)} - 1 \]

      8. associate--r+ 41.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{\color{blue}{\left(0 - -4\right) - x}}{-3}\right)} - 1 \]

      9. metadata-eval 41.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{\color{blue}{4} - x}{-3}\right)} - 1 \]

      10. metadata-eval 41.4%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{4 - x}{\color{blue}{-3}}\right)} - 1 \]

   10. Applied egg-rr 41.4%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{4 - x}{-3}\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 54.8%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y} \cdot \frac{4 - x}{-3}\right)\right)} \]

       2. expm1-log1p 98.7%

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

       3. div-sub 98.7%

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

       4. metadata-eval 98.7%

          \[\leadsto \frac{x}{y} \cdot \left(\color{blue}{-1.3333333333333333} - \frac{x}{-3}\right) \]

   12. Simplified 98.7%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-1.3333333333333333 - \frac{x}{-3}\right)} \]

   if -1.75 < x < 1.69999999999999996

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 99.0%

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

      1. *-commutative 99.0%

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

   4. Simplified 99.0%

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

   if 1.69999999999999996 < x

   1. Initial program 87.3%

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

   2. Taylor expanded in x around inf 86.7%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 86.7%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 86.7%

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

      3. distribute-rgt-out 86.7%

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

   4. Simplified 86.7%

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

      1. associate-/l* 99.1%

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

      2. associate-/r/ 99.2%

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

   6. Applied egg-rr 99.2%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{x}{y} \cdot \left(-1.3333333333333333 - \frac{x}{-3}\right)\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \frac{x}{y \cdot 3}\\ \end{array} \]

Alternative 8: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{x + -4}{\frac{3}{\frac{x}{y}}}\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \frac{x}{y \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.75)
   (/ (+ x -4.0) (/ 3.0 (/ x y)))
   (if (<= x 1.7)
     (/ (+ 3.0 (* x -4.0)) (* y 3.0))
     (* (+ x -4.0) (/ x (* y 3.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = (x + -4.0) / (3.0 / (x / y));
	} else if (x <= 1.7) {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	} else {
		tmp = (x + -4.0) * (x / (y * 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 <= (-1.75d0)) then
        tmp = (x + (-4.0d0)) / (3.0d0 / (x / y))
    else if (x <= 1.7d0) then
        tmp = (3.0d0 + (x * (-4.0d0))) / (y * 3.0d0)
    else
        tmp = (x + (-4.0d0)) * (x / (y * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = (x + -4.0) / (3.0 / (x / y));
	} else if (x <= 1.7) {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	} else {
		tmp = (x + -4.0) * (x / (y * 3.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.75:
		tmp = (x + -4.0) / (3.0 / (x / y))
	elif x <= 1.7:
		tmp = (3.0 + (x * -4.0)) / (y * 3.0)
	else:
		tmp = (x + -4.0) * (x / (y * 3.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.75)
		tmp = Float64(Float64(x + -4.0) / Float64(3.0 / Float64(x / y)));
	elseif (x <= 1.7)
		tmp = Float64(Float64(3.0 + Float64(x * -4.0)) / Float64(y * 3.0));
	else
		tmp = Float64(Float64(x + -4.0) * Float64(x / Float64(y * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.75)
		tmp = (x + -4.0) / (3.0 / (x / y));
	elseif (x <= 1.7)
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	else
		tmp = (x + -4.0) * (x / (y * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.75], N[(N[(x + -4.0), $MachinePrecision] / N[(3.0 / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7], N[(N[(3.0 + N[(x * -4.0), $MachinePrecision]), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + -4.0), $MachinePrecision] * N[(x / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75

   1. Initial program 90.4%

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

   2. Taylor expanded in x around inf 89.3%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 89.3%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 89.3%

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

      3. distribute-rgt-out 89.3%

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

   4. Simplified 89.3%

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

      1. associate-/l* 98.7%

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

      2. associate-/r/ 98.7%

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

   6. Applied egg-rr 98.7%

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

      1. *-commutative 98.7%

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

      2. clear-num 98.7%

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

      3. un-div-inv 98.8%

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

      4. *-commutative 98.8%

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

      5. associate-/l* 98.7%

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

   8. Applied egg-rr 98.7%

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

   if -1.75 < x < 1.69999999999999996

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 99.0%

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

      1. *-commutative 99.0%

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

   4. Simplified 99.0%

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

   if 1.69999999999999996 < x

   1. Initial program 87.3%

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

   2. Taylor expanded in x around inf 86.7%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 86.7%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 86.7%

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

      3. distribute-rgt-out 86.7%

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

   4. Simplified 86.7%

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

      1. associate-/l* 99.1%

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

      2. associate-/r/ 99.2%

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

   6. Applied egg-rr 99.2%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{x + -4}{\frac{3}{\frac{x}{y}}}\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \frac{x}{y \cdot 3}\\ \end{array} \]

