Average Error: 0.0 → 0.0
Time: 5.6s
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 r745023 = x;
        double r745024 = y;
        double r745025 = z;
        double r745026 = r745024 - r745025;
        double r745027 = t;
        double r745028 = r745027 - r745023;
        double r745029 = r745026 * r745028;
        double r745030 = r745023 + r745029;
        return r745030;
}
↓
double f(double x, double y, double z, double t) {
        double r745031 = t;
        double r745032 = x;
        double r745033 = r745031 - r745032;
        double r745034 = y;
        double r745035 = z;
        double r745036 = r745034 - r745035;
        double r745037 = fma(r745033, r745036, r745032);
        return r745037;
}

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 2020039 +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))))