Average Error: 0.0 → 0.0
Time: 7.3s
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 r778061 = x;
        double r778062 = y;
        double r778063 = z;
        double r778064 = r778062 - r778063;
        double r778065 = t;
        double r778066 = r778065 - r778061;
        double r778067 = r778064 * r778066;
        double r778068 = r778061 + r778067;
        return r778068;
}
↓
double f(double x, double y, double z, double t) {
        double r778069 = t;
        double r778070 = x;
        double r778071 = r778069 - r778070;
        double r778072 = y;
        double r778073 = z;
        double r778074 = r778072 - r778073;
        double r778075 = fma(r778071, r778074, r778070);
        return r778075;
}

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 2020100 +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))))