Average Error: 0.1 → 0
Time: 26.6s
Precision: 64
\[\left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right) \cdot d1\right) \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right)\right) \cdot d1\]
↓
\[{d1}^{10}\]
\left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right) \cdot d1\right) \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right)\right) \cdot d1
↓
{d1}^{10}
double f(double d1) {
        double r3772996 = d1;
        double r3772997 = r3772996 * r3772996;
        double r3772998 = r3772996 * r3772997;
        double r3772999 = r3772998 * r3772996;
        double r3773000 = r3772999 * r3772996;
        double r3773001 = r3773000 * r3772997;
        double r3773002 = r3773001 * r3772996;
        double r3773003 = r3772996 * r3773002;
        double r3773004 = r3773003 * r3772996;
        return r3773004;
}
↓
double f(double d1) {
        double r3773005 = d1;
        double r3773006 = 10.0;
        double r3773007 = pow(r3773005, r3773006);
        return r3773007;
}

Error

Bits error versus d1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0
Herbie0
\[{d1}^{10}\]

Derivation

  1. Initial program 0.1

    \[\left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right) \cdot d1\right) \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right)\right) \cdot d1\]

  2. Taylor expanded around -inf 0.1

    \[\leadsto \left(d1 \cdot \left(\left(\left(\color{blue}{{d1}^{4}} \cdot d1\right) \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right)\right) \cdot d1\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{d1}^{9}} \cdot d1\]

  4. Taylor expanded around inf 0

    \[\leadsto \color{blue}{{d1}^{10}}\]

  5. Final simplification0

    \[\leadsto {d1}^{10}\]

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(FPCore (d1)
  :name "FastMath test5"

  :herbie-target
  (pow d1 10)

  (* (* d1 (* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)) d1))