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

Average Error: 50.02% → 20.94%

Time: 8.5s

Precision: binary64

Cost: 8536

Math

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

↓

\[\begin{array}{l} t_0 := y \cdot \left(y \cdot -4\right)\\ t_1 := x \cdot x + y \cdot \left(y \cdot 4\right)\\ t_2 := \frac{x \cdot x + t_0}{t_1}\\ t_3 := \mathsf{fma}\left(0.5, \frac{x}{y} \cdot \frac{x}{y}, -1\right)\\ \mathbf{if}\;x \cdot x \leq 5 \cdot 10^{-285}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-244}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-86}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot x \leq 10^{+124}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, x, t_0\right)}{t_1}\\ \mathbf{elif}\;x \cdot x \leq 4 \cdot 10^{+139}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{+184}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{x} \cdot \frac{y}{x}, -8, 1\right)\\ \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (* y -4.0)))
        (t_1 (+ (* x x) (* y (* y 4.0))))
        (t_2 (/ (+ (* x x) t_0) t_1))
        (t_3 (fma 0.5 (* (/ x y) (/ x y)) -1.0)))
   (if (<= (* x x) 5e-285)
     t_3
     (if (<= (* x x) 5e-244)
       t_2
       (if (<= (* x x) 5e-86)
         t_3
         (if (<= (* x x) 1e+124)
           (/ (fma x x t_0) t_1)
           (if (<= (* x x) 4e+139)
             t_3
             (if (<= (* x x) 5e+184)
               t_2
               (fma (* (/ y x) (/ y x)) -8.0 1.0)))))))))

C

double code(double x, double y) {
	return ((x * x) - ((y * 4.0) * y)) / ((x * x) + ((y * 4.0) * y));
}

↓

double code(double x, double y) {
	double t_0 = y * (y * -4.0);
	double t_1 = (x * x) + (y * (y * 4.0));
	double t_2 = ((x * x) + t_0) / t_1;
	double t_3 = fma(0.5, ((x / y) * (x / y)), -1.0);
	double tmp;
	if ((x * x) <= 5e-285) {
		tmp = t_3;
	} else if ((x * x) <= 5e-244) {
		tmp = t_2;
	} else if ((x * x) <= 5e-86) {
		tmp = t_3;
	} else if ((x * x) <= 1e+124) {
		tmp = fma(x, x, t_0) / t_1;
	} else if ((x * x) <= 4e+139) {
		tmp = t_3;
	} else if ((x * x) <= 5e+184) {
		tmp = t_2;
	} else {
		tmp = fma(((y / x) * (y / x)), -8.0, 1.0);
	}
	return tmp;
}

Julia

function code(x, y)
	return Float64(Float64(Float64(x * x) - Float64(Float64(y * 4.0) * y)) / Float64(Float64(x * x) + Float64(Float64(y * 4.0) * y)))
end

↓

function code(x, y)
	t_0 = Float64(y * Float64(y * -4.0))
	t_1 = Float64(Float64(x * x) + Float64(y * Float64(y * 4.0)))
	t_2 = Float64(Float64(Float64(x * x) + t_0) / t_1)
	t_3 = fma(0.5, Float64(Float64(x / y) * Float64(x / y)), -1.0)
	tmp = 0.0
	if (Float64(x * x) <= 5e-285)
		tmp = t_3;
	elseif (Float64(x * x) <= 5e-244)
		tmp = t_2;
	elseif (Float64(x * x) <= 5e-86)
		tmp = t_3;
	elseif (Float64(x * x) <= 1e+124)
		tmp = Float64(fma(x, x, t_0) / t_1);
	elseif (Float64(x * x) <= 4e+139)
		tmp = t_3;
	elseif (Float64(x * x) <= 5e+184)
		tmp = t_2;
	else
		tmp = fma(Float64(Float64(y / x) * Float64(y / x)), -8.0, 1.0);
	end
	return tmp
end

Wolfram

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

↓

code[x_, y_] := Block[{t$95$0 = N[(y * N[(y * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * x), $MachinePrecision] + N[(y * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * x), $MachinePrecision] + t$95$0), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(0.5 * N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]}, If[LessEqual[N[(x * x), $MachinePrecision], 5e-285], t$95$3, If[LessEqual[N[(x * x), $MachinePrecision], 5e-244], t$95$2, If[LessEqual[N[(x * x), $MachinePrecision], 5e-86], t$95$3, If[LessEqual[N[(x * x), $MachinePrecision], 1e+124], N[(N[(x * x + t$95$0), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[N[(x * x), $MachinePrecision], 4e+139], t$95$3, If[LessEqual[N[(x * x), $MachinePrecision], 5e+184], t$95$2, N[(N[(N[(y / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision] * -8.0 + 1.0), $MachinePrecision]]]]]]]]]]]

