Average Error: 5.7 → 0.2
Time: 2.7s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1 - x}{y} \cdot \left(1 - 0.333333333333333315 \cdot x\right)\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1 - x}{y} \cdot \left(1 - 0.333333333333333315 \cdot x\right)
double code(double x, double y) {
	return (((1.0 - x) * (3.0 - x)) / (y * 3.0));
}
↓
double code(double x, double y) {
	return (((1.0 - x) / y) * (1.0 - (0.3333333333333333 * x)));
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.7
Target0.1
Herbie0.2
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.7

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  2. Using strategy rm

  3. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{1 - x}{y} \cdot \frac{3 - x}{3}}\]

  4. Taylor expanded around 0 0.2

    \[\leadsto \frac{1 - x}{y} \cdot \color{blue}{\left(1 - 0.333333333333333315 \cdot x\right)}\]

  5. Final simplification0.2

    \[\leadsto \frac{1 - x}{y} \cdot \left(1 - 0.333333333333333315 \cdot x\right)\]

Reproduce

herbie shell --seed 2020103 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1 x) y) (/ (- 3 x) 3))

  (/ (* (- 1 x) (- 3 x)) (* y 3)))