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

Percentage Accurate: 65.4% → 99.9%

Time: 11.0s

Precision: binary64

Cost: 7940

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x + -1}{y \cdot y}\\ t_1 := \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -11500:\\ \;\;\;\;\left(x + \left(\frac{1 - x}{{y}^{3}} + t_1\right)\right) + t_0\\ \mathbf{elif}\;y \leq 300000:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(x + t_1\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (+ x -1.0) (* y y))) (t_1 (/ (- 1.0 x) y)))
   (if (<= y -11500.0)
     (+ (+ x (+ (/ (- 1.0 x) (pow y 3.0)) t_1)) t_0)
     (if (<= y 300000.0)
       (+ 1.0 (* y (/ (+ x -1.0) (+ y 1.0))))
       (+ t_0 (+ x t_1))))))

C

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

↓

double code(double x, double y) {
	double t_0 = (x + -1.0) / (y * y);
	double t_1 = (1.0 - x) / y;
	double tmp;
	if (y <= -11500.0) {
		tmp = (x + (((1.0 - x) / pow(y, 3.0)) + t_1)) + t_0;
	} else if (y <= 300000.0) {
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)));
	} else {
		tmp = t_0 + (x + t_1);
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x + (-1.0d0)) / (y * y)
    t_1 = (1.0d0 - x) / y
    if (y <= (-11500.0d0)) then
        tmp = (x + (((1.0d0 - x) / (y ** 3.0d0)) + t_1)) + t_0
    else if (y <= 300000.0d0) then
        tmp = 1.0d0 + (y * ((x + (-1.0d0)) / (y + 1.0d0)))
    else
        tmp = t_0 + (x + t_1)
    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 t_0 = (x + -1.0) / (y * y);
	double t_1 = (1.0 - x) / y;
	double tmp;
	if (y <= -11500.0) {
		tmp = (x + (((1.0 - x) / Math.pow(y, 3.0)) + t_1)) + t_0;
	} else if (y <= 300000.0) {
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)));
	} else {
		tmp = t_0 + (x + t_1);
	}
	return tmp;
}

Python

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

↓

def code(x, y):
	t_0 = (x + -1.0) / (y * y)
	t_1 = (1.0 - x) / y
	tmp = 0
	if y <= -11500.0:
		tmp = (x + (((1.0 - x) / math.pow(y, 3.0)) + t_1)) + t_0
	elif y <= 300000.0:
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)))
	else:
		tmp = t_0 + (x + t_1)
	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)
	t_0 = Float64(Float64(x + -1.0) / Float64(y * y))
	t_1 = Float64(Float64(1.0 - x) / y)
	tmp = 0.0
	if (y <= -11500.0)
		tmp = Float64(Float64(x + Float64(Float64(Float64(1.0 - x) / (y ^ 3.0)) + t_1)) + t_0);
	elseif (y <= 300000.0)
		tmp = Float64(1.0 + Float64(y * Float64(Float64(x + -1.0) / Float64(y + 1.0))));
	else
		tmp = Float64(t_0 + Float64(x + t_1));
	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)
	t_0 = (x + -1.0) / (y * y);
	t_1 = (1.0 - x) / y;
	tmp = 0.0;
	if (y <= -11500.0)
		tmp = (x + (((1.0 - x) / (y ^ 3.0)) + t_1)) + t_0;
	elseif (y <= 300000.0)
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)));
	else
		tmp = t_0 + (x + t_1);
	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_] := Block[{t$95$0 = N[(N[(x + -1.0), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -11500.0], N[(N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[y, 300000.0], N[(1.0 + N[(y * N[(N[(x + -1.0), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(x + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	65.4%
Target	99.7%
Herbie	99.9%

