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

Average Error: 22.7 → 0.0

Time: 17.3s

Precision: binary64

Cost: 20996

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \leq -11800:\\ \;\;\;\;\frac{x}{{y}^{2}} + \left(-1 \cdot \left(\frac{x + -1}{y} + \frac{x + -1}{{y}^{3}}\right) + \left(x - \frac{1}{{y}^{2}}\right)\right)\\ \mathbf{elif}\;y \leq 360000:\\ \;\;\;\;1 - y \cdot \frac{1 - x}{1 + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} + \left(\frac{x + -1}{{y}^{2}} + \left(x - \frac{x}{y}\right)\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y)
 :precision binary64
 (if (<= y -11800.0)
   (+
    (/ x (pow y 2.0))
    (+
     (* -1.0 (+ (/ (+ x -1.0) y) (/ (+ x -1.0) (pow y 3.0))))
     (- x (/ 1.0 (pow y 2.0)))))
   (if (<= y 360000.0)
     (- 1.0 (* y (/ (- 1.0 x) (+ 1.0 y))))
     (+ (/ 1.0 y) (+ (/ (+ x -1.0) (pow y 2.0)) (- x (/ x y)))))))

C

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

↓

double code(double x, double y) {
	double tmp;
	if (y <= -11800.0) {
		tmp = (x / pow(y, 2.0)) + ((-1.0 * (((x + -1.0) / y) + ((x + -1.0) / pow(y, 3.0)))) + (x - (1.0 / pow(y, 2.0))));
	} else if (y <= 360000.0) {
		tmp = 1.0 - (y * ((1.0 - x) / (1.0 + y)));
	} else {
		tmp = (1.0 / y) + (((x + -1.0) / pow(y, 2.0)) + (x - (x / y)));
	}
	return tmp;
}

Fortran

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

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-11800.0d0)) then
        tmp = (x / (y ** 2.0d0)) + (((-1.0d0) * (((x + (-1.0d0)) / y) + ((x + (-1.0d0)) / (y ** 3.0d0)))) + (x - (1.0d0 / (y ** 2.0d0))))
    else if (y <= 360000.0d0) then
        tmp = 1.0d0 - (y * ((1.0d0 - x) / (1.0d0 + y)))
    else
        tmp = (1.0d0 / y) + (((x + (-1.0d0)) / (y ** 2.0d0)) + (x - (x / y)))
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y) {
	double tmp;
	if (y <= -11800.0) {
		tmp = (x / Math.pow(y, 2.0)) + ((-1.0 * (((x + -1.0) / y) + ((x + -1.0) / Math.pow(y, 3.0)))) + (x - (1.0 / Math.pow(y, 2.0))));
	} else if (y <= 360000.0) {
		tmp = 1.0 - (y * ((1.0 - x) / (1.0 + y)));
	} else {
		tmp = (1.0 / y) + (((x + -1.0) / Math.pow(y, 2.0)) + (x - (x / y)));
	}
	return tmp;
}

Python

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

↓

def code(x, y):
	tmp = 0
	if y <= -11800.0:
		tmp = (x / math.pow(y, 2.0)) + ((-1.0 * (((x + -1.0) / y) + ((x + -1.0) / math.pow(y, 3.0)))) + (x - (1.0 / math.pow(y, 2.0))))
	elif y <= 360000.0:
		tmp = 1.0 - (y * ((1.0 - x) / (1.0 + y)))
	else:
		tmp = (1.0 / y) + (((x + -1.0) / math.pow(y, 2.0)) + (x - (x / y)))
	return tmp

Julia

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

↓

function code(x, y)
	tmp = 0.0
	if (y <= -11800.0)
		tmp = Float64(Float64(x / (y ^ 2.0)) + Float64(Float64(-1.0 * Float64(Float64(Float64(x + -1.0) / y) + Float64(Float64(x + -1.0) / (y ^ 3.0)))) + Float64(x - Float64(1.0 / (y ^ 2.0)))));
	elseif (y <= 360000.0)
		tmp = Float64(1.0 - Float64(y * Float64(Float64(1.0 - x) / Float64(1.0 + y))));
	else
		tmp = Float64(Float64(1.0 / y) + Float64(Float64(Float64(x + -1.0) / (y ^ 2.0)) + Float64(x - Float64(x / y))));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -11800.0)
		tmp = (x / (y ^ 2.0)) + ((-1.0 * (((x + -1.0) / y) + ((x + -1.0) / (y ^ 3.0)))) + (x - (1.0 / (y ^ 2.0))));
	elseif (y <= 360000.0)
		tmp = 1.0 - (y * ((1.0 - x) / (1.0 + y)));
	else
		tmp = (1.0 / y) + (((x + -1.0) / (y ^ 2.0)) + (x - (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_] := If[LessEqual[y, -11800.0], N[(N[(x / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 * N[(N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x - N[(1.0 / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 360000.0], N[(1.0 - N[(y * N[(N[(1.0 - x), $MachinePrecision] / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / y), $MachinePrecision] + N[(N[(N[(x + -1.0), $MachinePrecision] / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision] + N[(x - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	22.7
Target	0.2
Herbie	0.0

