Average Error: 23.2 → 19.3
Time: 19.3s
Precision: 64
\[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.219479179179928752539792709093514277923 \cdot 10^{112}:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \mathbf{elif}\;z \le 5.393088177919525543588651858528807956168 \cdot 10^{82}:\\ \;\;\;\;\left(z \cdot \left(t - a\right) + x \cdot y\right) \cdot \frac{1}{z \cdot \left(b - y\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \end{array}\]
\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.219479179179928752539792709093514277923 \cdot 10^{112}:\\
\;\;\;\;\frac{t}{b} - \frac{a}{b}\\

\mathbf{elif}\;z \le 5.393088177919525543588651858528807956168 \cdot 10^{82}:\\
\;\;\;\;\left(z \cdot \left(t - a\right) + x \cdot y\right) \cdot \frac{1}{z \cdot \left(b - y\right) + y}\\

\mathbf{else}:\\
\;\;\;\;\frac{t}{b} - \frac{a}{b}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r37154459 = x;
        double r37154460 = y;
        double r37154461 = r37154459 * r37154460;
        double r37154462 = z;
        double r37154463 = t;
        double r37154464 = a;
        double r37154465 = r37154463 - r37154464;
        double r37154466 = r37154462 * r37154465;
        double r37154467 = r37154461 + r37154466;
        double r37154468 = b;
        double r37154469 = r37154468 - r37154460;
        double r37154470 = r37154462 * r37154469;
        double r37154471 = r37154460 + r37154470;
        double r37154472 = r37154467 / r37154471;
        return r37154472;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r37154473 = z;
        double r37154474 = -1.2194791791799288e+112;
        bool r37154475 = r37154473 <= r37154474;
        double r37154476 = t;
        double r37154477 = b;
        double r37154478 = r37154476 / r37154477;
        double r37154479 = a;
        double r37154480 = r37154479 / r37154477;
        double r37154481 = r37154478 - r37154480;
        double r37154482 = 5.3930881779195255e+82;
        bool r37154483 = r37154473 <= r37154482;
        double r37154484 = r37154476 - r37154479;
        double r37154485 = r37154473 * r37154484;
        double r37154486 = x;
        double r37154487 = y;
        double r37154488 = r37154486 * r37154487;
        double r37154489 = r37154485 + r37154488;
        double r37154490 = 1.0;
        double r37154491 = r37154477 - r37154487;
        double r37154492 = r37154473 * r37154491;
        double r37154493 = r37154492 + r37154487;
        double r37154494 = r37154490 / r37154493;
        double r37154495 = r37154489 * r37154494;
        double r37154496 = r37154483 ? r37154495 : r37154481;
        double r37154497 = r37154475 ? r37154481 : r37154496;
        return r37154497;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original23.2
Target17.9
Herbie19.3
\[\frac{z \cdot t + y \cdot x}{y + z \cdot \left(b - y\right)} - \frac{a}{\left(b - y\right) + \frac{y}{z}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.2194791791799288e+112 or 5.3930881779195255e+82 < z

    1. Initial program 46.0

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

    3. Applied add-cube-cbrt46.2

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

    4. Applied associate-*l*46.2

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

    6. Applied clear-num46.2

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

    7. Simplified46.0

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

    8. Taylor expanded around inf 33.9

      \[\leadsto \color{blue}{\frac{t}{b} - \frac{a}{b}}\]

    if -1.2194791791799288e+112 < z < 5.3930881779195255e+82

    1. Initial program 11.9

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

    3. Applied div-inv12.0

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

  4. Final simplification19.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.219479179179928752539792709093514277923 \cdot 10^{112}:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \mathbf{elif}\;z \le 5.393088177919525543588651858528807956168 \cdot 10^{82}:\\ \;\;\;\;\left(z \cdot \left(t - a\right) + x \cdot y\right) \cdot \frac{1}{z \cdot \left(b - y\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"

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

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