FastMath dist4

Average Error: 0.0 → 0.0

Time: 25.0s

Precision: 64

Math

\[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1\]

↓

\[\left(\left(d1 \cdot d2 - d3 \cdot d1\right) + d1 \cdot d4\right) - d1 \cdot d1\]

C

double f(double d1, double d2, double d3, double d4) {
        double r9036462 = d1;
        double r9036463 = d2;
        double r9036464 = r9036462 * r9036463;
        double r9036465 = d3;
        double r9036466 = r9036462 * r9036465;
        double r9036467 = r9036464 - r9036466;
        double r9036468 = d4;
        double r9036469 = r9036468 * r9036462;
        double r9036470 = r9036467 + r9036469;
        double r9036471 = r9036462 * r9036462;
        double r9036472 = r9036470 - r9036471;
        return r9036472;
}

↓

double f(double d1, double d2, double d3, double d4) {
        double r9036473 = d1;
        double r9036474 = d2;
        double r9036475 = r9036473 * r9036474;
        double r9036476 = d3;
        double r9036477 = r9036476 * r9036473;
        double r9036478 = r9036475 - r9036477;
        double r9036479 = d4;
        double r9036480 = r9036473 * r9036479;
        double r9036481 = r9036478 + r9036480;
        double r9036482 = r9036473 * r9036473;
        double r9036483 = r9036481 - r9036482;
        return r9036483;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Bits error versus d4

Target

Original	0.0
Target	0.0
Herbie	0.0

\[d1 \cdot \left(\left(\left(d2 - d3\right) + d4\right) - d1\right)\]

Derivation

1. Initial program 0.0

   \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1\]

2. Final simplification 0.0

   \[\leadsto \left(\left(d1 \cdot d2 - d3 \cdot d1\right) + d1 \cdot d4\right) - d1 \cdot d1\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"

  :herbie-target
  (* d1 (- (+ (- d2 d3) d4) d1))

  (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)))