Average Error: 0.0 → 0.0
Time: 21.7s
Precision: 64
\[x + \left(y - z\right) \cdot \left(t - x\right)\]
↓
\[\mathsf{fma}\left(t - x, y - z, x\right)\]
x + \left(y - z\right) \cdot \left(t - x\right)
↓
\mathsf{fma}\left(t - x, y - z, x\right)
double f(double x, double y, double z, double t) {
        double r32861989 = x;
        double r32861990 = y;
        double r32861991 = z;
        double r32861992 = r32861990 - r32861991;
        double r32861993 = t;
        double r32861994 = r32861993 - r32861989;
        double r32861995 = r32861992 * r32861994;
        double r32861996 = r32861989 + r32861995;
        return r32861996;
}
↓
double f(double x, double y, double z, double t) {
        double r32861997 = t;
        double r32861998 = x;
        double r32861999 = r32861997 - r32861998;
        double r32862000 = y;
        double r32862001 = z;
        double r32862002 = r32862000 - r32862001;
        double r32862003 = fma(r32861999, r32862002, r32861998);
        return r32862003;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original0.0
Target0.0
Herbie0.0
\[x + \left(t \cdot \left(y - z\right) + \left(-x\right) \cdot \left(y - z\right)\right)\]

Derivation

  1. Initial program 0.0

    \[x + \left(y - z\right) \cdot \left(t - x\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, y - z, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(t - x, y - z, x\right)\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

  (+ x (* (- y z) (- t x))))