Average Error: 0.0 → 0.0
Time: 4.5s
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 r543101 = x;
        double r543102 = y;
        double r543103 = z;
        double r543104 = r543102 - r543103;
        double r543105 = t;
        double r543106 = r543105 - r543101;
        double r543107 = r543104 * r543106;
        double r543108 = r543101 + r543107;
        return r543108;
}
↓
double f(double x, double y, double z, double t) {
        double r543109 = t;
        double r543110 = x;
        double r543111 = r543109 - r543110;
        double r543112 = y;
        double r543113 = z;
        double r543114 = r543112 - r543113;
        double r543115 = fma(r543111, r543114, r543110);
        return r543115;
}

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 2019174 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"

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

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