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

Derivation

1. Split input into 3 regimes

2. if y < -11500

   1. Initial program 34.7%

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

   2. Simplified 54.4%

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

      [Start] 34.7%	\[ 1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
      sub-neg [=>] 34.7%	\[ \color{blue}{1 + \left(-\frac{\left(1 - x\right) \cdot y}{y + 1}\right)} \]
      distribute-neg-frac [=>] 34.7%	\[ 1 + \color{blue}{\frac{-\left(1 - x\right) \cdot y}{y + 1}} \]
      neg-mul-1 [=>] 34.7%	\[ 1 + \frac{\color{blue}{-1 \cdot \left(\left(1 - x\right) \cdot y\right)}}{y + 1} \]
      associate-*l/ [<=] 34.5%	\[ 1 + \color{blue}{\frac{-1}{y + 1} \cdot \left(\left(1 - x\right) \cdot y\right)} \]
      metadata-eval [<=] 34.5%	\[ 1 + \frac{\color{blue}{1 \cdot -1}}{y + 1} \cdot \left(\left(1 - x\right) \cdot y\right) \]
      associate-*l/ [<=] 34.5%	\[ 1 + \color{blue}{\left(\frac{1}{y + 1} \cdot -1\right)} \cdot \left(\left(1 - x\right) \cdot y\right) \]
      associate-/r/ [<=] 34.5%	\[ 1 + \color{blue}{\frac{1}{\frac{y + 1}{-1}}} \cdot \left(\left(1 - x\right) \cdot y\right) \]
      metadata-eval [<=] 34.5%	\[ 1 + \frac{\color{blue}{--1}}{\frac{y + 1}{-1}} \cdot \left(\left(1 - x\right) \cdot y\right) \]
      distribute-neg-frac [<=] 34.5%	\[ 1 + \color{blue}{\left(-\frac{-1}{\frac{y + 1}{-1}}\right)} \cdot \left(\left(1 - x\right) \cdot y\right) \]
      cancel-sign-sub-inv [<=] 34.5%	\[ \color{blue}{1 - \frac{-1}{\frac{y + 1}{-1}} \cdot \left(\left(1 - x\right) \cdot y\right)} \]
      associate-/r/ [<=] 34.5%	\[ 1 - \color{blue}{\frac{-1}{\frac{\frac{y + 1}{-1}}{\left(1 - x\right) \cdot y}}} \]
      associate-/r* [<=] 34.5%	\[ 1 - \frac{-1}{\color{blue}{\frac{y + 1}{-1 \cdot \left(\left(1 - x\right) \cdot y\right)}}} \]
      neg-mul-1 [<=] 34.5%	\[ 1 - \frac{-1}{\frac{y + 1}{\color{blue}{-\left(1 - x\right) \cdot y}}} \]
      associate-/r/ [=>] 34.5%	\[ 1 - \color{blue}{\frac{-1}{y + 1} \cdot \left(-\left(1 - x\right) \cdot y\right)} \]
      distribute-rgt-neg-in [<=] 34.5%	\[ 1 - \color{blue}{\left(-\frac{-1}{y + 1} \cdot \left(\left(1 - x\right) \cdot y\right)\right)} \]
      associate-/r/ [<=] 34.5%	\[ 1 - \left(-\color{blue}{\frac{-1}{\frac{y + 1}{\left(1 - x\right) \cdot y}}}\right) \]
      distribute-neg-frac [=>] 34.5%	\[ 1 - \color{blue}{\frac{--1}{\frac{y + 1}{\left(1 - x\right) \cdot y}}} \]
      metadata-eval [=>] 34.5%	\[ 1 - \frac{\color{blue}{1}}{\frac{y + 1}{\left(1 - x\right) \cdot y}} \]
      associate-/r/ [=>] 34.5%	\[ 1 - \color{blue}{\frac{1}{y + 1} \cdot \left(\left(1 - x\right) \cdot y\right)} \]

   3. Taylor expanded in y around -inf 99.9%

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

   4. Simplified 99.9%

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

      [Start] 99.9%	\[ \left(\frac{x}{{y}^{2}} + \left(-1 \cdot \frac{x - 1}{y} + \left(-1 \cdot \frac{x - 1}{{y}^{3}} + x\right)\right)\right) - \frac{1}{{y}^{2}} \]
      +-commutative [=>] 99.9%	\[ \color{blue}{\left(\left(-1 \cdot \frac{x - 1}{y} + \left(-1 \cdot \frac{x - 1}{{y}^{3}} + x\right)\right) + \frac{x}{{y}^{2}}\right)} - \frac{1}{{y}^{2}} \]
      associate--l+ [=>] 99.9%	\[ \color{blue}{\left(-1 \cdot \frac{x - 1}{y} + \left(-1 \cdot \frac{x - 1}{{y}^{3}} + x\right)\right) + \left(\frac{x}{{y}^{2}} - \frac{1}{{y}^{2}}\right)} \]

