Average Error: 1.4 → 1.0
Time: 12.9s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -186062994224651239424:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t} + x\\ \mathbf{elif}\;y \le 1.22452106600687926588900523708060487951 \cdot 10^{-94}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -186062994224651239424:\\
\;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t} + x\\

\mathbf{elif}\;y \le 1.22452106600687926588900523708060487951 \cdot 10^{-94}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r375086 = x;
        double r375087 = y;
        double r375088 = z;
        double r375089 = t;
        double r375090 = r375088 - r375089;
        double r375091 = a;
        double r375092 = r375091 - r375089;
        double r375093 = r375090 / r375092;
        double r375094 = r375087 * r375093;
        double r375095 = r375086 + r375094;
        return r375095;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r375096 = y;
        double r375097 = -1.8606299422465124e+20;
        bool r375098 = r375096 <= r375097;
        double r375099 = z;
        double r375100 = t;
        double r375101 = r375099 - r375100;
        double r375102 = a;
        double r375103 = r375102 - r375100;
        double r375104 = r375096 / r375103;
        double r375105 = r375101 * r375104;
        double r375106 = x;
        double r375107 = r375105 + r375106;
        double r375108 = 1.2245210660068793e-94;
        bool r375109 = r375096 <= r375108;
        double r375110 = r375096 * r375101;
        double r375111 = r375110 / r375103;
        double r375112 = r375106 + r375111;
        double r375113 = r375101 / r375103;
        double r375114 = r375096 * r375113;
        double r375115 = r375106 + r375114;
        double r375116 = r375109 ? r375112 : r375115;
        double r375117 = r375098 ? r375107 : r375116;
        return r375117;
}

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

Original1.4
Target0.4
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241069024247453646278348229 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.8606299422465124e+20

    1. Initial program 0.8

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

    3. Applied pow10.8

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

    4. Applied pow10.8

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

    5. Applied pow-prod-down0.8

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

    6. Simplified3.0

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

    if -1.8606299422465124e+20 < y < 1.2245210660068793e-94

    1. Initial program 2.2

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

    3. Applied associate-*r/0.3

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

    if 1.2245210660068793e-94 < y

    1. Initial program 0.5

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -186062994224651239424:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t} + x\\ \mathbf{elif}\;y \le 1.22452106600687926588900523708060487951 \cdot 10^{-94}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Reproduce

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

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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