Average Error: 0.0 → 0.0
Time: 22.8s
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 r34467021 = x;
        double r34467022 = y;
        double r34467023 = z;
        double r34467024 = r34467022 - r34467023;
        double r34467025 = t;
        double r34467026 = r34467025 - r34467021;
        double r34467027 = r34467024 * r34467026;
        double r34467028 = r34467021 + r34467027;
        return r34467028;
}
↓
double f(double x, double y, double z, double t) {
        double r34467029 = t;
        double r34467030 = x;
        double r34467031 = r34467029 - r34467030;
        double r34467032 = y;
        double r34467033 = z;
        double r34467034 = r34467032 - r34467033;
        double r34467035 = fma(r34467031, r34467034, r34467030);
        return r34467035;
}

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 2019164 +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))))