Average Error: 0.4 → 0.4
Time: 20.0s
Precision: 64
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
↓
\[\left(\left(\frac{1}{9.0} \cdot \frac{1.0}{x} + y\right) - 1.0\right) \cdot \left(3.0 \cdot \sqrt{x}\right)\]
\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)
↓
\left(\left(\frac{1}{9.0} \cdot \frac{1.0}{x} + y\right) - 1.0\right) \cdot \left(3.0 \cdot \sqrt{x}\right)
double f(double x, double y) {
        double r19207195 = 3.0;
        double r19207196 = x;
        double r19207197 = sqrt(r19207196);
        double r19207198 = r19207195 * r19207197;
        double r19207199 = y;
        double r19207200 = 1.0;
        double r19207201 = 9.0;
        double r19207202 = r19207196 * r19207201;
        double r19207203 = r19207200 / r19207202;
        double r19207204 = r19207199 + r19207203;
        double r19207205 = r19207204 - r19207200;
        double r19207206 = r19207198 * r19207205;
        return r19207206;
}
↓
double f(double x, double y) {
        double r19207207 = 1.0;
        double r19207208 = 9.0;
        double r19207209 = r19207207 / r19207208;
        double r19207210 = 1.0;
        double r19207211 = x;
        double r19207212 = r19207210 / r19207211;
        double r19207213 = r19207209 * r19207212;
        double r19207214 = y;
        double r19207215 = r19207213 + r19207214;
        double r19207216 = r19207215 - r19207210;
        double r19207217 = 3.0;
        double r19207218 = sqrt(r19207211);
        double r19207219 = r19207217 * r19207218;
        double r19207220 = r19207216 * r19207219;
        return r19207220;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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-/r*0.4

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

  5. Applied div-inv0.4

    \[\leadsto \left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \color{blue}{\frac{1.0}{x} \cdot \frac{1}{9.0}}\right) - 1.0\right)\]

  6. Final simplification0.4

    \[\leadsto \left(\left(\frac{1}{9.0} \cdot \frac{1.0}{x} + y\right) - 1.0\right) \cdot \left(3.0 \cdot \sqrt{x}\right)\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(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)))