Average Error: 0.0 → 0.0
Time: 7.1s
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 r838808 = x;
        double r838809 = y;
        double r838810 = z;
        double r838811 = r838809 - r838810;
        double r838812 = t;
        double r838813 = r838812 - r838808;
        double r838814 = r838811 * r838813;
        double r838815 = r838808 + r838814;
        return r838815;
}
↓
double f(double x, double y, double z, double t) {
        double r838816 = t;
        double r838817 = x;
        double r838818 = r838816 - r838817;
        double r838819 = y;
        double r838820 = z;
        double r838821 = r838819 - r838820;
        double r838822 = fma(r838818, r838821, r838817);
        return r838822;
}

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 2020036 +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))))