Average Error: 0.2 → 0.2
Time: 12.2s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{\frac{y}{3}}{\sqrt{x}}
double f(double x, double y) {
        double r420104 = 1.0;
        double r420105 = x;
        double r420106 = 9.0;
        double r420107 = r420105 * r420106;
        double r420108 = r420104 / r420107;
        double r420109 = r420104 - r420108;
        double r420110 = y;
        double r420111 = 3.0;
        double r420112 = sqrt(r420105);
        double r420113 = r420111 * r420112;
        double r420114 = r420110 / r420113;
        double r420115 = r420109 - r420114;
        return r420115;
}
↓
double f(double x, double y) {
        double r420116 = 1.0;
        double r420117 = x;
        double r420118 = 9.0;
        double r420119 = r420117 * r420118;
        double r420120 = r420116 / r420119;
        double r420121 = r420116 - r420120;
        double r420122 = y;
        double r420123 = 3.0;
        double r420124 = r420122 / r420123;
        double r420125 = sqrt(r420117);
        double r420126 = r420124 / r420125;
        double r420127 = r420121 - r420126;
        return r420127;
}

Error

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Bits error versus y

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Results

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Target

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

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 associate-/r*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019350 
(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)))))