Average Error: 14.5 → 11.9
Time: 6.3s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -4.25667840930416321 \cdot 10^{-59} \lor \neg \left(a \le 5.52140274263532811 \cdot 10^{-197}\right):\\ \;\;\;\;x + \left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;a \le -4.25667840930416321 \cdot 10^{-59} \lor \neg \left(a \le 5.52140274263532811 \cdot 10^{-197}\right):\\
\;\;\;\;x + \left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)\\

\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 r120065 = x;
        double r120066 = y;
        double r120067 = z;
        double r120068 = r120066 - r120067;
        double r120069 = t;
        double r120070 = r120069 - r120065;
        double r120071 = a;
        double r120072 = r120071 - r120067;
        double r120073 = r120070 / r120072;
        double r120074 = r120068 * r120073;
        double r120075 = r120065 + r120074;
        return r120075;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r120076 = a;
        double r120077 = -4.256678409304163e-59;
        bool r120078 = r120076 <= r120077;
        double r120079 = 5.521402742635328e-197;
        bool r120080 = r120076 <= r120079;
        double r120081 = !r120080;
        bool r120082 = r120078 || r120081;
        double r120083 = x;
        double r120084 = y;
        double r120085 = z;
        double r120086 = r120084 - r120085;
        double r120087 = cbrt(r120086);
        double r120088 = r120087 * r120087;
        double r120089 = r120076 - r120085;
        double r120090 = cbrt(r120089);
        double r120091 = r120090 * r120090;
        double r120092 = r120087 / r120091;
        double r120093 = t;
        double r120094 = r120093 - r120083;
        double r120095 = r120094 / r120090;
        double r120096 = r120092 * r120095;
        double r120097 = r120088 * r120096;
        double r120098 = r120083 + r120097;
        double r120099 = r120083 * r120084;
        double r120100 = r120099 / r120085;
        double r120101 = r120100 + r120093;
        double r120102 = r120093 * r120084;
        double r120103 = r120102 / r120085;
        double r120104 = r120101 - r120103;
        double r120105 = r120082 ? r120098 : r120104;
        return r120105;
}

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 a < -4.256678409304163e-59 or 5.521402742635328e-197 < a

    1. Initial program 11.0

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

    3. Applied add-cube-cbrt11.5

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

    4. Applied associate-*l*11.5

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

    6. Applied add-cube-cbrt11.5

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

    7. Applied *-un-lft-identity11.5

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

    8. Applied times-frac11.5

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

    9. Applied associate-*r*10.2

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

    10. Simplified10.2

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

    if -4.256678409304163e-59 < a < 5.521402742635328e-197

    1. Initial program 24.6

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

    2. Taylor expanded around inf 16.8

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

  4. Final simplification11.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -4.25667840930416321 \cdot 10^{-59} \lor \neg \left(a \le 5.52140274263532811 \cdot 10^{-197}\right):\\ \;\;\;\;x + \left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020034 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))