Average Error: 0.0 → 0.0
Time: 33.4s
Precision: 64
\[x + \left(y - z\right) \cdot \left(t - x\right)\]
↓
\[\mathsf{fma}\left(y - z, t - x, x\right)\]
x + \left(y - z\right) \cdot \left(t - x\right)
↓
\mathsf{fma}\left(y - z, t - x, x\right)
double f(double x, double y, double z, double t) {
        double r624061 = x;
        double r624062 = y;
        double r624063 = z;
        double r624064 = r624062 - r624063;
        double r624065 = t;
        double r624066 = r624065 - r624061;
        double r624067 = r624064 * r624066;
        double r624068 = r624061 + r624067;
        return r624068;
}
↓
double f(double x, double y, double z, double t) {
        double r624069 = y;
        double r624070 = z;
        double r624071 = r624069 - r624070;
        double r624072 = t;
        double r624073 = x;
        double r624074 = r624072 - r624073;
        double r624075 = fma(r624071, r624074, r624073);
        return r624075;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y - z, t - x, x\right)\]

Reproduce

herbie shell --seed 2019326 +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))))