   if -11500 < y < 3e5

   1. Initial program 100.0%

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

   2. Simplified 100.0%

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

      [Start] 100.0%	\[ 1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
      sub-neg [=>] 100.0%	\[ \color{blue}{1 + \left(-\frac{\left(1 - x\right) \cdot y}{y + 1}\right)} \]
      distribute-neg-frac [=>] 100.0%	\[ 1 + \color{blue}{\frac{-\left(1 - x\right) \cdot y}{y + 1}} \]
      neg-mul-1 [=>] 100.0%	\[ 1 + \frac{\color{blue}{-1 \cdot \left(\left(1 - x\right) \cdot y\right)}}{y + 1} \]
      associate-*l/ [<=] 100.0%	\[ 1 + \color{blue}{\frac{-1}{y + 1} \cdot \left(\left(1 - x\right) \cdot y\right)} \]
      metadata-eval [<=] 100.0%	\[ 1 + \frac{\color{blue}{1 \cdot -1}}{y + 1} \cdot \left(\left(1 - x\right) \cdot y\right) \]
      associate-*l/ [<=] 100.0%	\[ 1 + \color{blue}{\left(\frac{1}{y + 1} \cdot -1\right)} \cdot \left(\left(1 - x\right) \cdot y\right) \]
      associate-/r/ [<=] 100.0%	\[ 1 + \color{blue}{\frac{1}{\frac{y + 1}{-1}}} \cdot \left(\left(1 - x\right) \cdot y\right) \]
      metadata-eval [<=] 100.0%	\[ 1 + \frac{\color{blue}{--1}}{\frac{y + 1}{-1}} \cdot \left(\left(1 - x\right) \cdot y\right) \]
      distribute-neg-frac [<=] 100.0%	\[ 1 + \color{blue}{\left(-\frac{-1}{\frac{y + 1}{-1}}\right)} \cdot \left(\left(1 - x\right) \cdot y\right) \]
      cancel-sign-sub-inv [<=] 100.0%	\[ \color{blue}{1 - \frac{-1}{\frac{y + 1}{-1}} \cdot \left(\left(1 - x\right) \cdot y\right)} \]
      associate-/r/ [<=] 99.9%	\[ 1 - \color{blue}{\frac{-1}{\frac{\frac{y + 1}{-1}}{\left(1 - x\right) \cdot y}}} \]
      associate-/r* [<=] 99.9%	\[ 1 - \frac{-1}{\color{blue}{\frac{y + 1}{-1 \cdot \left(\left(1 - x\right) \cdot y\right)}}} \]
      neg-mul-1 [<=] 99.9%	\[ 1 - \frac{-1}{\frac{y + 1}{\color{blue}{-\left(1 - x\right) \cdot y}}} \]
      associate-/r/ [=>] 100.0%	\[ 1 - \color{blue}{\frac{-1}{y + 1} \cdot \left(-\left(1 - x\right) \cdot y\right)} \]
      distribute-rgt-neg-in [<=] 100.0%	\[ 1 - \color{blue}{\left(-\frac{-1}{y + 1} \cdot \left(\left(1 - x\right) \cdot y\right)\right)} \]
      associate-/r/ [<=] 99.9%	\[ 1 - \left(-\color{blue}{\frac{-1}{\frac{y + 1}{\left(1 - x\right) \cdot y}}}\right) \]
      distribute-neg-frac [=>] 99.9%	\[ 1 - \color{blue}{\frac{--1}{\frac{y + 1}{\left(1 - x\right) \cdot y}}} \]
      metadata-eval [=>] 99.9%	\[ 1 - \frac{\color{blue}{1}}{\frac{y + 1}{\left(1 - x\right) \cdot y}} \]
      associate-/r/ [=>] 100.0%	\[ 1 - \color{blue}{\frac{1}{y + 1} \cdot \left(\left(1 - x\right) \cdot y\right)} \]

