Average Error: 24.5 → 11.1
Time: 8.5s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -4.58960810667550706 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{y - z}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \sqrt[3]{\sqrt[3]{a - z}}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \mathbf{elif}\;a \le 7.16030570011128415 \cdot 10^{-200}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;a \le -4.58960810667550706 \cdot 10^{-129}:\\
\;\;\;\;x + \frac{y - z}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \sqrt[3]{\sqrt[3]{a - z}}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\

\mathbf{elif}\;a \le 7.16030570011128415 \cdot 10^{-200}:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r617317 = x;
        double r617318 = y;
        double r617319 = z;
        double r617320 = r617318 - r617319;
        double r617321 = t;
        double r617322 = r617321 - r617317;
        double r617323 = r617320 * r617322;
        double r617324 = a;
        double r617325 = r617324 - r617319;
        double r617326 = r617323 / r617325;
        double r617327 = r617317 + r617326;
        return r617327;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r617328 = a;
        double r617329 = -4.589608106675507e-129;
        bool r617330 = r617328 <= r617329;
        double r617331 = x;
        double r617332 = y;
        double r617333 = z;
        double r617334 = r617332 - r617333;
        double r617335 = r617328 - r617333;
        double r617336 = cbrt(r617335);
        double r617337 = r617336 * r617336;
        double r617338 = cbrt(r617337);
        double r617339 = r617336 * r617338;
        double r617340 = cbrt(r617336);
        double r617341 = r617339 * r617340;
        double r617342 = r617334 / r617341;
        double r617343 = t;
        double r617344 = r617343 - r617331;
        double r617345 = r617344 / r617336;
        double r617346 = r617342 * r617345;
        double r617347 = r617331 + r617346;
        double r617348 = 7.160305700111284e-200;
        bool r617349 = r617328 <= r617348;
        double r617350 = r617331 * r617332;
        double r617351 = r617350 / r617333;
        double r617352 = r617351 + r617343;
        double r617353 = r617343 * r617332;
        double r617354 = r617353 / r617333;
        double r617355 = r617352 - r617354;
        double r617356 = r617334 / r617337;
        double r617357 = r617356 * r617345;
        double r617358 = r617331 + r617357;
        double r617359 = r617349 ? r617355 : r617358;
        double r617360 = r617330 ? r617347 : r617359;
        return r617360;
}

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

Original24.5
Target12.0
Herbie11.1
\[\begin{array}{l} \mathbf{if}\;z \lt -1.25361310560950359 \cdot 10^{188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -4.589608106675507e-129

    1. Initial program 23.3

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

    3. Applied add-cube-cbrt23.6

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

    4. Applied times-frac10.1

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

    6. Applied add-cube-cbrt10.1

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

    7. Applied cbrt-prod10.2

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

    8. Applied associate-*r*10.2

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

    if -4.589608106675507e-129 < a < 7.160305700111284e-200

    1. Initial program 29.0

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

    2. Taylor expanded around inf 13.1

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

    if 7.160305700111284e-200 < a

    1. Initial program 23.5

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

    3. Applied add-cube-cbrt23.9

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

    4. Applied times-frac11.0

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

  4. Final simplification11.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -4.58960810667550706 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{y - z}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \sqrt[3]{\sqrt[3]{a - z}}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \mathbf{elif}\;a \le 7.16030570011128415 \cdot 10^{-200}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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))))