Average Error: 11.5 → 0.7
Time: 5.7s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -6.414154112854105407013291321620742388699 \cdot 10^{-121} \lor \neg \left(y \le 4.594501379393755892248903622673783295757 \cdot 10^{-163}\right):\\ \;\;\;\;x + \frac{y}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -6.414154112854105407013291321620742388699 \cdot 10^{-121} \lor \neg \left(y \le 4.594501379393755892248903622673783295757 \cdot 10^{-163}\right):\\
\;\;\;\;x + \frac{y}{\left(a - t\right) \cdot \frac{1}{z - t}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r685082 = x;
        double r685083 = y;
        double r685084 = z;
        double r685085 = t;
        double r685086 = r685084 - r685085;
        double r685087 = r685083 * r685086;
        double r685088 = a;
        double r685089 = r685088 - r685085;
        double r685090 = r685087 / r685089;
        double r685091 = r685082 + r685090;
        return r685091;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r685092 = y;
        double r685093 = -6.414154112854105e-121;
        bool r685094 = r685092 <= r685093;
        double r685095 = 4.594501379393756e-163;
        bool r685096 = r685092 <= r685095;
        double r685097 = !r685096;
        bool r685098 = r685094 || r685097;
        double r685099 = x;
        double r685100 = a;
        double r685101 = t;
        double r685102 = r685100 - r685101;
        double r685103 = 1.0;
        double r685104 = z;
        double r685105 = r685104 - r685101;
        double r685106 = r685103 / r685105;
        double r685107 = r685102 * r685106;
        double r685108 = r685092 / r685107;
        double r685109 = r685099 + r685108;
        double r685110 = r685092 * r685105;
        double r685111 = r685110 / r685102;
        double r685112 = r685099 + r685111;
        double r685113 = r685098 ? r685109 : r685112;
        return r685113;
}

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

Original11.5
Target1.4
Herbie0.7
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -6.414154112854105e-121 or 4.594501379393756e-163 < y

    1. Initial program 16.0

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

    3. Applied associate-/l*0.8

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

    5. Applied div-inv0.9

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

    if -6.414154112854105e-121 < y < 4.594501379393756e-163

    1. Initial program 0.3

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -6.414154112854105407013291321620742388699 \cdot 10^{-121} \lor \neg \left(y \le 4.594501379393755892248903622673783295757 \cdot 10^{-163}\right):\\ \;\;\;\;x + \frac{y}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(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))))