Target

Original	50.02%
Target	49.54%
Herbie	20.94%

\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} < 0.9743233849626781:\\ \;\;\;\;\frac{x \cdot x}{x \cdot x + \left(y \cdot y\right) \cdot 4} - \frac{\left(y \cdot y\right) \cdot 4}{x \cdot x + \left(y \cdot y\right) \cdot 4}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{x}{\sqrt{x \cdot x + \left(y \cdot y\right) \cdot 4}}\right)}^{2} - \frac{\left(y \cdot y\right) \cdot 4}{x \cdot x + \left(y \cdot y\right) \cdot 4}\\ \end{array} \]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x x) < 5.00000000000000018e-285 or 4.99999999999999998e-244 < (*.f64 x x) < 4.9999999999999999e-86 or 9.99999999999999948e123 < (*.f64 x x) < 4.00000000000000013e139

   1. Initial program 38.8

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

   2. Simplified 39.01

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot -4\right)}{\mathsf{fma}\left(x, x, y \cdot \left(y \cdot 4\right)\right)}} \]
      Proof

      [Start] 38.8	\[ \frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      fma-neg [=>] 38.79	\[ \frac{\color{blue}{\mathsf{fma}\left(x, x, -\left(y \cdot 4\right) \cdot y\right)}}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      *-commutative [=>] 38.79	\[ \frac{\mathsf{fma}\left(x, x, -\color{blue}{y \cdot \left(y \cdot 4\right)}\right)}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      associate-*r* [=>] 39.01	\[ \frac{\mathsf{fma}\left(x, x, -\color{blue}{\left(y \cdot y\right) \cdot 4}\right)}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      distribute-rgt-neg-in [=>] 39.01	\[ \frac{\mathsf{fma}\left(x, x, \color{blue}{\left(y \cdot y\right) \cdot \left(-4\right)}\right)}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      metadata-eval [=>] 39.01	\[ \frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot \color{blue}{-4}\right)}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      fma-def [=>] 39.01	\[ \frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot -4\right)}{\color{blue}{\mathsf{fma}\left(x, x, \left(y \cdot 4\right) \cdot y\right)}} \]
      *-commutative [=>] 39.01	\[ \frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot -4\right)}{\mathsf{fma}\left(x, x, \color{blue}{y \cdot \left(y \cdot 4\right)}\right)} \]

   3. Taylor expanded in x around 0 29.18

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2}}{{y}^{2}} - 1} \]

   4. Simplified 21.26

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, \frac{x}{y} \cdot \frac{x}{y}, -1\right)} \]
      Proof

      [Start] 29.18	\[ 0.5 \cdot \frac{{x}^{2}}{{y}^{2}} - 1 \]
      fma-neg [=>] 29.18	\[ \color{blue}{\mathsf{fma}\left(0.5, \frac{{x}^{2}}{{y}^{2}}, -1\right)} \]
      unpow2 [=>] 29.18	\[ \mathsf{fma}\left(0.5, \frac{\color{blue}{x \cdot x}}{{y}^{2}}, -1\right) \]
      unpow2 [=>] 29.18	\[ \mathsf{fma}\left(0.5, \frac{x \cdot x}{\color{blue}{y \cdot y}}, -1\right) \]
      times-frac [=>] 21.26	\[ \mathsf{fma}\left(0.5, \color{blue}{\frac{x}{y} \cdot \frac{x}{y}}, -1\right) \]
      metadata-eval [=>] 21.26	\[ \mathsf{fma}\left(0.5, \frac{x}{y} \cdot \frac{x}{y}, \color{blue}{-1}\right) \]

   if 5.00000000000000018e-285 < (*.f64 x x) < 4.99999999999999998e-244 or 4.00000000000000013e139 < (*.f64 x x) < 4.9999999999999999e184

   1. Initial program 27.86

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

   if 4.9999999999999999e-86 < (*.f64 x x) < 9.99999999999999948e123

   1. Initial program 25.85

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

   2. Taylor expanded in x around 0 25.85

      \[\leadsto \frac{\color{blue}{-4 \cdot {y}^{2} + {x}^{2}}}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]