\[\begin{array}{l} \mathbf{if}\;y < -3693.8482788297247:\\ \;\;\;\;\frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y < 6799310503.41891:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if y < -11800

   1. Initial program 45.2

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

   2. Simplified 28.2

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

      [Start] 45.2	\[ 1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
      rational.json-simplify-49 [=>] 28.2	\[ 1 - \color{blue}{y \cdot \frac{1 - x}{y + 1}} \]
      rational.json-simplify-1 [=>] 28.2	\[ 1 - y \cdot \frac{1 - x}{\color{blue}{1 + y}} \]
      rational.json-simplify-17 [=>] 28.2	\[ 1 - y \cdot \frac{1 - x}{\color{blue}{y - -1}} \]
      rational.json-simplify-50 [=>] 28.2	\[ 1 - y \cdot \color{blue}{\frac{-\left(1 - x\right)}{-1 - y}} \]
      rational.json-simplify-8 [=>] 28.2	\[ 1 - y \cdot \frac{\color{blue}{\left(1 - x\right) \cdot -1}}{-1 - y} \]
      rational.json-simplify-2 [=>] 28.2	\[ 1 - y \cdot \frac{\color{blue}{-1 \cdot \left(1 - x\right)}}{-1 - y} \]
      rational.json-simplify-49 [=>] 28.3	\[ 1 - y \cdot \color{blue}{\left(\left(1 - x\right) \cdot \frac{-1}{-1 - y}\right)} \]
      rational.json-simplify-2 [=>] 28.3	\[ 1 - y \cdot \color{blue}{\left(\frac{-1}{-1 - y} \cdot \left(1 - x\right)\right)} \]
      rational.json-simplify-2 [<=] 28.3	\[ 1 - y \cdot \color{blue}{\left(\left(1 - x\right) \cdot \frac{-1}{-1 - y}\right)} \]
      rational.json-simplify-49 [<=] 28.2	\[ 1 - y \cdot \color{blue}{\frac{-1 \cdot \left(1 - x\right)}{-1 - y}} \]
      rational.json-simplify-2 [<=] 28.2	\[ 1 - y \cdot \frac{\color{blue}{\left(1 - x\right) \cdot -1}}{-1 - y} \]
      rational.json-simplify-8 [<=] 28.2	\[ 1 - y \cdot \frac{\color{blue}{-\left(1 - x\right)}}{-1 - y} \]
      rational.json-simplify-50 [<=] 28.2	\[ 1 - y \cdot \color{blue}{\frac{1 - x}{y - -1}} \]
      rational.json-simplify-17 [<=] 28.2	\[ 1 - y \cdot \frac{1 - x}{\color{blue}{1 + y}} \]

   3. Taylor expanded in y around -inf 0.0

      \[\leadsto \color{blue}{\left(\frac{x}{{y}^{2}} + \left(-1 \cdot \frac{x - 1}{y} + \left(-1 \cdot \frac{x - 1}{{y}^{3}} + x\right)\right)\right) - \frac{1}{{y}^{2}}} \]

   4. Simplified 0.0

      \[\leadsto \color{blue}{\frac{x}{{y}^{2}} + \left(-1 \cdot \left(\frac{x + -1}{y} + \frac{x + -1}{{y}^{3}}\right) + \left(x - \frac{1}{{y}^{2}}\right)\right)} \]
      Proof

