Average Error: 0.2 → 0.2
Time: 31.1s
Precision: 64
\[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}\]
↓
\[1 - \left(\frac{1}{9 \cdot x} + \frac{y}{\sqrt{x} \cdot 3}\right)\]
\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}}
↓
1 - \left(\frac{1}{9 \cdot x} + \frac{y}{\sqrt{x} \cdot 3}\right)
double f(double x, double y) {
        double r14169001 = 1.0;
        double r14169002 = x;
        double r14169003 = 9.0;
        double r14169004 = r14169002 * r14169003;
        double r14169005 = r14169001 / r14169004;
        double r14169006 = r14169001 - r14169005;
        double r14169007 = y;
        double r14169008 = 3.0;
        double r14169009 = sqrt(r14169002);
        double r14169010 = r14169008 * r14169009;
        double r14169011 = r14169007 / r14169010;
        double r14169012 = r14169006 - r14169011;
        return r14169012;
}
↓
double f(double x, double y) {
        double r14169013 = 1.0;
        double r14169014 = 9.0;
        double r14169015 = x;
        double r14169016 = r14169014 * r14169015;
        double r14169017 = r14169013 / r14169016;
        double r14169018 = y;
        double r14169019 = sqrt(r14169015);
        double r14169020 = 3.0;
        double r14169021 = r14169019 * r14169020;
        double r14169022 = r14169018 / r14169021;
        double r14169023 = r14169017 + r14169022;
        double r14169024 = r14169013 - r14169023;
        return r14169024;
}

Error

Bits error versus x

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--l-0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019171 +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)))))