Average Error: 14.2 → 6.3
Time: 20.4s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -5.175543709426314317899237427278029417013 \cdot 10^{-293} \lor \neg \left(x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le 0.0\right):\\ \;\;\;\;\left(t - x\right) \cdot \frac{y - z}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;t + \left(\frac{y}{\frac{z}{x}} - y \cdot \frac{t}{z}\right)\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -5.175543709426314317899237427278029417013 \cdot 10^{-293} \lor \neg \left(x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le 0.0\right):\\
\;\;\;\;\left(t - x\right) \cdot \frac{y - z}{a - z} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r110401 = x;
        double r110402 = y;
        double r110403 = z;
        double r110404 = r110402 - r110403;
        double r110405 = t;
        double r110406 = r110405 - r110401;
        double r110407 = a;
        double r110408 = r110407 - r110403;
        double r110409 = r110406 / r110408;
        double r110410 = r110404 * r110409;
        double r110411 = r110401 + r110410;
        return r110411;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r110412 = x;
        double r110413 = t;
        double r110414 = r110413 - r110412;
        double r110415 = a;
        double r110416 = z;
        double r110417 = r110415 - r110416;
        double r110418 = r110414 / r110417;
        double r110419 = y;
        double r110420 = r110419 - r110416;
        double r110421 = r110418 * r110420;
        double r110422 = r110412 + r110421;
        double r110423 = -5.175543709426314e-293;
        bool r110424 = r110422 <= r110423;
        double r110425 = 0.0;
        bool r110426 = r110422 <= r110425;
        double r110427 = !r110426;
        bool r110428 = r110424 || r110427;
        double r110429 = r110420 / r110417;
        double r110430 = r110414 * r110429;
        double r110431 = r110430 + r110412;
        double r110432 = r110416 / r110412;
        double r110433 = r110419 / r110432;
        double r110434 = r110413 / r110416;
        double r110435 = r110419 * r110434;
        double r110436 = r110433 - r110435;
        double r110437 = r110413 + r110436;
        double r110438 = r110428 ? r110431 : r110437;
        return r110438;
}

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

Derivation

  1. Split input into 2 regimes

  2. if (+ x (* (- y z) (/ (- t x) (- a z)))) < -5.175543709426314e-293 or 0.0 < (+ x (* (- y z) (/ (- t x) (- a z))))

    1. Initial program 7.1

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

    3. Applied clear-num7.4

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

    5. Applied associate-/r/7.2

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

    6. Applied associate-*r*4.1

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

    7. Simplified4.0

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

    if -5.175543709426314e-293 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 0.0

    1. Initial program 60.9

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

    3. Applied add-cube-cbrt60.6

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

    4. Applied *-un-lft-identity60.6

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{1 \cdot \left(t - x\right)}}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}\]

    5. Applied times-frac60.6

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)}\]

    6. Applied associate-*r*60.0

      \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \frac{1}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{t - x}{\sqrt[3]{a - z}}}\]

    7. Simplified59.9

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

    8. Taylor expanded around inf 25.6

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

    9. Simplified21.2

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

  4. Final simplification6.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le -5.175543709426314317899237427278029417013 \cdot 10^{-293} \lor \neg \left(x + \frac{t - x}{a - z} \cdot \left(y - z\right) \le 0.0\right):\\ \;\;\;\;\left(t - x\right) \cdot \frac{y - z}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;t + \left(\frac{y}{\frac{z}{x}} - y \cdot \frac{t}{z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  (+ x (* (- y z) (/ (- t x) (- a z)))))