Average Error: 0.4 → 0.4
Time: 15.0s
Precision: 64
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
↓
\[3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{9.0 \cdot x}\right) - 1.0\right)\right)\]
\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)
↓
3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{9.0 \cdot x}\right) - 1.0\right)\right)
double f(double x, double y) {
        double r23216200 = 3.0;
        double r23216201 = x;
        double r23216202 = sqrt(r23216201);
        double r23216203 = r23216200 * r23216202;
        double r23216204 = y;
        double r23216205 = 1.0;
        double r23216206 = 9.0;
        double r23216207 = r23216201 * r23216206;
        double r23216208 = r23216205 / r23216207;
        double r23216209 = r23216204 + r23216208;
        double r23216210 = r23216209 - r23216205;
        double r23216211 = r23216203 * r23216210;
        return r23216211;
}
↓
double f(double x, double y) {
        double r23216212 = 3.0;
        double r23216213 = x;
        double r23216214 = sqrt(r23216213);
        double r23216215 = y;
        double r23216216 = 1.0;
        double r23216217 = 9.0;
        double r23216218 = r23216217 * r23216213;
        double r23216219 = r23216216 / r23216218;
        double r23216220 = r23216215 + r23216219;
        double r23216221 = r23216220 - r23216216;
        double r23216222 = r23216214 * r23216221;
        double r23216223 = r23216212 * r23216222;
        return r23216223;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

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Target

Original0.4
Target0.4
Herbie0.4
\[3.0 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1.0}{x \cdot 9.0} - 1.0\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.4

    \[\leadsto \color{blue}{3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)}\]

  4. Final simplification0.4

    \[\leadsto 3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{9.0 \cdot x}\right) - 1.0\right)\right)\]

Reproduce

herbie shell --seed 2019168 
(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)))