Average Error: 24.9 → 10.1
Time: 18.7s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.198410335343120851233733027827244153918 \cdot 10^{-46} \lor \neg \left(a \le 5.860858455533554327064444366829914979601 \cdot 10^{-230}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \left(\frac{1}{a - z} \cdot \left(y - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{\frac{z}{y}} - \frac{t}{\frac{z}{y}}\right) + t\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;a \le -1.198410335343120851233733027827244153918 \cdot 10^{-46} \lor \neg \left(a \le 5.860858455533554327064444366829914979601 \cdot 10^{-230}\right):\\
\;\;\;\;x + \left(t - x\right) \cdot \left(\frac{1}{a - z} \cdot \left(y - z\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{x}{\frac{z}{y}} - \frac{t}{\frac{z}{y}}\right) + t\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r302460 = x;
        double r302461 = y;
        double r302462 = z;
        double r302463 = r302461 - r302462;
        double r302464 = t;
        double r302465 = r302464 - r302460;
        double r302466 = r302463 * r302465;
        double r302467 = a;
        double r302468 = r302467 - r302462;
        double r302469 = r302466 / r302468;
        double r302470 = r302460 + r302469;
        return r302470;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r302471 = a;
        double r302472 = -1.1984103353431209e-46;
        bool r302473 = r302471 <= r302472;
        double r302474 = 5.860858455533554e-230;
        bool r302475 = r302471 <= r302474;
        double r302476 = !r302475;
        bool r302477 = r302473 || r302476;
        double r302478 = x;
        double r302479 = t;
        double r302480 = r302479 - r302478;
        double r302481 = 1.0;
        double r302482 = z;
        double r302483 = r302471 - r302482;
        double r302484 = r302481 / r302483;
        double r302485 = y;
        double r302486 = r302485 - r302482;
        double r302487 = r302484 * r302486;
        double r302488 = r302480 * r302487;
        double r302489 = r302478 + r302488;
        double r302490 = r302482 / r302485;
        double r302491 = r302478 / r302490;
        double r302492 = r302479 / r302490;
        double r302493 = r302491 - r302492;
        double r302494 = r302493 + r302479;
        double r302495 = r302477 ? r302489 : r302494;
        return r302495;
}

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

Original24.9
Target11.8
Herbie10.1
\[\begin{array}{l} \mathbf{if}\;z \lt -1.253613105609503593846459977496550767343 \cdot 10^{188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -1.1984103353431209e-46 or 5.860858455533554e-230 < a

    1. Initial program 23.7

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

    2. Simplified9.3

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

    4. Applied div-inv9.4

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

    if -1.1984103353431209e-46 < a < 5.860858455533554e-230

    1. Initial program 28.7

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

    2. Simplified18.9

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

    4. Applied div-inv19.0

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

    5. Taylor expanded around inf 18.1

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

    6. Simplified12.5

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

  4. Final simplification10.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.198410335343120851233733027827244153918 \cdot 10^{-46} \lor \neg \left(a \le 5.860858455533554327064444366829914979601 \cdot 10^{-230}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \left(\frac{1}{a - z} \cdot \left(y - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{\frac{z}{y}} - \frac{t}{\frac{z}{y}}\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(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))))