Average Error: 3.9 → 1.2
Time: 14.0s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le 1.5801305016597386 \cdot 10^{-18}:\\ \;\;\;\;\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;y \le 1.5801305016597386 \cdot 10^{-18}:\\
\;\;\;\;\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r518554 = x;
        double r518555 = y;
        double r518556 = z;
        double r518557 = 3.0;
        double r518558 = r518556 * r518557;
        double r518559 = r518555 / r518558;
        double r518560 = r518554 - r518559;
        double r518561 = t;
        double r518562 = r518558 * r518555;
        double r518563 = r518561 / r518562;
        double r518564 = r518560 + r518563;
        return r518564;
}
↓
double f(double x, double y, double z, double t) {
        double r518565 = y;
        double r518566 = 1.5801305016597386e-18;
        bool r518567 = r518565 <= r518566;
        double r518568 = x;
        double r518569 = 1.0;
        double r518570 = z;
        double r518571 = 3.0;
        double r518572 = r518570 * r518571;
        double r518573 = r518572 / r518565;
        double r518574 = r518569 / r518573;
        double r518575 = r518568 - r518574;
        double r518576 = t;
        double r518577 = r518576 / r518572;
        double r518578 = r518577 / r518565;
        double r518579 = r518575 + r518578;
        double r518580 = r518565 / r518572;
        double r518581 = r518568 - r518580;
        double r518582 = r518569 / r518570;
        double r518583 = r518576 / r518571;
        double r518584 = r518583 / r518565;
        double r518585 = r518582 * r518584;
        double r518586 = r518581 + r518585;
        double r518587 = r518567 ? r518579 : r518586;
        return r518587;
}

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
Target1.6
Herbie1.2
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if y < 1.5801305016597386e-18

    1. Initial program 5.1

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

    3. Applied associate-/r*1.6

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

    5. Applied clear-num1.6

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

    if 1.5801305016597386e-18 < y

    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*1.6

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

    5. Applied *-un-lft-identity1.6

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

    6. Applied *-un-lft-identity1.6

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

    7. Applied times-frac1.7

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

    8. Applied times-frac0.2

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

    9. Simplified0.2

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le 1.5801305016597386 \cdot 10^{-18}:\\ \;\;\;\;\left(x - \frac{1}{\frac{z \cdot 3}{y}}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))