Average Error: 6.0 → 6.0
Time: 11.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
x + \frac{y \cdot \left(z - t\right)}{a}
double f(double x, double y, double z, double t, double a) {
        double r267565 = x;
        double r267566 = y;
        double r267567 = z;
        double r267568 = t;
        double r267569 = r267567 - r267568;
        double r267570 = r267566 * r267569;
        double r267571 = a;
        double r267572 = r267570 / r267571;
        double r267573 = r267565 + r267572;
        return r267573;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r267574 = x;
        double r267575 = y;
        double r267576 = z;
        double r267577 = t;
        double r267578 = r267576 - r267577;
        double r267579 = r267575 * r267578;
        double r267580 = a;
        double r267581 = r267579 / r267580;
        double r267582 = r267574 + r267581;
        return r267582;
}

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

Original6.0
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 3 regimes

  2. if (* y (- z t)) < -8.764602780454589e+245

    1. Initial program 39.7

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

    3. Applied associate-/l*0.6

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

    if -8.764602780454589e+245 < (* y (- z t)) < 1.2359170032311252e+159

    1. Initial program 0.4

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

    if 1.2359170032311252e+159 < (* y (- z t))

    1. Initial program 21.2

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

    3. Applied associate-/l*1.5

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

    5. Applied div-inv1.5

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

    6. Applied add-cube-cbrt2.2

      \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{a \cdot \frac{1}{z - t}}\]

    7. Applied times-frac6.6

      \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{a} \cdot \frac{\sqrt[3]{y}}{\frac{1}{z - t}}}\]

    8. Simplified6.6

      \[\leadsto x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{a} \cdot \color{blue}{\left(\left(z - t\right) \cdot \sqrt[3]{y}\right)}\]

    9. Taylor expanded around 0 21.2

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

    10. Simplified1.6

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

  4. Final simplification6.0

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

Reproduce

herbie shell --seed 2019297 
(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)))