      [Start] 0.0	\[ \left(\frac{x}{{y}^{2}} + \left(-1 \cdot \frac{x - 1}{y} + \left(-1 \cdot \frac{x - 1}{{y}^{3}} + x\right)\right)\right) - \frac{1}{{y}^{2}} \]
      rational.json-simplify-1 [=>] 0.0	\[ \color{blue}{\left(\left(-1 \cdot \frac{x - 1}{y} + \left(-1 \cdot \frac{x - 1}{{y}^{3}} + x\right)\right) + \frac{x}{{y}^{2}}\right)} - \frac{1}{{y}^{2}} \]
      rational.json-simplify-48 [=>] 0.0	\[ \color{blue}{\frac{x}{{y}^{2}} + \left(\left(-1 \cdot \frac{x - 1}{y} + \left(-1 \cdot \frac{x - 1}{{y}^{3}} + x\right)\right) - \frac{1}{{y}^{2}}\right)} \]
      rational.json-simplify-41 [<=] 0.0	\[ \frac{x}{{y}^{2}} + \left(\color{blue}{\left(x + \left(-1 \cdot \frac{x - 1}{y} + -1 \cdot \frac{x - 1}{{y}^{3}}\right)\right)} - \frac{1}{{y}^{2}}\right) \]
      rational.json-simplify-48 [=>] 0.0	\[ \frac{x}{{y}^{2}} + \color{blue}{\left(\left(-1 \cdot \frac{x - 1}{y} + -1 \cdot \frac{x - 1}{{y}^{3}}\right) + \left(x - \frac{1}{{y}^{2}}\right)\right)} \]
      rational.json-simplify-1 [=>] 0.0	\[ \frac{x}{{y}^{2}} + \left(\color{blue}{\left(-1 \cdot \frac{x - 1}{{y}^{3}} + -1 \cdot \frac{x - 1}{y}\right)} + \left(x - \frac{1}{{y}^{2}}\right)\right) \]
      rational.json-simplify-2 [=>] 0.0	\[ \frac{x}{{y}^{2}} + \left(\left(-1 \cdot \frac{x - 1}{{y}^{3}} + \color{blue}{\frac{x - 1}{y} \cdot -1}\right) + \left(x - \frac{1}{{y}^{2}}\right)\right) \]
      rational.json-simplify-51 [=>] 0.0	\[ \frac{x}{{y}^{2}} + \left(\color{blue}{-1 \cdot \left(\frac{x - 1}{y} + \frac{x - 1}{{y}^{3}}\right)} + \left(x - \frac{1}{{y}^{2}}\right)\right) \]
      rational.json-simplify-15 [<=] 0.0	\[ \frac{x}{{y}^{2}} + \left(-1 \cdot \left(\frac{\color{blue}{x + -1}}{y} + \frac{x - 1}{{y}^{3}}\right) + \left(x - \frac{1}{{y}^{2}}\right)\right) \]
      rational.json-simplify-15 [<=] 0.0	\[ \frac{x}{{y}^{2}} + \left(-1 \cdot \left(\frac{x + -1}{y} + \frac{\color{blue}{x + -1}}{{y}^{3}}\right) + \left(x - \frac{1}{{y}^{2}}\right)\right) \]

   if -11800 < y < 3.6e5

   1. Initial program 0.0

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

   2. Simplified 0.1

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

      [Start] 0.0	\[ 1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
      rational.json-simplify-49 [=>] 0.1	\[ 1 - \color{blue}{y \cdot \frac{1 - x}{y + 1}} \]
      rational.json-simplify-1 [=>] 0.1	\[ 1 - y \cdot \frac{1 - x}{\color{blue}{1 + y}} \]
      rational.json-simplify-17 [=>] 0.1	\[ 1 - y \cdot \frac{1 - x}{\color{blue}{y - -1}} \]
      rational.json-simplify-50 [=>] 0.1	\[ 1 - y \cdot \color{blue}{\frac{-\left(1 - x\right)}{-1 - y}} \]
      rational.json-simplify-8 [=>] 0.1	\[ 1 - y \cdot \frac{\color{blue}{\left(1 - x\right) \cdot -1}}{-1 - y} \]
      rational.json-simplify-2 [=>] 0.1	\[ 1 - y \cdot \frac{\color{blue}{-1 \cdot \left(1 - x\right)}}{-1 - y} \]
      rational.json-simplify-49 [=>] 0.1	\[ 1 - y \cdot \color{blue}{\left(\left(1 - x\right) \cdot \frac{-1}{-1 - y}\right)} \]
      rational.json-simplify-2 [=>] 0.1	\[ 1 - y \cdot \color{blue}{\left(\frac{-1}{-1 - y} \cdot \left(1 - x\right)\right)} \]
      rational.json-simplify-2 [<=] 0.1	\[ 1 - y \cdot \color{blue}{\left(\left(1 - x\right) \cdot \frac{-1}{-1 - y}\right)} \]
      rational.json-simplify-49 [<=] 0.1	\[ 1 - y \cdot \color{blue}{\frac{-1 \cdot \left(1 - x\right)}{-1 - y}} \]
      rational.json-simplify-2 [<=] 0.1	\[ 1 - y \cdot \frac{\color{blue}{\left(1 - x\right) \cdot -1}}{-1 - y} \]
      rational.json-simplify-8 [<=] 0.1	\[ 1 - y \cdot \frac{\color{blue}{-\left(1 - x\right)}}{-1 - y} \]
      rational.json-simplify-50 [<=] 0.1	\[ 1 - y \cdot \color{blue}{\frac{1 - x}{y - -1}} \]
      rational.json-simplify-17 [<=] 0.1	\[ 1 - y \cdot \frac{1 - x}{\color{blue}{1 + y}} \]

