Average Error: 6.1 → 6.0
Time: 11.6s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[x + \frac{y}{\frac{a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
x + \frac{y}{\frac{a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r437468 = x;
        double r437469 = y;
        double r437470 = z;
        double r437471 = t;
        double r437472 = r437470 - r437471;
        double r437473 = r437469 * r437472;
        double r437474 = a;
        double r437475 = r437473 / r437474;
        double r437476 = r437468 + r437475;
        return r437476;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r437477 = x;
        double r437478 = y;
        double r437479 = a;
        double r437480 = z;
        double r437481 = t;
        double r437482 = r437480 - r437481;
        double r437483 = r437479 / r437482;
        double r437484 = r437478 / r437483;
        double r437485 = r437477 + r437484;
        return r437485;
}

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

Original6.1
Target0.7
Herbie6.0
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -1.2476201594046643e+220 or 3.6844202068931295e+217 < (* y (- z t))

    1. Initial program 31.5

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

    3. Applied associate-/l*0.9

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z - t}}}\]

    if -1.2476201594046643e+220 < (* y (- z t)) < 3.6844202068931295e+217

    1. Initial program 0.4

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

    3. Applied div-inv0.4

      \[\leadsto x + \color{blue}{\left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification6.0

    \[\leadsto x + \frac{y}{\frac{a}{z - t}}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (if (< y -1.07612662163899753e-10) (+ x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.8944268627920891e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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