Average Error: 2.3 → 2.0
Time: 24.0s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.848006757289778925957145203255673293895 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;t \le 2.183217079640586700165253323759060557375 \cdot 10^{-41}:\\ \;\;\;\;\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;t \le -3.848006757289778925957145203255673293895 \cdot 10^{-115}:\\
\;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\

\mathbf{elif}\;t \le 2.183217079640586700165253323759060557375 \cdot 10^{-41}:\\
\;\;\;\;\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r94678095 = x;
        double r94678096 = y;
        double r94678097 = r94678095 / r94678096;
        double r94678098 = z;
        double r94678099 = t;
        double r94678100 = r94678098 - r94678099;
        double r94678101 = r94678097 * r94678100;
        double r94678102 = r94678101 + r94678099;
        return r94678102;
}
↓
double f(double x, double y, double z, double t) {
        double r94678103 = t;
        double r94678104 = -3.848006757289779e-115;
        bool r94678105 = r94678103 <= r94678104;
        double r94678106 = x;
        double r94678107 = y;
        double r94678108 = r94678106 / r94678107;
        double r94678109 = z;
        double r94678110 = r94678109 - r94678103;
        double r94678111 = r94678108 * r94678110;
        double r94678112 = r94678111 + r94678103;
        double r94678113 = 2.1832170796405867e-41;
        bool r94678114 = r94678103 <= r94678113;
        double r94678115 = 1.0;
        double r94678116 = cbrt(r94678107);
        double r94678117 = r94678116 * r94678116;
        double r94678118 = r94678115 / r94678117;
        double r94678119 = r94678106 / r94678116;
        double r94678120 = r94678119 * r94678110;
        double r94678121 = r94678118 * r94678120;
        double r94678122 = r94678121 + r94678103;
        double r94678123 = r94678114 ? r94678122 : r94678112;
        double r94678124 = r94678105 ? r94678112 : r94678123;
        return r94678124;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.3
Target2.5
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -3.848006757289779e-115 or 2.1832170796405867e-41 < t

    1. Initial program 0.5

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

    if -3.848006757289779e-115 < t < 2.1832170796405867e-41

    1. Initial program 4.9

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

    3. Applied add-cube-cbrt5.6

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

    4. Applied *-un-lft-identity5.6

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

    5. Applied times-frac5.6

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

    6. Applied associate-*l*3.9

      \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \left(z - t\right)\right)} + t\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.848006757289778925957145203255673293895 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;t \le 2.183217079640586700165253323759060557375 \cdot 10^{-41}:\\ \;\;\;\;\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

  (+ (* (/ x y) (- z t)) t))