Average Error: 6.3 → 0.8
Time: 5.3s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 7.216418262678561336985304880064040845772 \cdot 10^{301}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty:\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

\mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 7.216418262678561336985304880064040845772 \cdot 10^{301}:\\
\;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{z - x}{t}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r374388 = x;
        double r374389 = y;
        double r374390 = z;
        double r374391 = r374390 - r374388;
        double r374392 = r374389 * r374391;
        double r374393 = t;
        double r374394 = r374392 / r374393;
        double r374395 = r374388 + r374394;
        return r374395;
}
↓
double f(double x, double y, double z, double t) {
        double r374396 = x;
        double r374397 = y;
        double r374398 = z;
        double r374399 = r374398 - r374396;
        double r374400 = r374397 * r374399;
        double r374401 = t;
        double r374402 = r374400 / r374401;
        double r374403 = r374396 + r374402;
        double r374404 = -inf.0;
        bool r374405 = r374403 <= r374404;
        double r374406 = r374401 / r374399;
        double r374407 = r374397 / r374406;
        double r374408 = r374396 + r374407;
        double r374409 = 7.216418262678561e+301;
        bool r374410 = r374403 <= r374409;
        double r374411 = r374399 / r374401;
        double r374412 = r374397 * r374411;
        double r374413 = r374396 + r374412;
        double r374414 = r374410 ? r374403 : r374413;
        double r374415 = r374405 ? r374408 : r374414;
        return r374415;
}

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
Herbie0.8
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-/l*0.2

      \[\leadsto x + \color{blue}{\frac{y}{\frac{t}{z - x}}}\]

    if -inf.0 < (+ x (/ (* y (- z x)) t)) < 7.216418262678561e+301

    1. Initial program 0.7

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

    if 7.216418262678561e+301 < (+ x (/ (* y (- z x)) t))

    1. Initial program 55.6

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

    3. Applied *-un-lft-identity55.6

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

    4. Applied times-frac3.2

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{z - x}{t}}\]

    5. Simplified3.2

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \le 7.216418262678561336985304880064040845772 \cdot 10^{301}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(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)))