   if 3.6e5 < y

   1. Initial program 46.1

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

   2. Simplified 28.9

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

      [Start] 46.1	\[ 1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
      rational.json-simplify-2 [=>] 46.1	\[ 1 - \frac{\color{blue}{y \cdot \left(1 - x\right)}}{y + 1} \]
      rational.json-simplify-49 [=>] 28.9	\[ 1 - \color{blue}{\left(1 - x\right) \cdot \frac{y}{y + 1}} \]
      rational.json-simplify-2 [=>] 28.9	\[ 1 - \color{blue}{\frac{y}{y + 1} \cdot \left(1 - x\right)} \]
      rational.json-simplify-35 [=>] 28.9	\[ 1 - \color{blue}{\frac{y + y}{\left(y + 1\right) + \left(y + 1\right)}} \cdot \left(1 - x\right) \]
      rational.json-simplify-7 [<=] 28.9	\[ 1 - \frac{y + y}{\color{blue}{\frac{\left(y + 1\right) + \left(y + 1\right)}{1}}} \cdot \left(1 - x\right) \]
      rational.json-simplify-61 [=>] 28.9	\[ 1 - \color{blue}{\frac{1}{\frac{\left(y + 1\right) + \left(y + 1\right)}{y + y}}} \cdot \left(1 - x\right) \]
      rational.json-simplify-7 [<=] 28.9	\[ 1 - \frac{1}{\frac{\left(y + 1\right) + \left(y + 1\right)}{y + y}} \cdot \color{blue}{\frac{1 - x}{1}} \]
      rational.json-simplify-55 [=>] 28.9	\[ 1 - \color{blue}{\frac{\frac{1 - x}{1}}{\frac{\frac{\left(y + 1\right) + \left(y + 1\right)}{y + y}}{1}}} \]
      rational.json-simplify-7 [=>] 28.9	\[ 1 - \frac{\color{blue}{1 - x}}{\frac{\frac{\left(y + 1\right) + \left(y + 1\right)}{y + y}}{1}} \]
      rational.json-simplify-7 [=>] 28.9	\[ 1 - \frac{1 - x}{\color{blue}{\frac{\left(y + 1\right) + \left(y + 1\right)}{y + y}}} \]
      rational.json-simplify-36 [=>] 28.9	\[ 1 - \frac{1 - x}{\color{blue}{\frac{y + 1}{y}}} \]
      rational.json-simplify-5 [<=] 28.9	\[ 1 - \frac{1 - x}{\frac{y + 1}{\color{blue}{y - 0}}} \]
      rational.json-simplify-50 [=>] 28.9	\[ 1 - \frac{1 - x}{\color{blue}{\frac{-\left(y + 1\right)}{0 - y}}} \]
      rational.json-simplify-12 [=>] 28.9	\[ 1 - \frac{1 - x}{\frac{\color{blue}{0 - \left(y + 1\right)}}{0 - y}} \]
      rational.json-simplify-1 [=>] 28.9	\[ 1 - \frac{1 - x}{\frac{0 - \color{blue}{\left(1 + y\right)}}{0 - y}} \]
      rational.json-simplify-17 [=>] 28.9	\[ 1 - \frac{1 - x}{\frac{0 - \color{blue}{\left(y - -1\right)}}{0 - y}} \]
      rational.json-simplify-45 [<=] 28.9	\[ 1 - \frac{1 - x}{\frac{\color{blue}{-1 - \left(y - 0\right)}}{0 - y}} \]
      rational.json-simplify-5 [=>] 28.9	\[ 1 - \frac{1 - x}{\frac{-1 - \color{blue}{y}}{0 - y}} \]
      rational.json-simplify-12 [<=] 28.9	\[ 1 - \frac{1 - x}{\frac{-1 - y}{\color{blue}{-y}}} \]
      rational.json-simplify-8 [=>] 28.9	\[ 1 - \frac{1 - x}{\frac{-1 - y}{\color{blue}{y \cdot -1}}} \]
      rational.json-simplify-2 [=>] 28.9	\[ 1 - \frac{1 - x}{\frac{-1 - y}{\color{blue}{-1 \cdot y}}} \]
      rational.json-simplify-25 [=>] 28.9	\[ 1 - \frac{1 - x}{\color{blue}{\frac{-1}{-1} + \frac{1}{y}}} \]
      metadata-eval [=>] 28.9	\[ 1 - \frac{1 - x}{\color{blue}{1} + \frac{1}{y}} \]

