Average Error: 0.1 → 0.1
Time: 15.7s
Precision: 64
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[d1 \cdot \left(d3 + \left(3 + d2\right)\right)\]
\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3
↓
d1 \cdot \left(d3 + \left(3 + d2\right)\right)
double f(double d1, double d2, double d3) {
        double r180381 = d1;
        double r180382 = 3.0;
        double r180383 = r180381 * r180382;
        double r180384 = d2;
        double r180385 = r180381 * r180384;
        double r180386 = r180383 + r180385;
        double r180387 = d3;
        double r180388 = r180381 * r180387;
        double r180389 = r180386 + r180388;
        return r180389;
}
↓
double f(double d1, double d2, double d3) {
        double r180390 = d1;
        double r180391 = d3;
        double r180392 = 3.0;
        double r180393 = d2;
        double r180394 = r180392 + r180393;
        double r180395 = r180391 + r180394;
        double r180396 = r180390 * r180395;
        return r180396;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  :precision binary64

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

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