Average Error: 5.6 → 0.2
Time: 2.0s
Precision: binary64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(1 - x\right) \cdot \left(\frac{1}{y} - \frac{x}{y \cdot 3}\right)\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(1 - x\right) \cdot \left(\frac{1}{y} - \frac{x}{y \cdot 3}\right)
(FPCore (x y) :precision binary64 (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))
↓
(FPCore (x y) :precision binary64 (* (- 1.0 x) (- (/ 1.0 y) (/ x (* y 3.0)))))
double code(double x, double y) {
	return (((double) (((double) (1.0 - x)) * ((double) (3.0 - x)))) / ((double) (y * 3.0)));
}
↓
double code(double x, double y) {
	return ((double) (((double) (1.0 - x)) * ((double) ((1.0 / y) - (x / ((double) (y * 3.0)))))));
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original5.6
Target0.1
Herbie0.2
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.6

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]

  2. Simplified0.4

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

  4. Applied div-sub0.4

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

  5. Simplified0.2

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

  6. Final simplification0.2

    \[\leadsto \left(1 - x\right) \cdot \left(\frac{1}{y} - \frac{x}{y \cdot 3}\right)\]

Reproduce

herbie shell --seed 2020198 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0))

  (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))