Average Error: 0.4 → 0.4
Time: 10.2s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\]
\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{1}{x \cdot 9}\right) - 1\right)\right)
double f(double x, double y) {
        double r676037 = 3.0;
        double r676038 = x;
        double r676039 = sqrt(r676038);
        double r676040 = r676037 * r676039;
        double r676041 = y;
        double r676042 = 1.0;
        double r676043 = 9.0;
        double r676044 = r676038 * r676043;
        double r676045 = r676042 / r676044;
        double r676046 = r676041 + r676045;
        double r676047 = r676046 - r676042;
        double r676048 = r676040 * r676047;
        return r676048;
}
↓
double f(double x, double y) {
        double r676049 = 3.0;
        double r676050 = x;
        double r676051 = sqrt(r676050);
        double r676052 = y;
        double r676053 = 1.0;
        double r676054 = 9.0;
        double r676055 = r676050 * r676054;
        double r676056 = r676053 / r676055;
        double r676057 = r676052 + r676056;
        double r676058 = r676057 - r676053;
        double r676059 = r676051 * r676058;
        double r676060 = r676049 * r676059;
        return r676060;
}

Error

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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. Final simplification0.4

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

Reproduce

herbie shell --seed 2020034 +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)))