Average Error: 0.0 → 0.0
Time: 12.4s
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 r1492207 = x;
        double r1492208 = y;
        double r1492209 = z;
        double r1492210 = r1492208 - r1492209;
        double r1492211 = t;
        double r1492212 = r1492211 - r1492207;
        double r1492213 = r1492210 * r1492212;
        double r1492214 = r1492207 + r1492213;
        return r1492214;
}
↓
double f(double x, double y, double z, double t) {
        double r1492215 = t;
        double r1492216 = x;
        double r1492217 = r1492215 - r1492216;
        double r1492218 = y;
        double r1492219 = z;
        double r1492220 = r1492218 - r1492219;
        double r1492221 = fma(r1492217, r1492220, r1492216);
        return r1492221;
}

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 2019194 +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))))