Average Error: 10.9 → 0.9
Time: 14.6s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -8.221766270881260680781617468110851043872 \cdot 10^{83}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t} + x\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a - t} \le 3.617347282531532552438490010295973375078 \cdot 10^{225}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -8.221766270881260680781617468110851043872 \cdot 10^{83}:\\
\;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t} + x\\

\mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a - t} \le 3.617347282531532552438490010295973375078 \cdot 10^{225}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r370087 = x;
        double r370088 = y;
        double r370089 = z;
        double r370090 = t;
        double r370091 = r370089 - r370090;
        double r370092 = r370088 * r370091;
        double r370093 = a;
        double r370094 = r370093 - r370090;
        double r370095 = r370092 / r370094;
        double r370096 = r370087 + r370095;
        return r370096;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r370097 = y;
        double r370098 = z;
        double r370099 = t;
        double r370100 = r370098 - r370099;
        double r370101 = r370097 * r370100;
        double r370102 = a;
        double r370103 = r370102 - r370099;
        double r370104 = r370101 / r370103;
        double r370105 = -8.221766270881261e+83;
        bool r370106 = r370104 <= r370105;
        double r370107 = r370097 / r370103;
        double r370108 = r370100 * r370107;
        double r370109 = x;
        double r370110 = r370108 + r370109;
        double r370111 = 3.6173472825315326e+225;
        bool r370112 = r370104 <= r370111;
        double r370113 = r370109 + r370104;
        double r370114 = r370103 / r370100;
        double r370115 = r370097 / r370114;
        double r370116 = r370109 + r370115;
        double r370117 = r370112 ? r370113 : r370116;
        double r370118 = r370106 ? r370110 : r370117;
        return r370118;
}

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

Target

Original10.9
Target1.3
Herbie0.9
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* y (- z t)) (- a t)) < -8.221766270881261e+83

    1. Initial program 30.5

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

    3. Applied *-un-lft-identity30.5

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

    4. Applied times-frac3.0

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

    5. Simplified3.0

      \[\leadsto x + \color{blue}{y} \cdot \frac{z - t}{a - t}\]
    6. Using strategy rm

    7. Applied pow13.0

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

    8. Applied pow13.0

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

    9. Applied pow-prod-down3.0

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

    10. Simplified3.2

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

    if -8.221766270881261e+83 < (/ (* y (- z t)) (- a t)) < 3.6173472825315326e+225

    1. Initial program 0.2

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

    3. Applied *-un-lft-identity0.2

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

    4. Applied times-frac0.9

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

    5. Simplified0.9

      \[\leadsto x + \color{blue}{y} \cdot \frac{z - t}{a - t}\]
    6. Using strategy rm

    7. Applied associate-*r/0.2

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

    if 3.6173472825315326e+225 < (/ (* y (- z t)) (- a t))

    1. Initial program 51.8

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

    3. Applied associate-/l*1.8

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -8.221766270881260680781617468110851043872 \cdot 10^{83}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t} + x\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a - t} \le 3.617347282531532552438490010295973375078 \cdot 10^{225}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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