Average Error: 0.0 → 0.0
Time: 13.0s
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 r37083023 = x;
        double r37083024 = y;
        double r37083025 = z;
        double r37083026 = r37083024 - r37083025;
        double r37083027 = t;
        double r37083028 = r37083027 - r37083023;
        double r37083029 = r37083026 * r37083028;
        double r37083030 = r37083023 + r37083029;
        return r37083030;
}
↓
double f(double x, double y, double z, double t) {
        double r37083031 = t;
        double r37083032 = x;
        double r37083033 = r37083031 - r37083032;
        double r37083034 = y;
        double r37083035 = z;
        double r37083036 = r37083034 - r37083035;
        double r37083037 = fma(r37083033, r37083036, r37083032);
        return r37083037;
}

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 2019192 +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))))