Alternative 9: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{x + -4}{\frac{y}{\frac{x}{3}}}\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \frac{x}{y \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.75)
   (/ (+ x -4.0) (/ y (/ x 3.0)))
   (if (<= x 1.7)
     (/ (+ 3.0 (* x -4.0)) (* y 3.0))
     (* (+ x -4.0) (/ x (* y 3.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = (x + -4.0) / (y / (x / 3.0));
	} else if (x <= 1.7) {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	} else {
		tmp = (x + -4.0) * (x / (y * 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 <= (-1.75d0)) then
        tmp = (x + (-4.0d0)) / (y / (x / 3.0d0))
    else if (x <= 1.7d0) then
        tmp = (3.0d0 + (x * (-4.0d0))) / (y * 3.0d0)
    else
        tmp = (x + (-4.0d0)) * (x / (y * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = (x + -4.0) / (y / (x / 3.0));
	} else if (x <= 1.7) {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	} else {
		tmp = (x + -4.0) * (x / (y * 3.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.75:
		tmp = (x + -4.0) / (y / (x / 3.0))
	elif x <= 1.7:
		tmp = (3.0 + (x * -4.0)) / (y * 3.0)
	else:
		tmp = (x + -4.0) * (x / (y * 3.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.75)
		tmp = Float64(Float64(x + -4.0) / Float64(y / Float64(x / 3.0)));
	elseif (x <= 1.7)
		tmp = Float64(Float64(3.0 + Float64(x * -4.0)) / Float64(y * 3.0));
	else
		tmp = Float64(Float64(x + -4.0) * Float64(x / Float64(y * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.75)
		tmp = (x + -4.0) / (y / (x / 3.0));
	elseif (x <= 1.7)
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	else
		tmp = (x + -4.0) * (x / (y * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.75], N[(N[(x + -4.0), $MachinePrecision] / N[(y / N[(x / 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7], N[(N[(3.0 + N[(x * -4.0), $MachinePrecision]), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + -4.0), $MachinePrecision] * N[(x / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75

   1. Initial program 90.4%

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

   2. Taylor expanded in x around inf 89.3%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 89.3%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 89.3%

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

      3. distribute-rgt-out 89.3%

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

   4. Simplified 89.3%

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

      1. associate-/l* 98.7%

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

      2. associate-/r/ 98.7%

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

   6. Applied egg-rr 98.7%

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

      1. *-commutative 98.7%

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

      2. clear-num 98.7%

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

      3. un-div-inv 98.8%

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

      4. *-commutative 98.8%

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

      5. associate-/l* 98.7%

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

   8. Applied egg-rr 98.7%

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

   9. Taylor expanded in x around 0 98.7%

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

       1. associate-*r/ 98.8%

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

       2. *-commutative 98.8%

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

       3. associate-/l* 98.8%

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

   11. Simplified 98.8%

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

   if -1.75 < x < 1.69999999999999996

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 99.0%

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

      1. *-commutative 99.0%

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

   4. Simplified 99.0%

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

   if 1.69999999999999996 < x

   1. Initial program 87.3%

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

   2. Taylor expanded in x around inf 86.7%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 86.7%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 86.7%

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

      3. distribute-rgt-out 86.7%

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

   4. Simplified 86.7%

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

      1. associate-/l* 99.1%

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

      2. associate-/r/ 99.2%

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

   6. Applied egg-rr 99.2%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{x + -4}{\frac{y}{\frac{x}{3}}}\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \frac{x}{y \cdot 3}\\ \end{array} \]

Alternative 10: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

   1. *-commutative 93.8%

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

   2. associate-*l/ 99.7%

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

   3. *-commutative 99.7%

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

   4. *-lft-identity 99.7%

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

   5. associate-*l/ 99.5%

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

   6. *-commutative 99.5%

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

   7. *-commutative 99.5%

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

   8. associate-/r* 99.5%

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

   9. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 11: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

   1. *-commutative 93.8%

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

   2. associate-*r/ 99.6%

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

   3. *-commutative 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 12: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

