Average Error: 3.9 → 0.4
Time: 4.1s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.1361300744902736 \cdot 10^{22}:\\ \;\;\;\;x + \left(t \cdot \frac{\frac{1}{z \cdot 3}}{y} - \frac{\frac{y}{z}}{3}\right)\\ \mathbf{elif}\;t \le 5.46097822804766331 \cdot 10^{49}:\\ \;\;\;\;x + \left(\frac{1}{z} \cdot \frac{\frac{t}{3}}{y} - \frac{\frac{y}{z}}{3}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \le -3.1361300744902736 \cdot 10^{22}:\\
\;\;\;\;x + \left(t \cdot \frac{\frac{1}{z \cdot 3}}{y} - \frac{\frac{y}{z}}{3}\right)\\

\mathbf{elif}\;t \le 5.46097822804766331 \cdot 10^{49}:\\
\;\;\;\;x + \left(\frac{1}{z} \cdot \frac{\frac{t}{3}}{y} - \frac{\frac{y}{z}}{3}\right)\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r731588 = x;
        double r731589 = y;
        double r731590 = z;
        double r731591 = 3.0;
        double r731592 = r731590 * r731591;
        double r731593 = r731589 / r731592;
        double r731594 = r731588 - r731593;
        double r731595 = t;
        double r731596 = r731592 * r731589;
        double r731597 = r731595 / r731596;
        double r731598 = r731594 + r731597;
        return r731598;
}
↓
double f(double x, double y, double z, double t) {
        double r731599 = t;
        double r731600 = -3.1361300744902736e+22;
        bool r731601 = r731599 <= r731600;
        double r731602 = x;
        double r731603 = 1.0;
        double r731604 = z;
        double r731605 = 3.0;
        double r731606 = r731604 * r731605;
        double r731607 = r731603 / r731606;
        double r731608 = y;
        double r731609 = r731607 / r731608;
        double r731610 = r731599 * r731609;
        double r731611 = r731608 / r731604;
        double r731612 = r731611 / r731605;
        double r731613 = r731610 - r731612;
        double r731614 = r731602 + r731613;
        double r731615 = 5.460978228047663e+49;
        bool r731616 = r731599 <= r731615;
        double r731617 = r731603 / r731604;
        double r731618 = r731599 / r731605;
        double r731619 = r731618 / r731608;
        double r731620 = r731617 * r731619;
        double r731621 = r731620 - r731612;
        double r731622 = r731602 + r731621;
        double r731623 = r731608 / r731606;
        double r731624 = r731602 - r731623;
        double r731625 = r731605 * r731608;
        double r731626 = r731604 * r731625;
        double r731627 = r731599 / r731626;
        double r731628 = r731624 + r731627;
        double r731629 = r731616 ? r731622 : r731628;
        double r731630 = r731601 ? r731614 : r731629;
        return r731630;
}

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
Target1.7
Herbie0.4
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -3.1361300744902736e+22

    1. Initial program 0.5

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

    3. Applied associate-/r*2.7

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

    5. Applied associate-/r*2.7

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

    7. Applied sub-neg2.7

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

    8. Applied associate-+l+2.7

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

    9. Simplified2.7

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

    11. Applied *-un-lft-identity2.7

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

    12. Applied div-inv2.8

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

    13. Applied times-frac0.4

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

    14. Simplified0.4

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

    if -3.1361300744902736e+22 < t < 5.460978228047663e+49

    1. Initial program 5.8

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

    3. Applied associate-/r*1.1

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

    5. Applied associate-/r*1.1

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

    7. Applied sub-neg1.1

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

    8. Applied associate-+l+1.1

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

    9. Simplified1.1

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

    11. Applied *-un-lft-identity1.1

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

    12. Applied *-un-lft-identity1.1

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

    13. Applied times-frac1.1

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

    14. Applied times-frac0.3

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

    15. Simplified0.3

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

    if 5.460978228047663e+49 < t

    1. Initial program 0.6

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

    3. Applied associate-*l*0.6

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.1361300744902736 \cdot 10^{22}:\\ \;\;\;\;x + \left(t \cdot \frac{\frac{1}{z \cdot 3}}{y} - \frac{\frac{y}{z}}{3}\right)\\ \mathbf{elif}\;t \le 5.46097822804766331 \cdot 10^{49}:\\ \;\;\;\;x + \left(\frac{1}{z} \cdot \frac{\frac{t}{3}}{y} - \frac{\frac{y}{z}}{3}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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))))