Average Error: 0.4 → 0.4
Time: 35.5s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(\frac{1}{x \cdot 9} - 1\right) + y\right)\right)\]
\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(\frac{1}{x \cdot 9} - 1\right) + y\right)\right)
double f(double x, double y) {
        double r308100 = 3.0;
        double r308101 = x;
        double r308102 = sqrt(r308101);
        double r308103 = r308100 * r308102;
        double r308104 = y;
        double r308105 = 1.0;
        double r308106 = 9.0;
        double r308107 = r308101 * r308106;
        double r308108 = r308105 / r308107;
        double r308109 = r308104 + r308108;
        double r308110 = r308109 - r308105;
        double r308111 = r308103 * r308110;
        return r308111;
}
↓
double f(double x, double y) {
        double r308112 = 3.0;
        double r308113 = x;
        double r308114 = sqrt(r308113);
        double r308115 = 1.0;
        double r308116 = 9.0;
        double r308117 = r308113 * r308116;
        double r308118 = r308115 / r308117;
        double r308119 = r308118 - r308115;
        double r308120 = y;
        double r308121 = r308119 + r308120;
        double r308122 = r308114 * r308121;
        double r308123 = r308112 * r308122;
        return r308123;
}

Error

Bits error versus x

Bits error versus y

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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-*l*0.4

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

  4. Simplified0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (* 3 (+ (* y (sqrt x)) (* (- (/ 1 (* x 9)) 1) (sqrt x))))

  (* (* 3 (sqrt x)) (- (+ y (/ 1 (* x 9))) 1)))