Average Error: 24.0 → 10.5
Time: 5.8s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.0969435282516095 \cdot 10^{215} \lor \neg \left(z \le 1.718372949138872 \cdot 10^{114}\right):\\ \;\;\;\;y \cdot \left(\frac{x}{z} - \frac{t}{z}\right) + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{1} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.0969435282516095 \cdot 10^{215} \lor \neg \left(z \le 1.718372949138872 \cdot 10^{114}\right):\\
\;\;\;\;y \cdot \left(\frac{x}{z} - \frac{t}{z}\right) + t\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r632435 = x;
        double r632436 = y;
        double r632437 = z;
        double r632438 = r632436 - r632437;
        double r632439 = t;
        double r632440 = r632439 - r632435;
        double r632441 = r632438 * r632440;
        double r632442 = a;
        double r632443 = r632442 - r632437;
        double r632444 = r632441 / r632443;
        double r632445 = r632435 + r632444;
        return r632445;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r632446 = z;
        double r632447 = -2.0969435282516095e+215;
        bool r632448 = r632446 <= r632447;
        double r632449 = 1.718372949138872e+114;
        bool r632450 = r632446 <= r632449;
        double r632451 = !r632450;
        bool r632452 = r632448 || r632451;
        double r632453 = y;
        double r632454 = x;
        double r632455 = r632454 / r632446;
        double r632456 = t;
        double r632457 = r632456 / r632446;
        double r632458 = r632455 - r632457;
        double r632459 = r632453 * r632458;
        double r632460 = r632459 + r632456;
        double r632461 = r632453 - r632446;
        double r632462 = cbrt(r632461);
        double r632463 = r632462 * r632462;
        double r632464 = a;
        double r632465 = r632464 - r632446;
        double r632466 = cbrt(r632465);
        double r632467 = r632463 / r632466;
        double r632468 = 1.0;
        double r632469 = cbrt(r632468);
        double r632470 = r632469 * r632466;
        double r632471 = r632462 / r632470;
        double r632472 = r632456 - r632454;
        double r632473 = r632472 / r632466;
        double r632474 = r632471 * r632473;
        double r632475 = r632467 * r632474;
        double r632476 = r632454 + r632475;
        double r632477 = r632452 ? r632460 : r632476;
        return r632477;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original24.0
Target11.8
Herbie10.5
\[\begin{array}{l} \mathbf{if}\;z \lt -1.25361310560950359 \cdot 10^{188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.0969435282516095e+215 or 1.718372949138872e+114 < z

    1. Initial program 46.8

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

    3. Applied add-cube-cbrt47.1

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

    4. Applied times-frac24.9

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

    6. Applied add-cube-cbrt24.6

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

    7. Applied times-frac24.6

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

    8. Applied associate-*l*24.7

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

    9. Taylor expanded around inf 25.0

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

    10. Simplified16.8

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

    if -2.0969435282516095e+215 < z < 1.718372949138872e+114

    1. Initial program 15.8

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

    3. Applied add-cube-cbrt16.3

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

    4. Applied times-frac8.6

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

    6. Applied add-cube-cbrt8.6

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

    7. Applied times-frac8.6

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

    8. Applied associate-*l*8.3

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

    10. Applied *-un-lft-identity8.3

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

    11. Applied cbrt-prod8.3

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

  4. Final simplification10.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.0969435282516095 \cdot 10^{215} \lor \neg \left(z \le 1.718372949138872 \cdot 10^{114}\right):\\ \;\;\;\;y \cdot \left(\frac{x}{z} - \frac{t}{z}\right) + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{1} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020049 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

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