Average Error: 0.1 → 0.1
Time: 2.4s
Precision: 64
\[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
↓
\[d1 \cdot 3 + d1 \cdot \left(d2 + d3\right)\]
\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3
↓
d1 \cdot 3 + d1 \cdot \left(d2 + d3\right)
double f(double d1, double d2, double d3) {
        double r296078 = d1;
        double r296079 = 3.0;
        double r296080 = r296078 * r296079;
        double r296081 = d2;
        double r296082 = r296078 * r296081;
        double r296083 = r296080 + r296082;
        double r296084 = d3;
        double r296085 = r296078 * r296084;
        double r296086 = r296083 + r296085;
        return r296086;
}
↓
double f(double d1, double d2, double d3) {
        double r296087 = d1;
        double r296088 = 3.0;
        double r296089 = r296087 * r296088;
        double r296090 = d2;
        double r296091 = d3;
        double r296092 = r296090 + r296091;
        double r296093 = r296087 * r296092;
        double r296094 = r296089 + r296093;
        return r296094;
}

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. Using strategy rm

  3. Applied associate-+l+0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020024 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  :precision binary64

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

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