Average Error: 24.5 → 8.6
Time: 18.0s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le -5.94158773471745396 \cdot 10^{-307} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le 0.0\right):\\ \;\;\;\;x + \left(\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{y - z}}{\frac{\sqrt[3]{a - z}}{\frac{\sqrt[3]{t - x} \cdot {\left(\sqrt[3]{\sqrt[3]{t - x}}\right)}^{3}}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]
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 -5.94158773471745396 \cdot 10^{-307} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le 0.0\right):\\
\;\;\;\;x + \left(\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{y - z}}{\frac{\sqrt[3]{a - z}}{\frac{\sqrt[3]{t - x} \cdot {\left(\sqrt[3]{\sqrt[3]{t - x}}\right)}^{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}}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r781204 = x;
        double r781205 = y;
        double r781206 = z;
        double r781207 = r781205 - r781206;
        double r781208 = t;
        double r781209 = r781208 - r781204;
        double r781210 = r781207 * r781209;
        double r781211 = a;
        double r781212 = r781211 - r781206;
        double r781213 = r781210 / r781212;
        double r781214 = r781204 + r781213;
        return r781214;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r781215 = x;
        double r781216 = y;
        double r781217 = z;
        double r781218 = r781216 - r781217;
        double r781219 = t;
        double r781220 = r781219 - r781215;
        double r781221 = r781218 * r781220;
        double r781222 = a;
        double r781223 = r781222 - r781217;
        double r781224 = r781221 / r781223;
        double r781225 = r781215 + r781224;
        double r781226 = -5.941587734717454e-307;
        bool r781227 = r781225 <= r781226;
        double r781228 = 0.0;
        bool r781229 = r781225 <= r781228;
        double r781230 = !r781229;
        bool r781231 = r781227 || r781230;
        double r781232 = cbrt(r781218);
        double r781233 = r781232 * r781232;
        double r781234 = cbrt(r781223);
        double r781235 = r781233 / r781234;
        double r781236 = cbrt(r781220);
        double r781237 = cbrt(r781236);
        double r781238 = 3.0;
        double r781239 = pow(r781237, r781238);
        double r781240 = r781236 * r781239;
        double r781241 = r781234 * r781234;
        double r781242 = cbrt(r781241);
        double r781243 = r781240 / r781242;
        double r781244 = r781234 / r781243;
        double r781245 = r781232 / r781244;
        double r781246 = r781235 * r781245;
        double r781247 = cbrt(r781234);
        double r781248 = r781236 / r781247;
        double r781249 = r781246 * r781248;
        double r781250 = r781215 + r781249;
        double r781251 = r781215 * r781216;
        double r781252 = r781251 / r781217;
        double r781253 = r781252 + r781219;
        double r781254 = r781219 * r781216;
        double r781255 = r781254 / r781217;
        double r781256 = r781253 - r781255;
        double r781257 = r781231 ? r781250 : r781256;
        return r781257;
}

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
Target11.7
Herbie8.6
\[\begin{array}{l} \mathbf{if}\;z \lt -1.25361310560950359 \cdot 10^{188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* (- y z) (- t x)) (- a z))) < -5.941587734717454e-307 or 0.0 < (+ x (/ (* (- y z) (- t x)) (- a z)))

    1. Initial program 21.3

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

    3. Applied add-cube-cbrt21.8

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

    4. Applied times-frac8.2

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

    6. Applied add-cube-cbrt8.3

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

    7. Applied cbrt-prod8.3

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

    8. Applied add-cube-cbrt8.5

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

    9. Applied times-frac8.5

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

    10. Applied associate-*r*8.0

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

    12. Applied add-cube-cbrt8.1

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

    14. Applied add-cube-cbrt8.1

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

    15. Applied times-frac8.1

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

    16. Applied associate-*l*7.7

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

    17. Simplified7.8

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

    if -5.941587734717454e-307 < (+ x (/ (* (- y z) (- t x)) (- a z))) < 0.0

    1. Initial program 61.2

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

    2. Taylor expanded around inf 17.8

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

  4. Final simplification8.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le -5.94158773471745396 \cdot 10^{-307} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \le 0.0\right):\\ \;\;\;\;x + \left(\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{y - z}}{\frac{\sqrt[3]{a - z}}{\frac{\sqrt[3]{t - x} \cdot {\left(\sqrt[3]{\sqrt[3]{t - x}}\right)}^{3}}{\sqrt[3]{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{\sqrt[3]{a - z}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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))))