Average Error: 14.7 → 7.3
Time: 7.1s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -1.156506321277581653214891910831195950706 \cdot 10^{-297}:\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{a - z}\right) \cdot \frac{\sqrt[3]{1}}{\frac{1}{t - x}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{a - z} \cdot \sqrt[3]{1}\right)}{\frac{1}{t - x}}\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -1.156506321277581653214891910831195950706 \cdot 10^{-297}:\\
\;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{a - z}\right) \cdot \frac{\sqrt[3]{1}}{\frac{1}{t - x}}\\

\mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\left(y - z\right) \cdot \left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{a - z} \cdot \sqrt[3]{1}\right)}{\frac{1}{t - x}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r130109 = x;
        double r130110 = y;
        double r130111 = z;
        double r130112 = r130110 - r130111;
        double r130113 = t;
        double r130114 = r130113 - r130109;
        double r130115 = a;
        double r130116 = r130115 - r130111;
        double r130117 = r130114 / r130116;
        double r130118 = r130112 * r130117;
        double r130119 = r130109 + r130118;
        return r130119;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r130120 = x;
        double r130121 = y;
        double r130122 = z;
        double r130123 = r130121 - r130122;
        double r130124 = t;
        double r130125 = r130124 - r130120;
        double r130126 = a;
        double r130127 = r130126 - r130122;
        double r130128 = r130125 / r130127;
        double r130129 = r130123 * r130128;
        double r130130 = r130120 + r130129;
        double r130131 = -1.1565063212775817e-297;
        bool r130132 = r130130 <= r130131;
        double r130133 = 1.0;
        double r130134 = cbrt(r130133);
        double r130135 = r130134 * r130134;
        double r130136 = r130135 / r130127;
        double r130137 = r130123 * r130136;
        double r130138 = r130133 / r130125;
        double r130139 = r130134 / r130138;
        double r130140 = r130137 * r130139;
        double r130141 = r130120 + r130140;
        double r130142 = 0.0;
        bool r130143 = r130130 <= r130142;
        double r130144 = r130120 * r130121;
        double r130145 = r130144 / r130122;
        double r130146 = r130145 + r130124;
        double r130147 = r130124 * r130121;
        double r130148 = r130147 / r130122;
        double r130149 = r130146 - r130148;
        double r130150 = r130136 * r130134;
        double r130151 = r130123 * r130150;
        double r130152 = r130151 / r130138;
        double r130153 = r130120 + r130152;
        double r130154 = r130143 ? r130149 : r130153;
        double r130155 = r130132 ? r130141 : r130154;
        return r130155;
}

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 3 regimes

  2. if (+ x (* (- y z) (/ (- t x) (- a z)))) < -1.1565063212775817e-297

    1. Initial program 7.3

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

    3. Applied clear-num7.6

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

    5. Applied div-inv7.7

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

    6. Applied add-cube-cbrt7.7

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

    7. Applied times-frac7.4

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

    8. Applied associate-*r*4.4

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

    if -1.1565063212775817e-297 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 0.0

    1. Initial program 61.2

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

    2. Taylor expanded around inf 27.6

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

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

    1. Initial program 7.4

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

    3. Applied clear-num7.6

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

    5. Applied div-inv7.7

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

    6. Applied add-cube-cbrt7.7

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

    7. Applied times-frac7.5

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

    8. Applied associate-*r*3.7

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

    10. Applied associate-*r/3.7

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

    11. Simplified3.7

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

  4. Final simplification7.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -1.156506321277581653214891910831195950706 \cdot 10^{-297}:\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{a - z}\right) \cdot \frac{\sqrt[3]{1}}{\frac{1}{t - x}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 0.0:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{a - z} \cdot \sqrt[3]{1}\right)}{\frac{1}{t - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(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)))))