Average Error: 0.2 → 0.2
Time: 13.3s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{\frac{1}{x}}{9}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{\frac{1}{x}}{9}\right) - y \cdot \frac{1}{3 \cdot \sqrt{x}}
double f(double x, double y) {
        double r335368 = 1.0;
        double r335369 = x;
        double r335370 = 9.0;
        double r335371 = r335369 * r335370;
        double r335372 = r335368 / r335371;
        double r335373 = r335368 - r335372;
        double r335374 = y;
        double r335375 = 3.0;
        double r335376 = sqrt(r335369);
        double r335377 = r335375 * r335376;
        double r335378 = r335374 / r335377;
        double r335379 = r335373 - r335378;
        return r335379;
}
↓
double f(double x, double y) {
        double r335380 = 1.0;
        double r335381 = x;
        double r335382 = r335380 / r335381;
        double r335383 = 9.0;
        double r335384 = r335382 / r335383;
        double r335385 = r335380 - r335384;
        double r335386 = y;
        double r335387 = 1.0;
        double r335388 = 3.0;
        double r335389 = sqrt(r335381);
        double r335390 = r335388 * r335389;
        double r335391 = r335387 / r335390;
        double r335392 = r335386 * r335391;
        double r335393 = r335385 - r335392;
        return r335393;
}

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. Simplified0.2

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

  4. Applied div-inv0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019235 
(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)))))