   if 3e5 < y

   1. Initial program 39.4%

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

   2. Simplified 58.8%

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

      [Start] 39.4%	\[ 1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
      sub-neg [=>] 39.4%	\[ \color{blue}{1 + \left(-\frac{\left(1 - x\right) \cdot y}{y + 1}\right)} \]
      distribute-neg-frac [=>] 39.4%	\[ 1 + \color{blue}{\frac{-\left(1 - x\right) \cdot y}{y + 1}} \]
      neg-mul-1 [=>] 39.4%	\[ 1 + \frac{\color{blue}{-1 \cdot \left(\left(1 - x\right) \cdot y\right)}}{y + 1} \]
      associate-*l/ [<=] 39.6%	\[ 1 + \color{blue}{\frac{-1}{y + 1} \cdot \left(\left(1 - x\right) \cdot y\right)} \]
      metadata-eval [<=] 39.6%	\[ 1 + \frac{\color{blue}{1 \cdot -1}}{y + 1} \cdot \left(\left(1 - x\right) \cdot y\right) \]
      associate-*l/ [<=] 39.6%	\[ 1 + \color{blue}{\left(\frac{1}{y + 1} \cdot -1\right)} \cdot \left(\left(1 - x\right) \cdot y\right) \]
      associate-/r/ [<=] 39.6%	\[ 1 + \color{blue}{\frac{1}{\frac{y + 1}{-1}}} \cdot \left(\left(1 - x\right) \cdot y\right) \]
      metadata-eval [<=] 39.6%	\[ 1 + \frac{\color{blue}{--1}}{\frac{y + 1}{-1}} \cdot \left(\left(1 - x\right) \cdot y\right) \]
      distribute-neg-frac [<=] 39.6%	\[ 1 + \color{blue}{\left(-\frac{-1}{\frac{y + 1}{-1}}\right)} \cdot \left(\left(1 - x\right) \cdot y\right) \]
      cancel-sign-sub-inv [<=] 39.6%	\[ \color{blue}{1 - \frac{-1}{\frac{y + 1}{-1}} \cdot \left(\left(1 - x\right) \cdot y\right)} \]
      associate-/r/ [<=] 39.3%	\[ 1 - \color{blue}{\frac{-1}{\frac{\frac{y + 1}{-1}}{\left(1 - x\right) \cdot y}}} \]
      associate-/r* [<=] 39.3%	\[ 1 - \frac{-1}{\color{blue}{\frac{y + 1}{-1 \cdot \left(\left(1 - x\right) \cdot y\right)}}} \]
      neg-mul-1 [<=] 39.3%	\[ 1 - \frac{-1}{\frac{y + 1}{\color{blue}{-\left(1 - x\right) \cdot y}}} \]
      associate-/r/ [=>] 39.6%	\[ 1 - \color{blue}{\frac{-1}{y + 1} \cdot \left(-\left(1 - x\right) \cdot y\right)} \]
      distribute-rgt-neg-in [<=] 39.6%	\[ 1 - \color{blue}{\left(-\frac{-1}{y + 1} \cdot \left(\left(1 - x\right) \cdot y\right)\right)} \]
      associate-/r/ [<=] 39.3%	\[ 1 - \left(-\color{blue}{\frac{-1}{\frac{y + 1}{\left(1 - x\right) \cdot y}}}\right) \]
      distribute-neg-frac [=>] 39.3%	\[ 1 - \color{blue}{\frac{--1}{\frac{y + 1}{\left(1 - x\right) \cdot y}}} \]
      metadata-eval [=>] 39.3%	\[ 1 - \frac{\color{blue}{1}}{\frac{y + 1}{\left(1 - x\right) \cdot y}} \]
      associate-/r/ [=>] 39.6%	\[ 1 - \color{blue}{\frac{1}{y + 1} \cdot \left(\left(1 - x\right) \cdot y\right)} \]

