Average Error: 15.9 → 8.3
Time: 14.9s
Precision: 64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -9.63291531175125 \cdot 10^{-116}:\\ \;\;\;\;x + \left(y - \frac{y}{a - t} \cdot \left(z - t\right)\right)\\ \mathbf{elif}\;a \le 1.5343352289819368 \cdot 10^{-165}:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{a - t} \cdot \left(z - t\right)\right)\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -9.63291531175125 \cdot 10^{-116}:\\
\;\;\;\;x + \left(y - \frac{y}{a - t} \cdot \left(z - t\right)\right)\\

\mathbf{elif}\;a \le 1.5343352289819368 \cdot 10^{-165}:\\
\;\;\;\;\frac{y \cdot z}{t} + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r27719446 = x;
        double r27719447 = y;
        double r27719448 = r27719446 + r27719447;
        double r27719449 = z;
        double r27719450 = t;
        double r27719451 = r27719449 - r27719450;
        double r27719452 = r27719451 * r27719447;
        double r27719453 = a;
        double r27719454 = r27719453 - r27719450;
        double r27719455 = r27719452 / r27719454;
        double r27719456 = r27719448 - r27719455;
        return r27719456;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r27719457 = a;
        double r27719458 = -9.63291531175125e-116;
        bool r27719459 = r27719457 <= r27719458;
        double r27719460 = x;
        double r27719461 = y;
        double r27719462 = t;
        double r27719463 = r27719457 - r27719462;
        double r27719464 = r27719461 / r27719463;
        double r27719465 = z;
        double r27719466 = r27719465 - r27719462;
        double r27719467 = r27719464 * r27719466;
        double r27719468 = r27719461 - r27719467;
        double r27719469 = r27719460 + r27719468;
        double r27719470 = 1.5343352289819368e-165;
        bool r27719471 = r27719457 <= r27719470;
        double r27719472 = r27719461 * r27719465;
        double r27719473 = r27719472 / r27719462;
        double r27719474 = r27719473 + r27719460;
        double r27719475 = r27719471 ? r27719474 : r27719469;
        double r27719476 = r27719459 ? r27719469 : r27719475;
        return r27719476;
}

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

Original15.9
Target8.6
Herbie8.3
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt -1.3664970889390727 \cdot 10^{-07}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \lt 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -9.63291531175125e-116 or 1.5343352289819368e-165 < a

    1. Initial program 14.4

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

    3. Applied *-un-lft-identity14.4

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

    4. Applied times-frac9.5

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

    5. Simplified9.5

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

    7. Applied associate--l+7.6

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

    if -9.63291531175125e-116 < a < 1.5343352289819368e-165

    1. Initial program 20.3

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

    3. Applied *-un-lft-identity20.3

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

    4. Applied times-frac19.9

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

    5. Simplified19.9

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

    7. Applied associate--l+13.3

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

    8. Taylor expanded around inf 10.2

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

  4. Final simplification8.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -9.63291531175125 \cdot 10^{-116}:\\ \;\;\;\;x + \left(y - \frac{y}{a - t} \cdot \left(z - t\right)\right)\\ \mathbf{elif}\;a \le 1.5343352289819368 \cdot 10^{-165}:\\ \;\;\;\;\frac{y \cdot z}{t} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{a - t} \cdot \left(z - t\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(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 (- 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 (- a t))) y))))

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