Average Error: 0.0 → 0.0
Time: 1.5s
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 r720572 = x;
        double r720573 = y;
        double r720574 = z;
        double r720575 = r720573 - r720574;
        double r720576 = t;
        double r720577 = r720576 - r720572;
        double r720578 = r720575 * r720577;
        double r720579 = r720572 + r720578;
        return r720579;
}
↓
double f(double x, double y, double z, double t) {
        double r720580 = t;
        double r720581 = x;
        double r720582 = r720580 - r720581;
        double r720583 = y;
        double r720584 = z;
        double r720585 = r720583 - r720584;
        double r720586 = fma(r720582, r720585, r720581);
        return r720586;
}

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 2020001 +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))))