Average Error: 0.2 → 0.2
Time: 5.9s
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 r369707 = 1.0;
        double r369708 = x;
        double r369709 = 9.0;
        double r369710 = r369708 * r369709;
        double r369711 = r369707 / r369710;
        double r369712 = r369707 - r369711;
        double r369713 = y;
        double r369714 = 3.0;
        double r369715 = sqrt(r369708);
        double r369716 = r369714 * r369715;
        double r369717 = r369713 / r369716;
        double r369718 = r369712 - r369717;
        return r369718;
}
↓
double f(double x, double y) {
        double r369719 = 1.0;
        double r369720 = x;
        double r369721 = r369719 / r369720;
        double r369722 = 9.0;
        double r369723 = r369721 / r369722;
        double r369724 = r369719 - r369723;
        double r369725 = y;
        double r369726 = 1.0;
        double r369727 = 3.0;
        double r369728 = sqrt(r369720);
        double r369729 = r369727 * r369728;
        double r369730 = r369726 / r369729;
        double r369731 = r369725 * r369730;
        double r369732 = r369724 - r369731;
        return r369732;
}

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

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

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

  5. Applied div-inv0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(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)))))