Average Error: 3.7 → 0.4
Time: 12.2s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -15821052806207.40625:\\ \;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + 0.3333333333333333148296162562473909929395 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;t \le 2285.050982389833734487183392047882080078:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \le -15821052806207.40625:\\
\;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + 0.3333333333333333148296162562473909929395 \cdot \frac{t}{z \cdot y}\\

\mathbf{elif}\;t \le 2285.050982389833734487183392047882080078:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\

\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 r485562 = x;
        double r485563 = y;
        double r485564 = z;
        double r485565 = 3.0;
        double r485566 = r485564 * r485565;
        double r485567 = r485563 / r485566;
        double r485568 = r485562 - r485567;
        double r485569 = t;
        double r485570 = r485566 * r485563;
        double r485571 = r485569 / r485570;
        double r485572 = r485568 + r485571;
        return r485572;
}
↓
double f(double x, double y, double z, double t) {
        double r485573 = t;
        double r485574 = -15821052806207.406;
        bool r485575 = r485573 <= r485574;
        double r485576 = x;
        double r485577 = 1.0;
        double r485578 = z;
        double r485579 = r485577 / r485578;
        double r485580 = y;
        double r485581 = 3.0;
        double r485582 = r485580 / r485581;
        double r485583 = r485579 * r485582;
        double r485584 = r485576 - r485583;
        double r485585 = 0.3333333333333333;
        double r485586 = r485578 * r485580;
        double r485587 = r485573 / r485586;
        double r485588 = r485585 * r485587;
        double r485589 = r485584 + r485588;
        double r485590 = 2285.0509823898337;
        bool r485591 = r485573 <= r485590;
        double r485592 = r485578 * r485581;
        double r485593 = r485580 / r485592;
        double r485594 = r485576 - r485593;
        double r485595 = r485577 / r485592;
        double r485596 = r485573 / r485580;
        double r485597 = r485595 * r485596;
        double r485598 = r485594 + r485597;
        double r485599 = r485581 * r485580;
        double r485600 = r485578 * r485599;
        double r485601 = r485573 / r485600;
        double r485602 = r485594 + r485601;
        double r485603 = r485591 ? r485598 : r485602;
        double r485604 = r485575 ? r485589 : r485603;
        return r485604;
}

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

Original3.7
Target1.6
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 < -15821052806207.406

    1. Initial program 0.8

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

    3. Applied associate-/r*2.6

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

    5. Applied *-un-lft-identity2.6

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

    6. Applied times-frac2.7

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

    7. Taylor expanded around 0 0.9

      \[\leadsto \left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + \color{blue}{0.3333333333333333148296162562473909929395 \cdot \frac{t}{z \cdot y}}\]

    if -15821052806207.406 < t < 2285.0509823898337

    1. Initial program 5.7

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

    3. Applied *-un-lft-identity5.7

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

    4. Applied times-frac0.2

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

    if 2285.0509823898337 < t

    1. Initial program 0.7

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

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -15821052806207.40625:\\ \;\;\;\;\left(x - \frac{1}{z} \cdot \frac{y}{3}\right) + 0.3333333333333333148296162562473909929395 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;t \le 2285.050982389833734487183392047882080078:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019304 
(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))))