   3. Simplified 25.85

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, x, y \cdot \left(y \cdot -4\right)\right)}}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      Proof

      [Start] 25.85	\[ \frac{-4 \cdot {y}^{2} + {x}^{2}}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      unpow2 [=>] 25.85	\[ \frac{-4 \cdot {y}^{2} + \color{blue}{x \cdot x}}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      *-commutative [=>] 25.85	\[ \frac{\color{blue}{{y}^{2} \cdot -4} + x \cdot x}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      unpow2 [=>] 25.85	\[ \frac{\color{blue}{\left(y \cdot y\right)} \cdot -4 + x \cdot x}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      associate-*r* [<=] 25.85	\[ \frac{\color{blue}{y \cdot \left(y \cdot -4\right)} + x \cdot x}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      +-commutative [<=] 25.85	\[ \frac{\color{blue}{x \cdot x + y \cdot \left(y \cdot -4\right)}}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      fma-def [=>] 25.85	\[ \frac{\color{blue}{\mathsf{fma}\left(x, x, y \cdot \left(y \cdot -4\right)\right)}}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]

   if 4.9999999999999999e184 < (*.f64 x x)

   1. Initial program 79.35

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

   2. Simplified 79.35

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot -4\right)}{\mathsf{fma}\left(x, x, y \cdot \left(y \cdot 4\right)\right)}} \]
      Proof

      [Start] 79.35	\[ \frac{x \cdot x - \left(y \cdot 4\right) \cdot y}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      fma-neg [=>] 79.35	\[ \frac{\color{blue}{\mathsf{fma}\left(x, x, -\left(y \cdot 4\right) \cdot y\right)}}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      *-commutative [=>] 79.35	\[ \frac{\mathsf{fma}\left(x, x, -\color{blue}{y \cdot \left(y \cdot 4\right)}\right)}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      associate-*r* [=>] 79.35	\[ \frac{\mathsf{fma}\left(x, x, -\color{blue}{\left(y \cdot y\right) \cdot 4}\right)}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      distribute-rgt-neg-in [=>] 79.35	\[ \frac{\mathsf{fma}\left(x, x, \color{blue}{\left(y \cdot y\right) \cdot \left(-4\right)}\right)}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      metadata-eval [=>] 79.35	\[ \frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot \color{blue}{-4}\right)}{x \cdot x + \left(y \cdot 4\right) \cdot y} \]
      fma-def [=>] 79.35	\[ \frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot -4\right)}{\color{blue}{\mathsf{fma}\left(x, x, \left(y \cdot 4\right) \cdot y\right)}} \]
      *-commutative [=>] 79.35	\[ \frac{\mathsf{fma}\left(x, x, \left(y \cdot y\right) \cdot -4\right)}{\mathsf{fma}\left(x, x, \color{blue}{y \cdot \left(y \cdot 4\right)}\right)} \]

   3. Taylor expanded in x around inf 25.96

      \[\leadsto \color{blue}{\left(1 + -4 \cdot \frac{{y}^{2}}{{x}^{2}}\right) - 4 \cdot \frac{{y}^{2}}{{x}^{2}}} \]

   4. Simplified 16.85

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{x} \cdot \frac{y}{x}, -8, 1\right)} \]
      Proof

      [Start] 25.96	\[ \left(1 + -4 \cdot \frac{{y}^{2}}{{x}^{2}}\right) - 4 \cdot \frac{{y}^{2}}{{x}^{2}} \]
      associate--l+ [=>] 25.95	\[ \color{blue}{1 + \left(-4 \cdot \frac{{y}^{2}}{{x}^{2}} - 4 \cdot \frac{{y}^{2}}{{x}^{2}}\right)} \]
      +-commutative [=>] 25.95	\[ \color{blue}{\left(-4 \cdot \frac{{y}^{2}}{{x}^{2}} - 4 \cdot \frac{{y}^{2}}{{x}^{2}}\right) + 1} \]
      distribute-rgt-out-- [=>] 25.95	\[ \color{blue}{\frac{{y}^{2}}{{x}^{2}} \cdot \left(-4 - 4\right)} + 1 \]
      metadata-eval [=>] 25.95	\[ \frac{{y}^{2}}{{x}^{2}} \cdot \color{blue}{-8} + 1 \]
      fma-def [=>] 25.95	\[ \color{blue}{\mathsf{fma}\left(\frac{{y}^{2}}{{x}^{2}}, -8, 1\right)} \]
      unpow2 [=>] 25.95	\[ \mathsf{fma}\left(\frac{\color{blue}{y \cdot y}}{{x}^{2}}, -8, 1\right) \]
      unpow2 [=>] 25.95	\[ \mathsf{fma}\left(\frac{y \cdot y}{\color{blue}{x \cdot x}}, -8, 1\right) \]
      times-frac [=>] 16.85	\[ \mathsf{fma}\left(\color{blue}{\frac{y}{x} \cdot \frac{y}{x}}, -8, 1\right) \]

