Average Error: 0.3 → 0
Time: 847.0ms
Precision: 64
\[d \cdot 10 + d \cdot 20\]
↓
\[d \cdot 30\]
double f(double d) {
        double r24374950 = d;
        double r24374951 = 10.0;
        double r24374952 = r24374950 * r24374951;
        double r24374953 = 20.0;
        double r24374954 = r24374950 * r24374953;
        double r24374955 = r24374952 + r24374954;
        return r24374955;
}
↓
double f(double d) {
        double r24374956 = d;
        double r24374957 = 30.0;
        double r24374958 = r24374956 * r24374957;
        return r24374958;
}


d \cdot 10 + d \cdot 20
↓
d \cdot 30

Error

Bits error versus d

Target

Original0.3
Target0
Herbie0
\[d \cdot 30\]

Derivation

  1. Initial program 0.3

    \[d \cdot 10 + d \cdot 20\]

  2. Simplified0

    \[\leadsto \color{blue}{d \cdot 30}\]

  3. Final simplification0

    \[\leadsto d \cdot 30\]

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (d)
  :name "FastMath test1"

  :herbie-target
  (* d 30)

  (+ (* d 10) (* d 20)))