Average Error: 0.1 → 0.1
Time: 1.2m
Precision: 64
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[\left(d2 + \left(d3 + 3\right)\right) \cdot d1\]
\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3
↓
\left(d2 + \left(d3 + 3\right)\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r34491225 = d1;
        double r34491226 = 3.0;
        double r34491227 = r34491225 * r34491226;
        double r34491228 = d2;
        double r34491229 = r34491225 * r34491228;
        double r34491230 = r34491227 + r34491229;
        double r34491231 = d3;
        double r34491232 = r34491225 * r34491231;
        double r34491233 = r34491230 + r34491232;
        return r34491233;
}
↓
double f(double d1, double d2, double d3) {
        double r34491234 = d2;
        double r34491235 = d3;
        double r34491236 = 3.0;
        double r34491237 = r34491235 + r34491236;
        double r34491238 = r34491234 + r34491237;
        double r34491239 = d1;
        double r34491240 = r34491238 * r34491239;
        return r34491240;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[d1 \cdot \left(\left(3 + d2\right) + d3\right)\]

Derivation

  1. Initial program 0.1

    \[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\left(\left(3 + d3\right) + d2\right) \cdot d1}\]

  3. Final simplification0.1

    \[\leadsto \left(d2 + \left(d3 + 3\right)\right) \cdot d1\]

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"

  :herbie-target
  (* d1 (+ (+ 3 d2) d3))

  (+ (+ (* d1 3) (* d1 d2)) (* d1 d3)))