Average Error: 0.4 → 0.4
Time: 16.1s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\sqrt{x} \cdot \left(\frac{1}{9 \cdot x} - 1\right) + \sqrt{x} \cdot y\right) \cdot 3\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\sqrt{x} \cdot \left(\frac{1}{9 \cdot x} - 1\right) + \sqrt{x} \cdot y\right) \cdot 3
double f(double x, double y) {
        double r33217034 = 3.0;
        double r33217035 = x;
        double r33217036 = sqrt(r33217035);
        double r33217037 = r33217034 * r33217036;
        double r33217038 = y;
        double r33217039 = 1.0;
        double r33217040 = 9.0;
        double r33217041 = r33217035 * r33217040;
        double r33217042 = r33217039 / r33217041;
        double r33217043 = r33217038 + r33217042;
        double r33217044 = r33217043 - r33217039;
        double r33217045 = r33217037 * r33217044;
        return r33217045;
}
↓
double f(double x, double y) {
        double r33217046 = x;
        double r33217047 = sqrt(r33217046);
        double r33217048 = 1.0;
        double r33217049 = 9.0;
        double r33217050 = r33217049 * r33217046;
        double r33217051 = r33217048 / r33217050;
        double r33217052 = r33217051 - r33217048;
        double r33217053 = r33217047 * r33217052;
        double r33217054 = y;
        double r33217055 = r33217047 * r33217054;
        double r33217056 = r33217053 + r33217055;
        double r33217057 = 3.0;
        double r33217058 = r33217056 * r33217057;
        return r33217058;
}

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. Using strategy rm

  5. Applied associate--l+0.4

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

  6. Applied distribute-lft-in0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019171 
(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)))