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

Percentage Accurate: 100.0% → 100.0%

Time: 6.5s

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{1 - y} \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto \frac{y - x}{y + -1} \]
4. Add Preprocessing

Alternative 2: 98.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 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. distribute-frac-neg 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. neg-sub0 100.0%

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

      9. associate--r- 100.0%

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

      10. metadata-eval 100.0%

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

      11. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 98.6%

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

      1. +-commutative 98.6%

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

      2. mul-1-neg 98.6%

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

      3. sub-neg 98.6%

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

      4. div-sub 98.6%

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

      5. sub-neg 98.6%

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

      6. +-commutative 98.6%

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

      7. mul-1-neg 98.6%

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

      8. metadata-eval 98.6%

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

      9. distribute-lft-in 98.6%

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

      10. metadata-eval 98.6%

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

      11. sub-neg 98.6%

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

      12. mul-1-neg 98.6%

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

      13. distribute-neg-frac 98.6%

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

      14. unsub-neg 98.6%

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

      15. sub-neg 98.6%

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

      16. metadata-eval 98.6%

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

   7. Simplified 98.6%

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

   if -1 < 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. distribute-frac-neg 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. neg-sub0 100.0%

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

      9. associate--r- 100.0%

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

      10. metadata-eval 100.0%

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

      11. +-commutative 100.0%

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

   3. Simplified 100.0%

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

      1. flip-+ 99.9%

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

      2. associate-/r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 97.7%

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

      1. mul-1-neg 97.7%

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

      2. unsub-neg 97.7%

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

   9. Simplified 97.7%

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

4. Final simplification 98.2%

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

Alternative 3: 98.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.75 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(-1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -0.75) (not (<= y 1.0)))
   (- 1.0 (/ x y))
   (* (- y x) (- -1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -0.75) || !(y <= 1.0)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = (y - 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 ((y <= (-0.75d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = (y - x) * ((-1.0d0) - y)
    end if
    code = tmp
end function

Java

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

Python

def code(x, y):
	tmp = 0
	if (y <= -0.75) or not (y <= 1.0):
		tmp = 1.0 - (x / y)
	else:
		tmp = (y - x) * (-1.0 - y)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -0.75], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.75 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. distribute-frac-neg 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. neg-sub0 100.0%

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

      9. associate--r- 100.0%

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

      10. metadata-eval 100.0%

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

      11. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 98.6%

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

      1. +-commutative 98.6%

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

      2. mul-1-neg 98.6%

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

      3. sub-neg 98.6%

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

      4. div-sub 98.6%

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

      5. sub-neg 98.6%

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

      6. +-commutative 98.6%

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

      7. mul-1-neg 98.6%

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

      8. metadata-eval 98.6%

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

      9. distribute-lft-in 98.6%

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

      10. metadata-eval 98.6%

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

      11. sub-neg 98.6%

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

      12. mul-1-neg 98.6%

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

      13. distribute-neg-frac 98.6%

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

      14. unsub-neg 98.6%

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

      15. sub-neg 98.6%

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

      16. metadata-eval 98.6%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in x around inf 98.1%

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

   if -0.75 < 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. distribute-frac-neg 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. neg-sub0 100.0%

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

      9. associate--r- 100.0%

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

      10. metadata-eval 100.0%

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

      11. +-commutative 100.0%

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

   3. Simplified 100.0%

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

      1. flip-+ 99.9%

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

      2. associate-/r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 97.7%

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

      1. mul-1-neg 97.7%

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

      2. unsub-neg 97.7%

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

   9. Simplified 97.7%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.75 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(-1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 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. distribute-frac-neg 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. neg-sub0 100.0%

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

      9. associate--r- 100.0%

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

      10. metadata-eval 100.0%

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

      11. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 98.6%

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

      1. +-commutative 98.6%

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

      2. mul-1-neg 98.6%

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

      3. sub-neg 98.6%

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

      4. div-sub 98.6%

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

      5. sub-neg 98.6%

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

      6. +-commutative 98.6%

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

      7. mul-1-neg 98.6%

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

      8. metadata-eval 98.6%

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

      9. distribute-lft-in 98.6%

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

      10. metadata-eval 98.6%

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

      11. sub-neg 98.6%

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

      12. mul-1-neg 98.6%

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

      13. distribute-neg-frac 98.6%

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

      14. unsub-neg 98.6%

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

      15. sub-neg 98.6%

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

      16. metadata-eval 98.6%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in x around inf 98.1%

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

   if -1 < 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. distribute-frac-neg 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. neg-sub0 100.0%

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

      9. associate--r- 100.0%

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

      10. metadata-eval 100.0%

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

      11. +-commutative 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 96.4%

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

4. Final simplification 97.2%

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

Alternative 5: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+15} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.8e+15) (not (<= y 1.0))) 1.0 (- x y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.8e+15) || !(y <= 1.0)) {
		tmp = 1.0;
	} 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 <= (-2.8d+15)) .or. (.not. (y <= 1.0d0))) then
        tmp = 1.0d0
    else
        tmp = x - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.8e+15) || !(y <= 1.0)) {
		tmp = 1.0;
	} else {
		tmp = x - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.8e+15) or not (y <= 1.0):
		tmp = 1.0
	else:
		tmp = x - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.8e+15) || !(y <= 1.0))
		tmp = 1.0;
	else
		tmp = Float64(x - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.8e+15) || ~((y <= 1.0)))
		tmp = 1.0;
	else
		tmp = x - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.8e+15], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], 1.0, N[(x - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e15 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. distribute-frac-neg 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. neg-sub0 100.0%

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

      9. associate--r- 100.0%

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

      10. metadata-eval 100.0%

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

      11. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 77.3%

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

   if -2.8e15 < 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. distribute-frac-neg 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. neg-sub0 100.0%

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

      9. associate--r- 100.0%

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

      10. metadata-eval 100.0%

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

      11. +-commutative 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 94.4%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+15} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x - y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-9}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.5e-9) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.5e-9) {
		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 <= (-2.5d-9)) 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 <= -2.5e-9) {
		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 <= -2.5e-9:
		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 <= -2.5e-9)
		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 <= -2.5e-9)
		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, -2.5e-9], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5000000000000001e-9 or 1 < y

   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. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. neg-sub0 99.9%

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

      9. associate--r- 99.9%

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

      10. metadata-eval 99.9%

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

      11. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 74.4%

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

   if -2.5000000000000001e-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. distribute-frac-neg 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. neg-sub0 100.0%

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

      9. associate--r- 100.0%

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

      10. metadata-eval 100.0%

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

      11. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 74.5%

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

Alternative 7: 38.0% 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. distribute-frac-neg 100.0%

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

   7. distribute-frac-neg2 100.0%

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

   8. neg-sub0 100.0%

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

   9. associate--r- 100.0%

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

   10. metadata-eval 100.0%

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

   11. +-commutative 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around inf 40.6%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024097 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))