Average Error: 0.0 → 0.0
Time: 23.4s
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 r504927 = x;
        double r504928 = y;
        double r504929 = z;
        double r504930 = r504928 - r504929;
        double r504931 = t;
        double r504932 = r504931 - r504927;
        double r504933 = r504930 * r504932;
        double r504934 = r504927 + r504933;
        return r504934;
}
↓
double f(double x, double y, double z, double t) {
        double r504935 = y;
        double r504936 = z;
        double r504937 = r504935 - r504936;
        double r504938 = t;
        double r504939 = x;
        double r504940 = r504938 - r504939;
        double r504941 = fma(r504937, r504940, r504939);
        return r504941;
}

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 2019323 +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))))