Average Error: 23.1 → 8.5
Time: 20.3s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} = -\infty:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t - x}{a - z} + x\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le -3.0404769334557312 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le 0.0:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}}\\ \end{array}\]
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} = -\infty:\\
\;\;\;\;\left(y - z\right) \cdot \frac{t - x}{a - z} + x\\

\mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le -3.0404769334557312 \cdot 10^{-273}:\\
\;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\

\mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le 0.0:\\
\;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\

\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 r28270467 = x;
        double r28270468 = y;
        double r28270469 = z;
        double r28270470 = r28270468 - r28270469;
        double r28270471 = t;
        double r28270472 = r28270471 - r28270467;
        double r28270473 = r28270470 * r28270472;
        double r28270474 = a;
        double r28270475 = r28270474 - r28270469;
        double r28270476 = r28270473 / r28270475;
        double r28270477 = r28270467 + r28270476;
        return r28270477;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r28270478 = x;
        double r28270479 = y;
        double r28270480 = z;
        double r28270481 = r28270479 - r28270480;
        double r28270482 = t;
        double r28270483 = r28270482 - r28270478;
        double r28270484 = r28270481 * r28270483;
        double r28270485 = a;
        double r28270486 = r28270485 - r28270480;
        double r28270487 = r28270484 / r28270486;
        double r28270488 = r28270478 + r28270487;
        double r28270489 = -inf.0;
        bool r28270490 = r28270488 <= r28270489;
        double r28270491 = r28270483 / r28270486;
        double r28270492 = r28270481 * r28270491;
        double r28270493 = r28270492 + r28270478;
        double r28270494 = -3.0404769334557312e-273;
        bool r28270495 = r28270488 <= r28270494;
        double r28270496 = 0.0;
        bool r28270497 = r28270488 <= r28270496;
        double r28270498 = r28270478 / r28270480;
        double r28270499 = r28270482 / r28270480;
        double r28270500 = r28270498 - r28270499;
        double r28270501 = r28270479 * r28270500;
        double r28270502 = r28270482 + r28270501;
        double r28270503 = cbrt(r28270481);
        double r28270504 = cbrt(r28270486);
        double r28270505 = r28270503 / r28270504;
        double r28270506 = r28270483 / r28270504;
        double r28270507 = r28270505 * r28270506;
        double r28270508 = r28270503 * r28270503;
        double r28270509 = r28270508 / r28270504;
        double r28270510 = r28270507 * r28270509;
        double r28270511 = r28270478 + r28270510;
        double r28270512 = r28270497 ? r28270502 : r28270511;
        double r28270513 = r28270495 ? r28270488 : r28270512;
        double r28270514 = r28270490 ? r28270493 : r28270513;
        return r28270514;
}

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

Original23.1
Target11.7
Herbie8.5
\[\begin{array}{l} \mathbf{if}\;z \lt -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \lt 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

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

    1. Initial program 60.9

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

    3. Applied *-un-lft-identity60.9

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

    4. Applied times-frac17.4

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

    5. Simplified17.4

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

    if -inf.0 < (+ x (/ (* (- y z) (- t x)) (- a z))) < -3.0404769334557312e-273

    1. Initial program 1.9

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

    if -3.0404769334557312e-273 < (+ x (/ (* (- y z) (- t x)) (- a z))) < 0.0

    1. Initial program 58.2

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

    3. Applied add-cube-cbrt58.1

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

    4. Applied times-frac58.0

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

    6. Applied add-cube-cbrt58.1

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

    7. Applied times-frac58.1

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

    8. Applied associate-*l*58.1

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

    9. Taylor expanded around inf 21.1

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

    10. Simplified23.3

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

    if 0.0 < (+ x (/ (* (- y z) (- t x)) (- a z)))

    1. Initial program 19.5

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

    3. Applied add-cube-cbrt20.0

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

    4. Applied times-frac8.0

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

    6. Applied add-cube-cbrt7.9

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

    7. Applied times-frac7.9

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

    8. Applied associate-*l*7.5

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

    10. Applied *-commutative7.5

      \[\leadsto x + \color{blue}{\left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification8.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} = -\infty:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t - x}{a - z} + x\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le -3.0404769334557312 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le 0.0:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(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))))