   3. Taylor expanded in y around inf 0.0

      \[\leadsto \color{blue}{\left(\frac{1}{y} + \left(-1 \cdot \frac{1 + -1 \cdot x}{{y}^{2}} + x\right)\right) - \frac{x}{y}} \]

   4. Simplified 0.0

      \[\leadsto \color{blue}{\frac{1}{y} + \left(\frac{x + -1}{{y}^{2}} + \left(x - \frac{x}{y}\right)\right)} \]
      Proof

      [Start] 0.0	\[ \left(\frac{1}{y} + \left(-1 \cdot \frac{1 + -1 \cdot x}{{y}^{2}} + x\right)\right) - \frac{x}{y} \]
      rational.json-simplify-1 [=>] 0.0	\[ \color{blue}{\left(\left(-1 \cdot \frac{1 + -1 \cdot x}{{y}^{2}} + x\right) + \frac{1}{y}\right)} - \frac{x}{y} \]
      rational.json-simplify-48 [=>] 0.0	\[ \color{blue}{\frac{1}{y} + \left(\left(-1 \cdot \frac{1 + -1 \cdot x}{{y}^{2}} + x\right) - \frac{x}{y}\right)} \]
      rational.json-simplify-1 [=>] 0.0	\[ \frac{1}{y} + \left(\color{blue}{\left(x + -1 \cdot \frac{1 + -1 \cdot x}{{y}^{2}}\right)} - \frac{x}{y}\right) \]
      rational.json-simplify-48 [=>] 0.0	\[ \frac{1}{y} + \color{blue}{\left(-1 \cdot \frac{1 + -1 \cdot x}{{y}^{2}} + \left(x - \frac{x}{y}\right)\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11800:\\ \;\;\;\;\frac{x}{{y}^{2}} + \left(-1 \cdot \left(\frac{x + -1}{y} + \frac{x + -1}{{y}^{3}}\right) + \left(x - \frac{1}{{y}^{2}}\right)\right)\\ \mathbf{elif}\;y \leq 360000:\\ \;\;\;\;1 - y \cdot \frac{1 - x}{1 + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} + \left(\frac{x + -1}{{y}^{2}} + \left(x - \frac{x}{y}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	0.1
Cost	7688

\[\begin{array}{l} t_0 := \frac{1}{y} + \left(\frac{x + -1}{{y}^{2}} + \left(x - \frac{x}{y}\right)\right)\\ \mathbf{if}\;y \leq -290000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 360000:\\ \;\;\;\;1 - y \cdot \frac{1 - x}{1 + y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.1
Cost	968

\[\begin{array}{l} t_0 := x + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -112000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 220000000:\\ \;\;\;\;1 - y \cdot \frac{1 - x}{1 + y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	0.1
Cost	968

\[\begin{array}{l} t_0 := x + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -130000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 220000000:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	8.9
Cost	780

\[\begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+14}:\\ \;\;\;\;1 - y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Error	1.1
Cost	712

\[\begin{array}{l} t_0 := x + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.2:\\ \;\;\;\;1 - y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	1.0
Cost	712

\[\begin{array}{l} t_0 := x + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1 - y \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	15.9
Cost	588

\[\begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{elif}\;y \leq 0.00011:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	15.6
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.00011:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	15.7
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.00011:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Error	39.0
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023064 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (if (< y -3693.8482788297247) (- (/ 1.0 y) (- (/ x y) x)) (if (< y 6799310503.41891) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) (- (/ 1.0 y) (- (/ x y) x))))

  (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))