Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, C

Percentage Accurate: 100.0% → 100.0%

Time: 4.8s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{1 - y} \]

2. Final simplification 100.0%

   \[\leadsto \frac{x - y}{1 - y} \]

Alternative 2: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-15}:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.2e+35)
   1.0
   (if (<= y -1.2e-8)
     (/ x (- 1.0 y))
     (if (<= y 2.85e-15) (- x y) (/ y (+ y -1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.2e+35) {
		tmp = 1.0;
	} else if (y <= -1.2e-8) {
		tmp = x / (1.0 - y);
	} else if (y <= 2.85e-15) {
		tmp = x - y;
	} else {
		tmp = y / (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-5.2d+35)) then
        tmp = 1.0d0
    else if (y <= (-1.2d-8)) then
        tmp = x / (1.0d0 - y)
    else if (y <= 2.85d-15) then
        tmp = x - y
    else
        tmp = y / (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5.2e+35) {
		tmp = 1.0;
	} else if (y <= -1.2e-8) {
		tmp = x / (1.0 - y);
	} else if (y <= 2.85e-15) {
		tmp = x - y;
	} else {
		tmp = y / (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.2e+35:
		tmp = 1.0
	elif y <= -1.2e-8:
		tmp = x / (1.0 - y)
	elif y <= 2.85e-15:
		tmp = x - y
	else:
		tmp = y / (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.2e+35)
		tmp = 1.0;
	elseif (y <= -1.2e-8)
		tmp = Float64(x / Float64(1.0 - y));
	elseif (y <= 2.85e-15)
		tmp = Float64(x - y);
	else
		tmp = Float64(y / Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.2e+35)
		tmp = 1.0;
	elseif (y <= -1.2e-8)
		tmp = x / (1.0 - y);
	elseif (y <= 2.85e-15)
		tmp = x - y;
	else
		tmp = y / (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.2e+35], 1.0, If[LessEqual[y, -1.2e-8], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.85e-15], N[(x - y), $MachinePrecision], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.20000000000000013e35

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{1 - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{1 - y} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + 1} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - 1\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 83.9%

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

   if -5.20000000000000013e35 < y < -1.19999999999999999e-8

   1. Initial program 99.9%

      \[\frac{x - y}{1 - y} \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{1 - y} \]

      4. associate-+l- 99.9%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{1 - y} \]

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + 1} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - 1\right)}} \]

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 72.9%

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

      1. sub-neg 72.9%

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

      2. metadata-eval 72.9%

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

      3. neg-mul-1 72.9%

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

      4. distribute-neg-frac 72.9%

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

      5. +-commutative 72.9%

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

   6. Simplified 72.9%

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

      1. frac-2neg 72.9%

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

      2. +-commutative 72.9%

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

      3. metadata-eval 72.9%

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

      4. sub-neg 72.9%

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

      5. div-inv 72.6%

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

      6. remove-double-neg 72.6%

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

      7. sub-neg 72.6%

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

      8. metadata-eval 72.6%

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

      9. distribute-neg-in 72.6%

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

      10. neg-mul-1 72.6%

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

      11. *-commutative 72.6%

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

      12. metadata-eval 72.6%

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

      13. fma-def 72.6%

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

   8. Applied egg-rr 72.6%

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

      1. associate-*r/ 72.9%

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

      2. *-rgt-identity 72.9%

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

      3. fma-udef 72.9%

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

      4. *-commutative 72.9%

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

      5. +-commutative 72.9%

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

      6. neg-mul-1 72.9%

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

      7. unsub-neg 72.9%

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

   10. Simplified 72.9%

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

   if -1.19999999999999999e-8 < y < 2.8500000000000002e-15

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{1 - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{1 - y} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + 1} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - 1\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 99.8%

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

   if 2.8500000000000002e-15 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{1 - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{1 - y} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + 1} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - 1\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 77.2%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-15}:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \]

Alternative 3: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.25) (not (<= y 1.0))) (+ 1.0 (/ (- 1.0 x) y)) (- x y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.25) || !(y <= 1.0)) {
		tmp = 1.0 + ((1.0 - x) / y);
	} else {
		tmp = x - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.25d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = 1.0d0 + ((1.0d0 - x) / y)
    else
        tmp = x - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.25) || !(y <= 1.0)) {
		tmp = 1.0 + ((1.0 - x) / y);
	} else {
		tmp = x - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.25) or not (y <= 1.0):
		tmp = 1.0 + ((1.0 - x) / y)
	else:
		tmp = x - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.25) || !(y <= 1.0))
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(x - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.25) || ~((y <= 1.0)))
		tmp = 1.0 + ((1.0 - x) / y);
	else
		tmp = x - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.25], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25 or 1 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{1 - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{1 - y} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + 1} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - 1\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-+r+ 99.0%

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

      3. mul-1-neg 99.0%

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

      4. unsub-neg 99.0%

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

      5. div-sub 99.0%

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

      6. unsub-neg 99.0%

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

      7. mul-1-neg 99.0%

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

      8. +-commutative 99.0%

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

      9. metadata-eval 99.0%

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

      10. distribute-lft-in 99.0%

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

      11. metadata-eval 99.0%

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

      12. sub-neg 99.0%

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

      13. associate-*r/ 99.0%

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

      14. +-commutative 99.0%

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

      15. associate-*r/ 99.0%

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

      16. sub-neg 99.0%

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

      17. metadata-eval 99.0%

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

      18. distribute-lft-in 99.0%

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

      19. metadata-eval 99.0%

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

      20. +-commutative 99.0%

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

      21. mul-1-neg 99.0%

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

      22. unsub-neg 99.0%

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

   6. Simplified 99.0%

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

   if -1.25 < y < 1

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{1 - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{1 - y} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + 1} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - 1\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 96.6%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - y\\ \end{array} \]

