Average Error: 0.2 → 0.3
Time: 17.6s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[\left(1 - \frac{1}{9 \cdot x}\right) - \frac{y}{\sqrt{x}} \cdot \frac{1}{3}\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
\left(1 - \frac{1}{9 \cdot x}\right) - \frac{y}{\sqrt{x}} \cdot \frac{1}{3}
double f(double x, double y) {
        double r274435 = 1.0;
        double r274436 = x;
        double r274437 = 9.0;
        double r274438 = r274436 * r274437;
        double r274439 = r274435 / r274438;
        double r274440 = r274435 - r274439;
        double r274441 = y;
        double r274442 = 3.0;
        double r274443 = sqrt(r274436);
        double r274444 = r274442 * r274443;
        double r274445 = r274441 / r274444;
        double r274446 = r274440 - r274445;
        return r274446;
}
↓
double f(double x, double y) {
        double r274447 = 1.0;
        double r274448 = 9.0;
        double r274449 = x;
        double r274450 = r274448 * r274449;
        double r274451 = r274447 / r274450;
        double r274452 = r274447 - r274451;
        double r274453 = y;
        double r274454 = sqrt(r274449);
        double r274455 = r274453 / r274454;
        double r274456 = 1.0;
        double r274457 = 3.0;
        double r274458 = r274456 / r274457;
        double r274459 = r274455 * r274458;
        double r274460 = r274452 - r274459;
        return r274460;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"

  :herbie-target
  (- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x))))

  (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))