Average Error: 0.1 → 0.1
Time: 3.7s
Precision: 64
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[d1 \cdot \left(\left(3 + d2\right) + d3\right)\]
\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3
↓
d1 \cdot \left(\left(3 + d2\right) + d3\right)
double f(double d1, double d2, double d3) {
        double r225364 = d1;
        double r225365 = 3.0;
        double r225366 = r225364 * r225365;
        double r225367 = d2;
        double r225368 = r225364 * r225367;
        double r225369 = r225366 + r225368;
        double r225370 = d3;
        double r225371 = r225364 * r225370;
        double r225372 = r225369 + r225371;
        return r225372;
}
↓
double f(double d1, double d2, double d3) {
        double r225373 = d1;
        double r225374 = 3.0;
        double r225375 = d2;
        double r225376 = r225374 + r225375;
        double r225377 = d3;
        double r225378 = r225376 + r225377;
        double r225379 = r225373 * r225378;
        return r225379;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  :precision binary64

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

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