Average Error: 6.2 → 2.5
Time: 3.8s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[x + \left(-\frac{y}{a}\right) \cdot \left(z - t\right)\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
x + \left(-\frac{y}{a}\right) \cdot \left(z - t\right)
double f(double x, double y, double z, double t, double a) {
        double r377514 = x;
        double r377515 = y;
        double r377516 = z;
        double r377517 = t;
        double r377518 = r377516 - r377517;
        double r377519 = r377515 * r377518;
        double r377520 = a;
        double r377521 = r377519 / r377520;
        double r377522 = r377514 - r377521;
        return r377522;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r377523 = x;
        double r377524 = y;
        double r377525 = a;
        double r377526 = r377524 / r377525;
        double r377527 = -r377526;
        double r377528 = z;
        double r377529 = t;
        double r377530 = r377528 - r377529;
        double r377531 = r377527 * r377530;
        double r377532 = r377523 + r377531;
        return r377532;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.2
Target0.7
Herbie2.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Initial program 6.2

    \[x - \frac{y \cdot \left(z - t\right)}{a}\]
  2. Using strategy rm

  3. Applied clear-num6.3

    \[\leadsto x - \color{blue}{\frac{1}{\frac{a}{y \cdot \left(z - t\right)}}}\]
  4. Using strategy rm

  5. Applied sub-neg6.3

    \[\leadsto \color{blue}{x + \left(-\frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\right)}\]

  6. Simplified2.5

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

  7. Final simplification2.5

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

Reproduce

herbie shell --seed 2020035 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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