Average Error: 0.0 → 0.0
Time: 13.0s
Precision: 64
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[d1 \cdot \left(\left(d3 + \left(d2 + 32\right)\right) + 5\right)\]
\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32
↓
d1 \cdot \left(\left(d3 + \left(d2 + 32\right)\right) + 5\right)
double f(double d1, double d2, double d3) {
        double r14160431 = d1;
        double r14160432 = d2;
        double r14160433 = r14160431 * r14160432;
        double r14160434 = d3;
        double r14160435 = 5.0;
        double r14160436 = r14160434 + r14160435;
        double r14160437 = r14160436 * r14160431;
        double r14160438 = r14160433 + r14160437;
        double r14160439 = 32.0;
        double r14160440 = r14160431 * r14160439;
        double r14160441 = r14160438 + r14160440;
        return r14160441;
}
↓
double f(double d1, double d2, double d3) {
        double r14160442 = d1;
        double r14160443 = d3;
        double r14160444 = d2;
        double r14160445 = 32.0;
        double r14160446 = r14160444 + r14160445;
        double r14160447 = r14160443 + r14160446;
        double r14160448 = 5.0;
        double r14160449 = r14160447 + r14160448;
        double r14160450 = r14160442 * r14160449;
        return r14160450;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\left(d3 + \left(32 + \left(d2 + 5\right)\right)\right) \cdot d1}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.0

    \[\leadsto \left(d3 + \left(32 + \left(d2 + 5\right)\right)\right) \cdot \color{blue}{\left(1 \cdot d1\right)}\]

  5. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(\left(d3 + \left(32 + \left(d2 + 5\right)\right)\right) \cdot 1\right) \cdot d1}\]

  6. Simplified0.0

    \[\leadsto \color{blue}{\left(5 + \left(d3 + \left(32 + d2\right)\right)\right)} \cdot d1\]

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019170 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"

  :herbie-target
  (* d1 (+ (+ 37.0 d3) d2))

  (+ (+ (* d1 d2) (* (+ d3 5.0) d1)) (* d1 32.0)))