Average Error: 2.1 → 2.3
Time: 18.9s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -4.072290433432052442760098322254515693988 \cdot 10^{-23}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;t \le -1.336117363059674131707044966713149076742 \cdot 10^{-223}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \mathbf{elif}\;t \le 7.81875512884679996695346065746985015342 \cdot 10^{-283}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;t \le 1.53684687189294249658677677918305964993 \cdot 10^{-157}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;t \le -4.072290433432052442760098322254515693988 \cdot 10^{-23}:\\
\;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\

\mathbf{elif}\;t \le -1.336117363059674131707044966713149076742 \cdot 10^{-223}:\\
\;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\

\mathbf{elif}\;t \le 7.81875512884679996695346065746985015342 \cdot 10^{-283}:\\
\;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\

\mathbf{elif}\;t \le 1.53684687189294249658677677918305964993 \cdot 10^{-157}:\\
\;\;\;\;x \cdot \frac{z - t}{y} + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r21586730 = x;
        double r21586731 = y;
        double r21586732 = r21586730 / r21586731;
        double r21586733 = z;
        double r21586734 = t;
        double r21586735 = r21586733 - r21586734;
        double r21586736 = r21586732 * r21586735;
        double r21586737 = r21586736 + r21586734;
        return r21586737;
}
↓
double f(double x, double y, double z, double t) {
        double r21586738 = t;
        double r21586739 = -4.0722904334320524e-23;
        bool r21586740 = r21586738 <= r21586739;
        double r21586741 = z;
        double r21586742 = r21586741 - r21586738;
        double r21586743 = x;
        double r21586744 = y;
        double r21586745 = r21586743 / r21586744;
        double r21586746 = r21586742 * r21586745;
        double r21586747 = r21586738 + r21586746;
        double r21586748 = -1.3361173630596741e-223;
        bool r21586749 = r21586738 <= r21586748;
        double r21586750 = r21586743 * r21586742;
        double r21586751 = r21586750 / r21586744;
        double r21586752 = r21586751 + r21586738;
        double r21586753 = 7.8187551288468e-283;
        bool r21586754 = r21586738 <= r21586753;
        double r21586755 = 1.5368468718929425e-157;
        bool r21586756 = r21586738 <= r21586755;
        double r21586757 = r21586742 / r21586744;
        double r21586758 = r21586743 * r21586757;
        double r21586759 = r21586758 + r21586738;
        double r21586760 = r21586756 ? r21586759 : r21586747;
        double r21586761 = r21586754 ? r21586747 : r21586760;
        double r21586762 = r21586749 ? r21586752 : r21586761;
        double r21586763 = r21586740 ? r21586747 : r21586762;
        return r21586763;
}

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

Original2.1
Target2.3
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -4.0722904334320524e-23 or -1.3361173630596741e-223 < t < 7.8187551288468e-283 or 1.5368468718929425e-157 < t

    1. Initial program 1.3

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

    if -4.0722904334320524e-23 < t < -1.3361173630596741e-223

    1. Initial program 3.2

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

    3. Applied *-un-lft-identity3.2

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

    4. Applied add-cube-cbrt3.8

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

    5. Applied times-frac3.9

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

    6. Applied associate-*l*3.0

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

    8. Applied associate-*l/3.7

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

    9. Applied frac-times5.1

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

    10. Simplified4.4

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

    11. Simplified4.4

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

    if 7.8187551288468e-283 < t < 1.5368468718929425e-157

    1. Initial program 4.9

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

    3. Applied div-inv4.9

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

    4. Applied associate-*l*5.1

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

    5. Simplified5.0

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -4.072290433432052442760098322254515693988 \cdot 10^{-23}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;t \le -1.336117363059674131707044966713149076742 \cdot 10^{-223}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \mathbf{elif}\;t \le 7.81875512884679996695346065746985015342 \cdot 10^{-283}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;t \le 1.53684687189294249658677677918305964993 \cdot 10^{-157}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019170 
(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))