3. Recombined 4 regimes into one program.

4. Final simplification 20.94

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 5 \cdot 10^{-285}:\\ \;\;\;\;\mathsf{fma}\left(0.5, \frac{x}{y} \cdot \frac{x}{y}, -1\right)\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-244}:\\ \;\;\;\;\frac{x \cdot x + y \cdot \left(y \cdot -4\right)}{x \cdot x + y \cdot \left(y \cdot 4\right)}\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-86}:\\ \;\;\;\;\mathsf{fma}\left(0.5, \frac{x}{y} \cdot \frac{x}{y}, -1\right)\\ \mathbf{elif}\;x \cdot x \leq 10^{+124}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, x, y \cdot \left(y \cdot -4\right)\right)}{x \cdot x + y \cdot \left(y \cdot 4\right)}\\ \mathbf{elif}\;x \cdot x \leq 4 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(0.5, \frac{x}{y} \cdot \frac{x}{y}, -1\right)\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{+184}:\\ \;\;\;\;\frac{x \cdot x + y \cdot \left(y \cdot -4\right)}{x \cdot x + y \cdot \left(y \cdot 4\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{x} \cdot \frac{y}{x}, -8, 1\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	20.94%
Cost	8536

\[\begin{array}{l} t_0 := \frac{x \cdot x + y \cdot \left(y \cdot -4\right)}{x \cdot x + y \cdot \left(y \cdot 4\right)}\\ t_1 := \mathsf{fma}\left(0.5, \frac{x}{y} \cdot \frac{x}{y}, -1\right)\\ \mathbf{if}\;x \cdot x \leq 5 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-244}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot x \leq 10^{+124}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot x \leq 4 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{+184}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{x} \cdot \frac{y}{x}, -8, 1\right)\\ \end{array} \]

Alternative 2
Error	21.01%
Cost	8276

\[\begin{array}{l} t_0 := \frac{x \cdot x + y \cdot \left(y \cdot -4\right)}{x \cdot x + y \cdot \left(y \cdot 4\right)}\\ t_1 := \mathsf{fma}\left(0.5, \frac{x}{y} \cdot \frac{x}{y}, -1\right)\\ \mathbf{if}\;x \cdot x \leq 5 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-244}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot x \leq 10^{+124}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot x \leq 4 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{+184}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{y \cdot 4}{x}\\ \end{array} \]

Alternative 3
Error	21.44%
Cost	2776

\[\begin{array}{l} t_0 := \frac{x \cdot x + y \cdot \left(y \cdot -4\right)}{x \cdot x + y \cdot \left(y \cdot 4\right)}\\ \mathbf{if}\;x \cdot x \leq 5 \cdot 10^{-285}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-244}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-86}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \cdot x \leq 10^{+124}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot x \leq 4 \cdot 10^{+139}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{+184}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{y \cdot 4}{x}\\ \end{array} \]

Alternative 4
Error	25.62%
Cost	1234

\[\begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-42} \lor \neg \left(x \leq 4.5 \cdot 10^{-61}\right) \land \left(x \leq 4800 \lor \neg \left(x \leq 7.5 \cdot 10^{+31}\right)\right):\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{y \cdot 4}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5
Error	25.97%
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-36}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-61}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+34}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	49.51%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023089 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:arcBetween from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))) 0.9743233849626781) (- (/ (* x x) (+ (* x x) (* (* y y) 4.0))) (/ (* (* y y) 4.0) (+ (* x x) (* (* y y) 4.0)))) (- (pow (/ x (sqrt (+ (* x x) (* (* y y) 4.0)))) 2.0) (/ (* (* y y) 4.0) (+ (* x x) (* (* y y) 4.0)))))

  (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))