Average Error: 0.0 → 0.0
Time: 17.5s
Precision: 64
\[x + \left(y - z\right) \cdot \left(t - x\right)\]
↓
\[\mathsf{fma}\left(y - z, t - x, x\right)\]
x + \left(y - z\right) \cdot \left(t - x\right)
↓
\mathsf{fma}\left(y - z, t - x, x\right)
double f(double x, double y, double z, double t) {
        double r596198 = x;
        double r596199 = y;
        double r596200 = z;
        double r596201 = r596199 - r596200;
        double r596202 = t;
        double r596203 = r596202 - r596198;
        double r596204 = r596201 * r596203;
        double r596205 = r596198 + r596204;
        return r596205;
}
↓
double f(double x, double y, double z, double t) {
        double r596206 = y;
        double r596207 = z;
        double r596208 = r596206 - r596207;
        double r596209 = t;
        double r596210 = x;
        double r596211 = r596209 - r596210;
        double r596212 = fma(r596208, r596211, r596210);
        return r596212;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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