Average Error: 6.2 → 5.7
Time: 35.1s
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 r361283 = x;
        double r361284 = y;
        double r361285 = z;
        double r361286 = t;
        double r361287 = r361285 - r361286;
        double r361288 = r361284 * r361287;
        double r361289 = a;
        double r361290 = r361288 / r361289;
        double r361291 = r361283 - r361290;
        return r361291;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r361292 = x;
        double r361293 = y;
        double r361294 = a;
        double r361295 = z;
        double r361296 = t;
        double r361297 = r361295 - r361296;
        double r361298 = r361294 / r361297;
        double r361299 = r361293 / r361298;
        double r361300 = r361292 - r361299;
        return r361300;
}

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
Target0.5
Herbie5.7
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -7.251701340672362e+52 or 1.0576402916802115e-15 < a

    1. Initial program 10.0

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

    3. Applied associate-/l*0.4

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

    if -7.251701340672362e+52 < a < 1.0576402916802115e-15

    1. Initial program 0.8

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

    3. Applied associate-/l*13.2

      \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{z - t}}}\]
    4. Using strategy rm

    5. Applied div-inv13.3

      \[\leadsto x - \frac{y}{\color{blue}{a \cdot \frac{1}{z - t}}}\]

    6. Applied *-un-lft-identity13.3

      \[\leadsto x - \frac{\color{blue}{1 \cdot y}}{a \cdot \frac{1}{z - t}}\]

    7. Applied times-frac0.9

      \[\leadsto x - \color{blue}{\frac{1}{a} \cdot \frac{y}{\frac{1}{z - t}}}\]

    8. Simplified0.9

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

  4. Final simplification5.7

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

Reproduce

herbie shell --seed 2019294 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.07612662163899753e-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)))