   1. div-inv 93.7%

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

   2. *-commutative 93.7%

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

   3. associate-/r* 93.7%

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

   4. metadata-eval 93.7%

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

   5. associate-*r* 99.5%

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

   6. *-commutative 99.5%

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

   7. associate-*r/ 99.8%

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

   8. metadata-eval 99.8%

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

   9. div-inv 99.8%

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

   10. div-sub 99.8%

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

   11. metadata-eval 99.8%

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

   12. sub-neg 99.8%

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

   13. div-inv 99.8%

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

   14. metadata-eval 99.8%

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

   15. distribute-rgt-neg-in 99.8%

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

   16. metadata-eval 99.8%

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

3. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

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

Alternative 13: 57.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75)
   (* (/ x y) -1.3333333333333333)
   (* 3.0 (/ 0.3333333333333333 y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = (x / y) * -1.3333333333333333;
	} else {
		tmp = 3.0 * (0.3333333333333333 / 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 = (x / y) * (-1.3333333333333333d0)
    else
        tmp = 3.0d0 * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = (x / y) * -1.3333333333333333;
	} else {
		tmp = 3.0 * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = (x / y) * -1.3333333333333333
	else:
		tmp = 3.0 * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(Float64(x / y) * -1.3333333333333333);
	else
		tmp = Float64(3.0 * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.75)
		tmp = (x / y) * -1.3333333333333333;
	else
		tmp = 3.0 * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(N[(x / y), $MachinePrecision] * -1.3333333333333333), $MachinePrecision], N[(3.0 * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.75

   1. Initial program 90.4%

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

   2. Taylor expanded in x around inf 89.3%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 89.3%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 89.3%

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

      3. distribute-rgt-out 89.3%

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

   4. Simplified 89.3%

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

   5. Taylor expanded in x around 0 29.9%

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

   if -0.75 < x

   1. Initial program 95.4%

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

   2. Taylor expanded in x around 0 66.6%

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

      1. div-inv 66.4%

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

      2. *-commutative 66.4%

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

      3. *-commutative 66.4%

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

      4. associate-/r* 66.5%

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

      5. metadata-eval 66.5%

         \[\leadsto \frac{\color{blue}{0.3333333333333333}}{y} \cdot 3 \]

   4. Applied egg-rr 66.5%

      \[\leadsto \color{blue}{\frac{0.3333333333333333}{y} \cdot 3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]

Alternative 14: 57.9% accurate, 1.6× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = (x / y) * -1.3333333333333333;
	} 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 = (x / y) * (-1.3333333333333333d0)
    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 = (x / y) * -1.3333333333333333;
	} else {
		tmp = 1.0 / y;
	}
	return tmp;
}

Python

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

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(Float64(x / y) * -1.3333333333333333);
	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 = (x / y) * -1.3333333333333333;
	else
		tmp = 1.0 / y;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -0.75

   1. Initial program 90.4%

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

   2. Taylor expanded in x around inf 89.3%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 89.3%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 89.3%

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

      3. distribute-rgt-out 89.3%

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

   4. Simplified 89.3%

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

   5. Taylor expanded in x around 0 29.9%

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

   if -0.75 < x

   1. Initial program 95.4%

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

   2. Taylor expanded in x around 0 66.6%

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

      1. *-un-lft-identity 66.6%

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

      2. *-commutative 66.6%

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

      3. *-commutative 66.6%

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

      4. associate-/r* 66.9%

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

      5. metadata-eval 66.9%

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

   4. Applied egg-rr 66.9%

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

4. Final simplification 55.3%

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

Alternative 15: 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 93.8%

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

   1. *-commutative 93.8%

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

   2. associate-*l/ 99.7%

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

   3. *-commutative 99.7%

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

   4. *-lft-identity 99.7%

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

   5. associate-*l/ 99.5%

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

   6. *-commutative 99.5%

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

   7. *-commutative 99.5%

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

   8. associate-/r* 99.5%

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

   9. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in x around 0 54.5%

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

5. Final simplification 54.5%

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

Alternative 16: 10.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \cdot -1.3333333333333333 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (/ x y) -1.3333333333333333))

C

double code(double x, double y) {
	return (x / y) * -1.3333333333333333;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x / y) * (-1.3333333333333333d0)
end function

Java

public static double code(double x, double y) {
	return (x / y) * -1.3333333333333333;
}

Python

def code(x, y):
	return (x / y) * -1.3333333333333333

Julia

function code(x, y)
	return Float64(Float64(x / y) * -1.3333333333333333)
end

MATLAB

function tmp = code(x, y)
	tmp = (x / y) * -1.3333333333333333;
end

Wolfram

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

Derivation

1. Initial program 93.8%

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

2. Taylor expanded in x around inf 50.0%

   \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
3. Step-by-step derivation

   1. +-commutative 50.0%

      \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

   2. unpow2 50.0%

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

   3. distribute-rgt-out 49.9%

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

4. Simplified 49.9%

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

5. Taylor expanded in x around 0 11.5%

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

6. Final simplification 11.5%

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

Alternative 17: 10.0% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

   1. times-frac 99.8%

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

   2. div-sub 99.8%

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

   3. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around inf 55.1%

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

   1. mul-1-neg 55.1%

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

   2. distribute-neg-frac 55.1%

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

6. Simplified 55.1%

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

7. Taylor expanded in x around 0 11.5%

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

   1. mul-1-neg 11.5%

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

9. Simplified 11.5%

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

10. Final simplification 11.5%

    \[\leadsto \frac{-x}{y} \]

Developer target: 99.8% 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 2023301 
(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)))