Average Error: 0.0 → 0.0
Time: 10.4s
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 r34927840 = x;
        double r34927841 = y;
        double r34927842 = z;
        double r34927843 = r34927841 - r34927842;
        double r34927844 = t;
        double r34927845 = r34927844 - r34927840;
        double r34927846 = r34927843 * r34927845;
        double r34927847 = r34927840 + r34927846;
        return r34927847;
}
↓
double f(double x, double y, double z, double t) {
        double r34927848 = t;
        double r34927849 = x;
        double r34927850 = r34927848 - r34927849;
        double r34927851 = y;
        double r34927852 = z;
        double r34927853 = r34927851 - r34927852;
        double r34927854 = fma(r34927850, r34927853, r34927849);
        return r34927854;
}

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 2019163 +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))))