Average Error: 16.6 → 7.1
Time: 16.7s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -9.281128316964414077236319093393947807034 \cdot 10^{-174} \lor \neg \left(a \le 5.065826005267877604225588672950525926339 \cdot 10^{-294}\right):\\ \;\;\;\;x + \left(y - y \cdot \frac{z - t}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -9.281128316964414077236319093393947807034 \cdot 10^{-174} \lor \neg \left(a \le 5.065826005267877604225588672950525926339 \cdot 10^{-294}\right):\\
\;\;\;\;x + \left(y - y \cdot \frac{z - t}{a - t}\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r456168 = x;
        double r456169 = y;
        double r456170 = r456168 + r456169;
        double r456171 = z;
        double r456172 = t;
        double r456173 = r456171 - r456172;
        double r456174 = r456173 * r456169;
        double r456175 = a;
        double r456176 = r456175 - r456172;
        double r456177 = r456174 / r456176;
        double r456178 = r456170 - r456177;
        return r456178;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r456179 = a;
        double r456180 = -9.281128316964414e-174;
        bool r456181 = r456179 <= r456180;
        double r456182 = 5.0658260052678776e-294;
        bool r456183 = r456179 <= r456182;
        double r456184 = !r456183;
        bool r456185 = r456181 || r456184;
        double r456186 = x;
        double r456187 = y;
        double r456188 = z;
        double r456189 = t;
        double r456190 = r456188 - r456189;
        double r456191 = r456179 - r456189;
        double r456192 = r456190 / r456191;
        double r456193 = r456187 * r456192;
        double r456194 = r456187 - r456193;
        double r456195 = r456186 + r456194;
        double r456196 = r456187 * r456188;
        double r456197 = r456196 / r456189;
        double r456198 = r456197 + r456186;
        double r456199 = r456185 ? r456195 : r456198;
        return r456199;
}

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

Original16.6
Target8.7
Herbie7.1
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.366497088939072697550672266103566343531 \cdot 10^{-7}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.475429344457723334351036314450840066235 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -9.281128316964414e-174 or 5.0658260052678776e-294 < a

    1. Initial program 15.9

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

    3. Applied associate--l+14.0

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

    4. Simplified8.4

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

    6. Applied div-inv9.0

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

    8. Applied associate-*l*7.7

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

    9. Simplified7.1

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

    if -9.281128316964414e-174 < a < 5.0658260052678776e-294

    1. Initial program 21.3

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

    2. Taylor expanded around inf 7.5

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

    3. Simplified7.5

      \[\leadsto \color{blue}{x + \frac{y \cdot z}{t}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification7.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -9.281128316964414077236319093393947807034 \cdot 10^{-174} \lor \neg \left(a \le 5.065826005267877604225588672950525926339 \cdot 10^{-294}\right):\\ \;\;\;\;x + \left(y - y \cdot \frac{z - t}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-07) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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