Average Error: 25.1 → 10.1
Time: 1.1m
Precision: 64
\[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le -2.335375383468043 \cdot 10^{-253}:\\ \;\;\;\;x + \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z}}} \cdot \left(\left(\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}}\right)\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le 4.422650758851032 \cdot 10^{-257}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le -2.335375383468043 \cdot 10^{-253}:\\
\;\;\;\;x + \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z}}} \cdot \left(\left(\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}}\right)\\

\mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le 4.422650758851032 \cdot 10^{-257}:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{y \cdot t}{z}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r30362434 = x;
        double r30362435 = y;
        double r30362436 = z;
        double r30362437 = r30362435 - r30362436;
        double r30362438 = t;
        double r30362439 = r30362438 - r30362434;
        double r30362440 = r30362437 * r30362439;
        double r30362441 = a;
        double r30362442 = r30362441 - r30362436;
        double r30362443 = r30362440 / r30362442;
        double r30362444 = r30362434 + r30362443;
        return r30362444;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r30362445 = x;
        double r30362446 = y;
        double r30362447 = z;
        double r30362448 = r30362446 - r30362447;
        double r30362449 = t;
        double r30362450 = r30362449 - r30362445;
        double r30362451 = r30362448 * r30362450;
        double r30362452 = a;
        double r30362453 = r30362452 - r30362447;
        double r30362454 = r30362451 / r30362453;
        double r30362455 = r30362445 + r30362454;
        double r30362456 = -2.335375383468043e-253;
        bool r30362457 = r30362455 <= r30362456;
        double r30362458 = cbrt(r30362450);
        double r30362459 = cbrt(r30362453);
        double r30362460 = cbrt(r30362459);
        double r30362461 = r30362458 / r30362460;
        double r30362462 = r30362459 * r30362459;
        double r30362463 = r30362448 / r30362462;
        double r30362464 = cbrt(r30362462);
        double r30362465 = cbrt(r30362464);
        double r30362466 = r30362465 * r30362465;
        double r30362467 = r30362458 / r30362466;
        double r30362468 = r30362463 * r30362467;
        double r30362469 = r30362458 / r30362465;
        double r30362470 = r30362468 * r30362469;
        double r30362471 = r30362461 * r30362470;
        double r30362472 = r30362445 + r30362471;
        double r30362473 = 4.422650758851032e-257;
        bool r30362474 = r30362455 <= r30362473;
        double r30362475 = r30362445 * r30362446;
        double r30362476 = r30362475 / r30362447;
        double r30362477 = r30362476 + r30362449;
        double r30362478 = r30362446 * r30362449;
        double r30362479 = r30362478 / r30362447;
        double r30362480 = r30362477 - r30362479;
        double r30362481 = cbrt(r30362448);
        double r30362482 = r30362481 / r30362459;
        double r30362483 = r30362450 / r30362459;
        double r30362484 = r30362482 * r30362483;
        double r30362485 = r30362481 * r30362481;
        double r30362486 = r30362485 / r30362459;
        double r30362487 = r30362484 * r30362486;
        double r30362488 = r30362445 + r30362487;
        double r30362489 = r30362474 ? r30362480 : r30362488;
        double r30362490 = r30362457 ? r30362472 : r30362489;
        return r30362490;
}

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

Original25.1
Target12.3
Herbie10.1
\[\begin{array}{l} \mathbf{if}\;z \lt -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \lt 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (+ x (/ (* (- y z) (- t x)) (- a z))) < -2.335375383468043e-253

    1. Initial program 22.0

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

    3. Applied add-cube-cbrt22.4

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

    4. Applied times-frac8.4

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

    6. Applied add-cube-cbrt8.4

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

    7. Applied cbrt-prod8.5

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

    8. Applied add-cube-cbrt8.6

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

    9. Applied times-frac8.7

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

    10. Applied associate-*r*8.2

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

    12. Applied add-cube-cbrt8.3

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

    13. Applied times-frac8.3

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

    14. Applied associate-*r*8.3

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

    if -2.335375383468043e-253 < (+ x (/ (* (- y z) (- t x)) (- a z))) < 4.422650758851032e-257

    1. Initial program 52.4

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

    2. Taylor expanded around inf 24.5

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

    if 4.422650758851032e-257 < (+ x (/ (* (- y z) (- t x)) (- a z)))

    1. Initial program 22.6

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

    3. Applied add-cube-cbrt23.2

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

    4. Applied times-frac9.1

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

    6. Applied add-cube-cbrt9.0

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

    7. Applied times-frac9.0

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

    8. Applied associate-*l*8.9

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

  4. Final simplification10.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le -2.335375383468043 \cdot 10^{-253}:\\ \;\;\;\;x + \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z}}} \cdot \left(\left(\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}}\right)\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le 4.422650758851032 \cdot 10^{-257}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"

  :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))))