Average Error: 0.0 → 0.0
Time: 5.1s
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 r816077 = x;
        double r816078 = y;
        double r816079 = z;
        double r816080 = r816078 - r816079;
        double r816081 = t;
        double r816082 = r816081 - r816077;
        double r816083 = r816080 * r816082;
        double r816084 = r816077 + r816083;
        return r816084;
}
↓
double f(double x, double y, double z, double t) {
        double r816085 = t;
        double r816086 = x;
        double r816087 = r816085 - r816086;
        double r816088 = y;
        double r816089 = z;
        double r816090 = r816088 - r816089;
        double r816091 = fma(r816087, r816090, r816086);
        return r816091;
}

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 2020047 +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))))