Average Error: 10.8 → 0.3
Time: 10.5s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 7.2611128830759547 \cdot 10^{284}\right):\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 7.2611128830759547 \cdot 10^{284}\right):\\
\;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\

\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 r681139 = x;
        double r681140 = y;
        double r681141 = z;
        double r681142 = t;
        double r681143 = r681141 - r681142;
        double r681144 = r681140 * r681143;
        double r681145 = a;
        double r681146 = r681145 - r681142;
        double r681147 = r681144 / r681146;
        double r681148 = r681139 + r681147;
        return r681148;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r681149 = y;
        double r681150 = z;
        double r681151 = t;
        double r681152 = r681150 - r681151;
        double r681153 = r681149 * r681152;
        double r681154 = a;
        double r681155 = r681154 - r681151;
        double r681156 = r681153 / r681155;
        double r681157 = -inf.0;
        bool r681158 = r681156 <= r681157;
        double r681159 = 7.261112883075955e+284;
        bool r681160 = r681156 <= r681159;
        double r681161 = !r681160;
        bool r681162 = r681158 || r681161;
        double r681163 = r681155 / r681149;
        double r681164 = r681152 / r681163;
        double r681165 = x;
        double r681166 = r681164 + r681165;
        double r681167 = r681165 + r681156;
        double r681168 = r681162 ? r681166 : r681167;
        return r681168;
}

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

Original10.8
Target1.2
Herbie0.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* y (- z t)) (- a t)) < -inf.0 or 7.261112883075955e+284 < (/ (* y (- z t)) (- a t))

    1. Initial program 62.2

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

    2. Simplified0.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)}\]
    3. Using strategy rm

    4. Applied clear-num0.9

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - t}{y}}}, z - t, x\right)\]
    5. Using strategy rm

    6. Applied fma-udef0.9

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

    7. Simplified0.7

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

    if -inf.0 < (/ (* y (- z t)) (- a t)) < 7.261112883075955e+284

    1. Initial program 0.2

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 7.2611128830759547 \cdot 10^{284}\right):\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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))))