FastMath test3

Average Error: 0.1 → 0.1

Time: 8.6s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double d1, double d2, double d3) {
        double r372626 = d1;
        double r372627 = 3.0;
        double r372628 = r372626 * r372627;
        double r372629 = d2;
        double r372630 = r372626 * r372629;
        double r372631 = r372628 + r372630;
        double r372632 = d3;
        double r372633 = r372626 * r372632;
        double r372634 = r372631 + r372633;
        return r372634;
}

↓

double f(double d1, double d2, double d3) {
        double r372635 = d1;
        double r372636 = 3.0;
        double r372637 = r372635 * r372636;
        double r372638 = d2;
        double r372639 = r372635 * r372638;
        double r372640 = r372637 + r372639;
        double r372641 = d3;
        double r372642 = r372635 * r372641;
        double r372643 = r372640 + r372642;
        return r372643;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Target

Original	0.1
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019350 
(FPCore (d1 d2 d3)
  :name "FastMath test3"
  :precision binary64

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

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