Average Error: 1.4 → 0.9
Time: 6.7s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \frac{z - t}{a - t} \le 1.0946169865901032 \cdot 10^{304}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + {\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)}^{1}\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \frac{z - t}{a - t} \le 1.0946169865901032 \cdot 10^{304}:\\
\;\;\;\;x + y \cdot \frac{z - t}{a - t}\\

\mathbf{else}:\\
\;\;\;\;x + {\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)}^{1}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r632325 = x;
        double r632326 = y;
        double r632327 = z;
        double r632328 = t;
        double r632329 = r632327 - r632328;
        double r632330 = a;
        double r632331 = r632330 - r632328;
        double r632332 = r632329 / r632331;
        double r632333 = r632326 * r632332;
        double r632334 = r632325 + r632333;
        return r632334;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r632335 = y;
        double r632336 = z;
        double r632337 = t;
        double r632338 = r632336 - r632337;
        double r632339 = a;
        double r632340 = r632339 - r632337;
        double r632341 = r632338 / r632340;
        double r632342 = r632335 * r632341;
        double r632343 = 1.0946169865901032e+304;
        bool r632344 = r632342 <= r632343;
        double r632345 = x;
        double r632346 = r632345 + r632342;
        double r632347 = r632335 * r632338;
        double r632348 = r632347 / r632340;
        double r632349 = 1.0;
        double r632350 = pow(r632348, r632349);
        double r632351 = r632345 + r632350;
        double r632352 = r632344 ? r632346 : r632351;
        return r632352;
}

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

Original1.4
Target0.4
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (/ (- z t) (- a t))) < 1.0946169865901032e+304

    1. Initial program 0.8

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

    if 1.0946169865901032e+304 < (* y (/ (- z t) (- a t)))

    1. Initial program 49.0

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

    3. Applied *-un-lft-identity49.0

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

    4. Applied add-cube-cbrt49.3

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

    5. Applied times-frac49.3

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

    6. Applied associate-*r*16.5

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

    7. Simplified16.5

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

    9. Applied pow116.5

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

    10. Applied pow116.5

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

    11. Applied pow116.5

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

    12. Applied pow116.5

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

    13. Applied pow-prod-down16.5

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

    14. Applied pow-prod-down16.5

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

    15. Applied pow-prod-down16.5

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

    16. Simplified10.6

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \frac{z - t}{a - t} \le 1.0946169865901032 \cdot 10^{304}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + {\left(\frac{y \cdot \left(z - t\right)}{a - t}\right)}^{1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020049 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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