Average Error: 6.3 → 1.5
Time: 3.7s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2117257699034317484720128 \lor \neg \left(t \le 4.298768646380980053593446645561660090143 \cdot 10^{-219}\right):\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right) + x\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z \cdot y}{t} - \frac{x \cdot y}{t}\right) + x\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -2117257699034317484720128 \lor \neg \left(t \le 4.298768646380980053593446645561660090143 \cdot 10^{-219}\right):\\
\;\;\;\;\frac{y}{t} \cdot \left(z - x\right) + x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r276456 = x;
        double r276457 = y;
        double r276458 = z;
        double r276459 = r276458 - r276456;
        double r276460 = r276457 * r276459;
        double r276461 = t;
        double r276462 = r276460 / r276461;
        double r276463 = r276456 + r276462;
        return r276463;
}
↓
double f(double x, double y, double z, double t) {
        double r276464 = t;
        double r276465 = -2.1172576990343175e+24;
        bool r276466 = r276464 <= r276465;
        double r276467 = 4.29876864638098e-219;
        bool r276468 = r276464 <= r276467;
        double r276469 = !r276468;
        bool r276470 = r276466 || r276469;
        double r276471 = y;
        double r276472 = r276471 / r276464;
        double r276473 = z;
        double r276474 = x;
        double r276475 = r276473 - r276474;
        double r276476 = r276472 * r276475;
        double r276477 = r276476 + r276474;
        double r276478 = r276473 * r276471;
        double r276479 = r276478 / r276464;
        double r276480 = r276474 * r276471;
        double r276481 = r276480 / r276464;
        double r276482 = r276479 - r276481;
        double r276483 = r276482 + r276474;
        double r276484 = r276470 ? r276477 : r276483;
        return r276484;
}

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

Original6.3
Target2.0
Herbie1.5
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if t < -2.1172576990343175e+24 or 4.29876864638098e-219 < t

    1. Initial program 7.8

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

    2. Simplified1.4

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)}\]
    3. Using strategy rm

    4. Applied fma-udef1.4

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

    if -2.1172576990343175e+24 < t < 4.29876864638098e-219

    1. Initial program 1.9

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

    2. Simplified3.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)}\]
    3. Using strategy rm

    4. Applied fma-udef3.9

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

    6. Applied add-cube-cbrt4.6

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

    7. Applied associate-*l*4.6

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

    8. Taylor expanded around 0 1.9

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2117257699034317484720128 \lor \neg \left(t \le 4.298768646380980053593446645561660090143 \cdot 10^{-219}\right):\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right) + x\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z \cdot y}{t} - \frac{x \cdot y}{t}\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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