Average Error: 0.2 → 0.3
Time: 12.5s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{1}{3} \cdot \frac{y}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{1}{3} \cdot \frac{y}{\sqrt{x}}
double f(double x, double y) {
        double r233101 = 1.0;
        double r233102 = x;
        double r233103 = 9.0;
        double r233104 = r233102 * r233103;
        double r233105 = r233101 / r233104;
        double r233106 = r233101 - r233105;
        double r233107 = y;
        double r233108 = 3.0;
        double r233109 = sqrt(r233102);
        double r233110 = r233108 * r233109;
        double r233111 = r233107 / r233110;
        double r233112 = r233106 - r233111;
        return r233112;
}
↓
double f(double x, double y) {
        double r233113 = 1.0;
        double r233114 = x;
        double r233115 = 9.0;
        double r233116 = r233114 * r233115;
        double r233117 = r233113 / r233116;
        double r233118 = r233113 - r233117;
        double r233119 = 1.0;
        double r233120 = 3.0;
        double r233121 = r233119 / r233120;
        double r233122 = y;
        double r233123 = sqrt(r233114);
        double r233124 = r233122 / r233123;
        double r233125 = r233121 * r233124;
        double r233126 = r233118 - r233125;
        return r233126;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.2
Target0.2
Herbie0.3
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]

Derivation

  1. Initial program 0.2

    \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.2

    \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{\color{blue}{1 \cdot y}}{3 \cdot \sqrt{x}}\]

  4. Applied times-frac0.3

    \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \color{blue}{\frac{1}{3} \cdot \frac{y}{\sqrt{x}}}\]

  5. Final simplification0.3

    \[\leadsto \left(1 - \frac{1}{x \cdot 9}\right) - \frac{1}{3} \cdot \frac{y}{\sqrt{x}}\]

Reproduce

herbie shell --seed 2019325 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (- (- 1 (/ (/ 1 x) 9)) (/ y (* 3 (sqrt x))))

  (- (- 1 (/ 1 (* x 9))) (/ y (* 3 (sqrt x)))))