Average Error: 0.4 → 0.4
Time: 21.7s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1\right)\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1\right)\right)
double f(double x, double y) {
        double r278098 = 3.0;
        double r278099 = x;
        double r278100 = sqrt(r278099);
        double r278101 = r278098 * r278100;
        double r278102 = y;
        double r278103 = 1.0;
        double r278104 = 9.0;
        double r278105 = r278099 * r278104;
        double r278106 = r278103 / r278105;
        double r278107 = r278102 + r278106;
        double r278108 = r278107 - r278103;
        double r278109 = r278101 * r278108;
        return r278109;
}
↓
double f(double x, double y) {
        double r278110 = 3.0;
        double r278111 = x;
        double r278112 = sqrt(r278111);
        double r278113 = y;
        double r278114 = 0.1111111111111111;
        double r278115 = r278114 / r278111;
        double r278116 = r278113 + r278115;
        double r278117 = 1.0;
        double r278118 = r278116 - r278117;
        double r278119 = r278112 * r278118;
        double r278120 = r278110 * r278119;
        return r278120;
}

Error

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Results

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Target

Original0.4
Target0.4
Herbie0.4
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

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

  3. Applied associate-/r*0.4

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

  5. Applied associate-*l*0.4

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

  6. Taylor expanded around 0 0.4

    \[\leadsto 3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \color{blue}{\frac{0.1111111111111111}{x}}\right) - 1\right)\right)\]

  7. Final simplification0.4

    \[\leadsto 3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1\right)\right)\]

Reproduce

herbie shell --seed 2019199 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

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

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