Alternative 4: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.25e+37)
   1.0
   (if (<= y -4.6e-9) (/ x (- 1.0 y)) (if (<= y 1.0) (- x y) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.25e+37) {
		tmp = 1.0;
	} else if (y <= -4.6e-9) {
		tmp = x / (1.0 - y);
	} else if (y <= 1.0) {
		tmp = x - y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.25d+37)) then
        tmp = 1.0d0
    else if (y <= (-4.6d-9)) then
        tmp = x / (1.0d0 - y)
    else if (y <= 1.0d0) then
        tmp = x - y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.25e+37) {
		tmp = 1.0;
	} else if (y <= -4.6e-9) {
		tmp = x / (1.0 - y);
	} else if (y <= 1.0) {
		tmp = x - y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.25e+37:
		tmp = 1.0
	elif y <= -4.6e-9:
		tmp = x / (1.0 - y)
	elif y <= 1.0:
		tmp = x - y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.25e+37)
		tmp = 1.0;
	elseif (y <= -4.6e-9)
		tmp = Float64(x / Float64(1.0 - y));
	elseif (y <= 1.0)
		tmp = Float64(x - y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.25e+37)
		tmp = 1.0;
	elseif (y <= -4.6e-9)
		tmp = x / (1.0 - y);
	elseif (y <= 1.0)
		tmp = x - y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.25e+37], 1.0, If[LessEqual[y, -4.6e-9], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], N[(x - y), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.24999999999999997e37 or 1 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{1 - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{1 - y} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + 1} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - 1\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 80.1%

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

   if -1.24999999999999997e37 < y < -4.5999999999999998e-9

   1. Initial program 99.9%

      \[\frac{x - y}{1 - y} \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{1 - y} \]

      4. associate-+l- 99.9%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{1 - y} \]

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + 1} \]

      10. associate-+l- 99.9%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - 1\right)}} \]

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 72.9%

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

      1. sub-neg 72.9%

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

      2. metadata-eval 72.9%

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

      3. neg-mul-1 72.9%

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

      4. distribute-neg-frac 72.9%

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

      5. +-commutative 72.9%

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

   6. Simplified 72.9%

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

      1. frac-2neg 72.9%

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

      2. +-commutative 72.9%

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

      3. metadata-eval 72.9%

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

      4. sub-neg 72.9%

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

      5. div-inv 72.6%

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

      6. remove-double-neg 72.6%

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

      7. sub-neg 72.6%

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

      8. metadata-eval 72.6%

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

      9. distribute-neg-in 72.6%

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

      10. neg-mul-1 72.6%

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

      11. *-commutative 72.6%

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

      12. metadata-eval 72.6%

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

      13. fma-def 72.6%

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

   8. Applied egg-rr 72.6%

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

      1. associate-*r/ 72.9%

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

      2. *-rgt-identity 72.9%

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

      3. fma-udef 72.9%

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

      4. *-commutative 72.9%

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

      5. +-commutative 72.9%

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

      6. neg-mul-1 72.9%

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

      7. unsub-neg 72.9%

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

   10. Simplified 72.9%

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

   if -4.5999999999999998e-9 < y < 1

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{1 - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{1 - y} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + 1} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - 1\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 99.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -12.8:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -12.8) 1.0 (if (<= y 1.0) (- x y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -12.8) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x - y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-12.8d0)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = x - y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -12.8) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x - y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -12.8:
		tmp = 1.0
	elif y <= 1.0:
		tmp = x - y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -12.8)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = Float64(x - y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -12.8)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x - y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -12.8], 1.0, If[LessEqual[y, 1.0], N[(x - y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -12.800000000000001 or 1 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{1 - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{1 - y} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + 1} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - 1\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 76.8%

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

   if -12.800000000000001 < y < 1

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{1 - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{1 - y} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + 1} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - 1\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 96.6%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12.8:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 73.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.122:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -0.122) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.122) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-0.122d0)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -0.122) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.122:
		tmp = 1.0
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.122)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.122)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.122], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -0.122 or 1 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{1 - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{1 - y} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + 1} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - 1\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 76.8%

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

   if -0.122 < y < 1

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{1 - y} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{1 - y} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

         \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + 1} \]

      10. associate-+l- 100.0%

          \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - 1\right)}} \]

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 73.5%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.122:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 39.1% accurate, 7.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{1 - y} \]
2. Step-by-step derivation

   1. sub-neg 100.0%

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

   2. +-commutative 100.0%

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

   3. neg-sub0 100.0%

      \[\leadsto \frac{\color{blue}{\left(0 - y\right)} + x}{1 - y} \]

   4. associate-+l- 100.0%

      \[\leadsto \frac{\color{blue}{0 - \left(y - x\right)}}{1 - y} \]

   5. sub0-neg 100.0%

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

   6. neg-mul-1 100.0%

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

   7. sub-neg 100.0%

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

   8. +-commutative 100.0%

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

   9. neg-sub0 100.0%

      \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{\left(0 - y\right)} + 1} \]

   10. associate-+l- 100.0%

       \[\leadsto \frac{-1 \cdot \left(y - x\right)}{\color{blue}{0 - \left(y - 1\right)}} \]

   11. sub0-neg 100.0%

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

   12. neg-mul-1 100.0%

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

   13. times-frac 100.0%

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

   14. metadata-eval 100.0%

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

   15. *-lft-identity 100.0%

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

   16. sub-neg 100.0%

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

   17. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in y around inf 40.7%

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

5. Final simplification 40.7%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023240 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))