Average Error: 0.4 → 0.4
Time: 19.9s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\left(y + \frac{1}{9 \cdot x}\right) - 1\right) \cdot \sqrt{x \cdot \left(3 \cdot 3\right)}\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\left(y + \frac{1}{9 \cdot x}\right) - 1\right) \cdot \sqrt{x \cdot \left(3 \cdot 3\right)}
double f(double x, double y) {
        double r22908022 = 3.0;
        double r22908023 = x;
        double r22908024 = sqrt(r22908023);
        double r22908025 = r22908022 * r22908024;
        double r22908026 = y;
        double r22908027 = 1.0;
        double r22908028 = 9.0;
        double r22908029 = r22908023 * r22908028;
        double r22908030 = r22908027 / r22908029;
        double r22908031 = r22908026 + r22908030;
        double r22908032 = r22908031 - r22908027;
        double r22908033 = r22908025 * r22908032;
        return r22908033;
}
↓
double f(double x, double y) {
        double r22908034 = y;
        double r22908035 = 1.0;
        double r22908036 = 9.0;
        double r22908037 = x;
        double r22908038 = r22908036 * r22908037;
        double r22908039 = r22908035 / r22908038;
        double r22908040 = r22908034 + r22908039;
        double r22908041 = r22908040 - r22908035;
        double r22908042 = 3.0;
        double r22908043 = r22908042 * r22908042;
        double r22908044 = r22908037 * r22908043;
        double r22908045 = sqrt(r22908044);
        double r22908046 = r22908041 * r22908045;
        return r22908046;
}

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 add-sqr-sqrt0.7

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

  5. Applied sqrt-unprod0.5

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

  6. Simplified0.4

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

  7. Final simplification0.4

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

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)))