Average Error: 0.0 → 0.0
Time: 6.7s
Precision: 64
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[\left(d2 + \left(37 + d3\right)\right) \cdot d1\]
double f(double d1, double d2, double d3) {
        double r51018255 = d1;
        double r51018256 = d2;
        double r51018257 = r51018255 * r51018256;
        double r51018258 = d3;
        double r51018259 = 5.0;
        double r51018260 = r51018258 + r51018259;
        double r51018261 = r51018260 * r51018255;
        double r51018262 = r51018257 + r51018261;
        double r51018263 = 32.0;
        double r51018264 = r51018255 * r51018263;
        double r51018265 = r51018262 + r51018264;
        return r51018265;
}
↓
double f(double d1, double d2, double d3) {
        double r51018266 = d2;
        double r51018267 = 37.0;
        double r51018268 = d3;
        double r51018269 = r51018267 + r51018268;
        double r51018270 = r51018266 + r51018269;
        double r51018271 = d1;
        double r51018272 = r51018270 * r51018271;
        return r51018272;
}


\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32
↓
\left(d2 + \left(37 + d3\right)\right) \cdot d1

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist3"

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

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