Average Error: 0.0 → 0.0
Time: 12.4s
Precision: 64
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[\left(\left(d3 + 37\right) + d2\right) \cdot d1\]
\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32
↓
\left(\left(d3 + 37\right) + d2\right) \cdot d1
double f(double d1, double d2, double d3) {
        double r11068959 = d1;
        double r11068960 = d2;
        double r11068961 = r11068959 * r11068960;
        double r11068962 = d3;
        double r11068963 = 5.0;
        double r11068964 = r11068962 + r11068963;
        double r11068965 = r11068964 * r11068959;
        double r11068966 = r11068961 + r11068965;
        double r11068967 = 32.0;
        double r11068968 = r11068959 * r11068967;
        double r11068969 = r11068966 + r11068968;
        return r11068969;
}
↓
double f(double d1, double d2, double d3) {
        double r11068970 = d3;
        double r11068971 = 37.0;
        double r11068972 = r11068970 + r11068971;
        double r11068973 = d2;
        double r11068974 = r11068972 + r11068973;
        double r11068975 = d1;
        double r11068976 = r11068974 * r11068975;
        return r11068976;
}

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

Original0.0
Target0.0
Herbie0.0
\[d1 \cdot \left(\left(37 + d3\right) + d2\right)\]

Derivation

  1. Initial program 0.0

    \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{d2 \cdot d1 + \left(d3 \cdot d1 + 37 \cdot d1\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{d1 \cdot \left(\left(d3 + 37\right) + d2\right)}\]

  4. Final simplification0.0

    \[\leadsto \left(\left(d3 + 37\right) + d2\right) \cdot d1\]

Reproduce

herbie shell --seed 2019164 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"

  :herbie-target
  (* d1 (+ (+ 37 d3) d2))

  (+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32)))