FastMath test3

Average Error: 0.1 → 0.0

Time: 9.4s

Precision: 64

Math

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

↓

\[d3 \cdot d1 + \mathsf{fma}\left(d1, 3, \left(d1 \cdot d2\right)\right)\]

C

double f(double d1, double d2, double d3) {
        double r9631955 = d1;
        double r9631956 = 3.0;
        double r9631957 = r9631955 * r9631956;
        double r9631958 = d2;
        double r9631959 = r9631955 * r9631958;
        double r9631960 = r9631957 + r9631959;
        double r9631961 = d3;
        double r9631962 = r9631955 * r9631961;
        double r9631963 = r9631960 + r9631962;
        return r9631963;
}

↓

double f(double d1, double d2, double d3) {
        double r9631964 = d3;
        double r9631965 = d1;
        double r9631966 = r9631964 * r9631965;
        double r9631967 = 3.0;
        double r9631968 = d2;
        double r9631969 = r9631965 * r9631968;
        double r9631970 = fma(r9631965, r9631967, r9631969);
        double r9631971 = r9631966 + r9631970;
        return r9631971;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Target

Original	0.1
Target	0.1
Herbie	0.0

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

Derivation

1. Initial program 0.1

   \[\left(d1 \cdot 3 + d1 \cdot d2\right) + d1 \cdot d3\]
2. Using strategy rm

3. Applied fma-def 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(d1, 3, \left(d1 \cdot d2\right)\right)} + d1 \cdot d3\]

4. Final simplification 0.0

   \[\leadsto d3 \cdot d1 + \mathsf{fma}\left(d1, 3, \left(d1 \cdot d2\right)\right)\]

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath test3"

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

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