   3. Taylor expanded in y around -inf 100.0%

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

   4. Simplified 100.0%

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

      [Start] 100.0%	\[ \left(\frac{x}{{y}^{2}} + \left(-1 \cdot \frac{x - 1}{y} + x\right)\right) - \frac{1}{{y}^{2}} \]
      +-commutative [=>] 100.0%	\[ \color{blue}{\left(\left(-1 \cdot \frac{x - 1}{y} + x\right) + \frac{x}{{y}^{2}}\right)} - \frac{1}{{y}^{2}} \]
      associate--l+ [=>] 100.0%	\[ \color{blue}{\left(-1 \cdot \frac{x - 1}{y} + x\right) + \left(\frac{x}{{y}^{2}} - \frac{1}{{y}^{2}}\right)} \]
      +-commutative [=>] 100.0%	\[ \color{blue}{\left(x + -1 \cdot \frac{x - 1}{y}\right)} + \left(\frac{x}{{y}^{2}} - \frac{1}{{y}^{2}}\right) \]
      mul-1-neg [=>] 100.0%	\[ \left(x + \color{blue}{\left(-\frac{x - 1}{y}\right)}\right) + \left(\frac{x}{{y}^{2}} - \frac{1}{{y}^{2}}\right) \]
      unsub-neg [=>] 100.0%	\[ \color{blue}{\left(x - \frac{x - 1}{y}\right)} + \left(\frac{x}{{y}^{2}} - \frac{1}{{y}^{2}}\right) \]
      sub-neg [=>] 100.0%	\[ \left(x - \frac{\color{blue}{x + \left(-1\right)}}{y}\right) + \left(\frac{x}{{y}^{2}} - \frac{1}{{y}^{2}}\right) \]
      metadata-eval [=>] 100.0%	\[ \left(x - \frac{x + \color{blue}{-1}}{y}\right) + \left(\frac{x}{{y}^{2}} - \frac{1}{{y}^{2}}\right) \]
      div-sub [<=] 100.0%	\[ \left(x - \frac{x + -1}{y}\right) + \color{blue}{\frac{x - 1}{{y}^{2}}} \]
      sub-neg [=>] 100.0%	\[ \left(x - \frac{x + -1}{y}\right) + \frac{\color{blue}{x + \left(-1\right)}}{{y}^{2}} \]
      metadata-eval [=>] 100.0%	\[ \left(x - \frac{x + -1}{y}\right) + \frac{x + \color{blue}{-1}}{{y}^{2}} \]
      unpow2 [=>] 100.0%	\[ \left(x - \frac{x + -1}{y}\right) + \frac{x + -1}{\color{blue}{y \cdot y}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11500:\\ \;\;\;\;\left(x + \left(\frac{1 - x}{{y}^{3}} + \frac{1 - x}{y}\right)\right) + \frac{x + -1}{y \cdot y}\\ \mathbf{elif}\;y \leq 300000:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -1}{y \cdot y} + \left(x + \frac{1 - x}{y}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	99.9%
Cost	7940

\[\begin{array}{l} t_0 := \frac{x + -1}{y \cdot y}\\ t_1 := \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -11500:\\ \;\;\;\;\left(x + \left(\frac{1 - x}{{y}^{3}} + t_1\right)\right) + t_0\\ \mathbf{elif}\;y \leq 300000:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(x + t_1\right)\\ \end{array} \]

Alternative 2
Accuracy	99.9%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;y \leq -205000 \lor \neg \left(y \leq 300000\right):\\ \;\;\;\;\frac{x + -1}{y \cdot y} + \left(x + \frac{1 - x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \end{array} \]

Alternative 3
Accuracy	99.8%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -200000000 \lor \neg \left(y \leq 340000000\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \end{array} \]

Alternative 4
Accuracy	99.0%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -4600 \lor \neg \left(y \leq 1150000\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{x}{y + 1}\\ \end{array} \]

Alternative 5
Accuracy	98.3%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.85\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(y \cdot x - y\right)\\ \end{array} \]

Alternative 6
Accuracy	98.6%
Cost	713

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

Alternative 7
Accuracy	85.8%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 6.8 \cdot 10^{-17}\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 8
Accuracy	98.1%
Cost	585

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

Alternative 9
Accuracy	73.4%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-17}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Accuracy	73.3%
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Accuracy	38.5%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023271 
(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))))