Average Error: 6.7 → 2.0
Time: 14.2s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)
double f(double x, double y, double z, double t) {
        double r405643 = x;
        double r405644 = y;
        double r405645 = z;
        double r405646 = r405645 - r405643;
        double r405647 = r405644 * r405646;
        double r405648 = t;
        double r405649 = r405647 / r405648;
        double r405650 = r405643 + r405649;
        return r405650;
}
↓
double f(double x, double y, double z, double t) {
        double r405651 = y;
        double r405652 = t;
        double r405653 = r405651 / r405652;
        double r405654 = z;
        double r405655 = x;
        double r405656 = r405654 - r405655;
        double r405657 = fma(r405653, r405656, r405655);
        return r405657;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original6.7
Target2.0
Herbie2.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.7

    \[x + \frac{y \cdot \left(z - x\right)}{t}\]

  2. Simplified2.0

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

  3. Final simplification2.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

  (+ x (/ (* y (- z x)) t)))