Average Error: 5.5 → 5.5
Time: 2.6s
Precision: 64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[x \cdot \left(1 + y \cdot y\right)\]
x \cdot \left(1 + y \cdot y\right)
↓
x \cdot \left(1 + y \cdot y\right)
double f(double x, double y) {
        double r478045 = x;
        double r478046 = 1.0;
        double r478047 = y;
        double r478048 = r478047 * r478047;
        double r478049 = r478046 + r478048;
        double r478050 = r478045 * r478049;
        return r478050;
}
↓
double f(double x, double y) {
        double r478051 = x;
        double r478052 = 1.0;
        double r478053 = y;
        double r478054 = r478053 * r478053;
        double r478055 = r478052 + r478054;
        double r478056 = r478051 * r478055;
        return r478056;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.5
Target0.1
Herbie5.5
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.5

    \[x \cdot \left(1 + y \cdot y\right)\]

  2. Final simplification5.5

    \[\leadsto x \cdot \left(1 + y \cdot y\right)\]

Reproduce

herbie shell --seed 2020062 
(FPCore (x y)
  :name "Numeric.Integration.TanhSinh:everywhere from integration-0.2.1"
  :precision binary64

  :herbie-target
  (+ x (* (* x y) y))

  (* x (+ 1 (* y y))))