Average Error: 5.7 → 0.1
Time: 10.6s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(1 - x\right) \cdot \left(\frac{1}{y} - \frac{x}{y \cdot 3}\right)\]
\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)
double f(double x, double y) {
        double r593796 = 1.0;
        double r593797 = x;
        double r593798 = r593796 - r593797;
        double r593799 = 3.0;
        double r593800 = r593799 - r593797;
        double r593801 = r593798 * r593800;
        double r593802 = y;
        double r593803 = r593802 * r593799;
        double r593804 = r593801 / r593803;
        return r593804;
}
↓
double f(double x, double y) {
        double r593805 = 1.0;
        double r593806 = x;
        double r593807 = r593805 - r593806;
        double r593808 = 1.0;
        double r593809 = y;
        double r593810 = r593808 / r593809;
        double r593811 = 3.0;
        double r593812 = r593809 * r593811;
        double r593813 = r593806 / r593812;
        double r593814 = r593810 - r593813;
        double r593815 = r593807 * r593814;
        return r593815;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 5.7

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

  2. Simplified0.3

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

  4. Applied div-sub0.3

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

  5. Simplified0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"

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

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