FastMath dist4

Average Error: 0.0 → 0.0

Time: 17.1s

Precision: 64

Math

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

↓

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

C

double f(double d1, double d2, double d3, double d4) {
        double r200974 = d1;
        double r200975 = d2;
        double r200976 = r200974 * r200975;
        double r200977 = d3;
        double r200978 = r200974 * r200977;
        double r200979 = r200976 - r200978;
        double r200980 = d4;
        double r200981 = r200980 * r200974;
        double r200982 = r200979 + r200981;
        double r200983 = r200974 * r200974;
        double r200984 = r200982 - r200983;
        return r200984;
}

↓

double f(double d1, double d2, double d3, double d4) {
        double r200985 = d1;
        double r200986 = d2;
        double r200987 = r200985 * r200986;
        double r200988 = d3;
        double r200989 = r200985 * r200988;
        double r200990 = r200987 - r200989;
        double r200991 = d4;
        double r200992 = r200991 * r200985;
        double r200993 = r200990 + r200992;
        double r200994 = r200985 * r200985;
        double r200995 = r200993 - r200994;
        return r200995;
}

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

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

Reproduce

herbie shell --seed 2019325 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  :precision binary64

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

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