Average Error: 0.4 → 0.4
Time: 3.6s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \cdot 3\right) \cdot \sqrt{x}\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \cdot 3\right) \cdot \sqrt{x}
double f(double x, double y) {
        double r392943 = 3.0;
        double r392944 = x;
        double r392945 = sqrt(r392944);
        double r392946 = r392943 * r392945;
        double r392947 = y;
        double r392948 = 1.0;
        double r392949 = 9.0;
        double r392950 = r392944 * r392949;
        double r392951 = r392948 / r392950;
        double r392952 = r392947 + r392951;
        double r392953 = r392952 - r392948;
        double r392954 = r392946 * r392953;
        return r392954;
}
↓
double f(double x, double y) {
        double r392955 = y;
        double r392956 = 1.0;
        double r392957 = x;
        double r392958 = 9.0;
        double r392959 = r392957 * r392958;
        double r392960 = r392956 / r392959;
        double r392961 = r392955 + r392960;
        double r392962 = r392961 - r392956;
        double r392963 = 3.0;
        double r392964 = r392962 * r392963;
        double r392965 = sqrt(r392957);
        double r392966 = r392964 * r392965;
        return r392966;
}

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 *-commutative0.4

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

  5. Applied associate-*r*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2020064 +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)))