Average Error: 0.0 → 0.0
Time: 13.5s
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 r965152 = x;
        double r965153 = y;
        double r965154 = z;
        double r965155 = r965153 - r965154;
        double r965156 = t;
        double r965157 = r965156 - r965152;
        double r965158 = r965155 * r965157;
        double r965159 = r965152 + r965158;
        return r965159;
}
↓
double f(double x, double y, double z, double t) {
        double r965160 = y;
        double r965161 = z;
        double r965162 = r965160 - r965161;
        double r965163 = t;
        double r965164 = x;
        double r965165 = r965163 - r965164;
        double r965166 = fma(r965162, r965165, r965164);
        return r965166;
}

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 2020046 +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))))