Average Error: 0.2 → 0.0
Time: 11.6s
Precision: 64
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[d1 \cdot \left(d2 + 30\right)\]
\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20
↓
d1 \cdot \left(d2 + 30\right)
double f(double d1, double d2) {
        double r167565 = d1;
        double r167566 = 10.0;
        double r167567 = r167565 * r167566;
        double r167568 = d2;
        double r167569 = r167565 * r167568;
        double r167570 = r167567 + r167569;
        double r167571 = 20.0;
        double r167572 = r167565 * r167571;
        double r167573 = r167570 + r167572;
        return r167573;
}
↓
double f(double d1, double d2) {
        double r167574 = d1;
        double r167575 = d2;
        double r167576 = 30.0;
        double r167577 = r167575 + r167576;
        double r167578 = r167574 * r167577;
        return r167578;
}

Error

Bits error versus d1

Bits error versus d2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
Herbie0.0
\[d1 \cdot \left(30 + d2\right)\]

Derivation

  1. Initial program 0.2

    \[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]

  2. Simplified0.0

    \[\leadsto \color{blue}{d1 \cdot \left(20 + \left(10 + d2\right)\right)}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto d1 \cdot \color{blue}{\left(d2 + 30\right)}\]

  4. Final simplification0.0

    \[\leadsto d1 \cdot \left(d2 + 30\right)\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"
  :precision binary64

  :herbie-target
  (* d1 (+ 30 d2))

  (+ (+ (* d1 10) (* d1 d2)) (* d1 20)))