Average Error: 3.9 → 0.3
Time: 12.5s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \le -2.315641800986653731087017149548046290874:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{1}{y}}{z \cdot 3}\\ \mathbf{elif}\;z \cdot 3 \le 2.181965382420920083950531709255992849268 \cdot 10^{-43}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot 3 \le -2.315641800986653731087017149548046290874:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{1}{y}}{z \cdot 3}\\

\mathbf{elif}\;z \cdot 3 \le 2.181965382420920083950531709255992849268 \cdot 10^{-43}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{y}}{z \cdot 3}\\

\mathbf{else}:\\
\;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r438370 = x;
        double r438371 = y;
        double r438372 = z;
        double r438373 = 3.0;
        double r438374 = r438372 * r438373;
        double r438375 = r438371 / r438374;
        double r438376 = r438370 - r438375;
        double r438377 = t;
        double r438378 = r438374 * r438371;
        double r438379 = r438377 / r438378;
        double r438380 = r438376 + r438379;
        return r438380;
}
↓
double f(double x, double y, double z, double t) {
        double r438381 = z;
        double r438382 = 3.0;
        double r438383 = r438381 * r438382;
        double r438384 = -2.3156418009866537;
        bool r438385 = r438383 <= r438384;
        double r438386 = x;
        double r438387 = y;
        double r438388 = r438387 / r438383;
        double r438389 = r438386 - r438388;
        double r438390 = t;
        double r438391 = 1.0;
        double r438392 = r438391 / r438387;
        double r438393 = r438392 / r438383;
        double r438394 = r438390 * r438393;
        double r438395 = r438389 + r438394;
        double r438396 = 2.18196538242092e-43;
        bool r438397 = r438383 <= r438396;
        double r438398 = r438390 / r438387;
        double r438399 = r438398 / r438383;
        double r438400 = r438389 + r438399;
        double r438401 = r438391 / r438381;
        double r438402 = r438387 / r438382;
        double r438403 = r438401 * r438402;
        double r438404 = r438386 - r438403;
        double r438405 = r438383 * r438387;
        double r438406 = r438390 / r438405;
        double r438407 = r438404 + r438406;
        double r438408 = r438397 ? r438400 : r438407;
        double r438409 = r438385 ? r438395 : r438408;
        return r438409;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.9
Target1.9
Herbie0.3
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 3 regimes

  2. if (* z 3.0) < -2.3156418009866537

    1. Initial program 0.4

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt0.6

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

    4. Applied times-frac2.0

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

    6. Applied div-inv2.0

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

    7. Applied associate-*r*1.4

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

    8. Simplified1.2

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{t}{z \cdot 3}} \cdot \frac{1}{y}\]
    9. Using strategy rm

    10. Applied div-inv1.2

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

    11. Applied associate-*l*0.4

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

    12. Simplified0.4

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

    if -2.3156418009866537 < (* z 3.0) < 2.18196538242092e-43

    1. Initial program 12.1

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt12.3

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

    4. Applied times-frac1.1

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

    6. Applied associate-*l/0.6

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

    7. Simplified0.3

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

    if 2.18196538242092e-43 < (* z 3.0)

    1. Initial program 0.3

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity0.3

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

    4. Applied times-frac0.4

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \le -2.315641800986653731087017149548046290874:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t \cdot \frac{\frac{1}{y}}{z \cdot 3}\\ \mathbf{elif}\;z \cdot 3 \le 2.181965382420920083950531709255992849268 \cdot 10^{-43}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y))

  (+ (- x (/ y (* z 3))) (/ t (* (* z 3) y))))