Average Error: 10.6 → 0.7
Time: 5.7s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{a - t} = -inf.0 \lor \neg \left(x + \frac{y \cdot \left(z - t\right)}{a - t} \le -1.866487279816731 \cdot 10^{-197}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{a - t} = -inf.0 \lor \neg \left(x + \frac{y \cdot \left(z - t\right)}{a - t} \le -1.866487279816731 \cdot 10^{-197}\right):\\
\;\;\;\;x + y \cdot \frac{z - t}{a - t}\\

\mathbf{else}:\\
\;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (y * ((double) (z - t)))) / ((double) (a - t))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((((double) (x + ((double) (((double) (y * ((double) (z - t)))) / ((double) (a - t)))))) <= -inf.0) || !(((double) (x + ((double) (((double) (y * ((double) (z - t)))) / ((double) (a - t)))))) <= -1.8664872798167307e-197))) {
		VAR = ((double) (x + ((double) (y * ((double) (((double) (z - t)) / ((double) (a - t))))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (y * ((double) (z - t)))) * ((double) (1.0 / ((double) (a - t))))))));
	}
	return VAR;
}

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

Original10.6
Target1.2
Herbie0.7
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* y (- z t)) (- a t))) < -inf.0 or -1.866487279816731e-197 < (+ x (/ (* y (- z t)) (- a t)))

    1. Initial program 17.8

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

    2. Simplified1.1

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

    if -inf.0 < (+ x (/ (* y (- z t)) (- a t))) < -1.866487279816731e-197

    1. Initial program 0.1

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

    2. Simplified1.7

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

    4. Applied div-inv1.7

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

    5. Applied associate-*r*0.2

      \[\leadsto x + \color{blue}{\left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{a - t} = -inf.0 \lor \neg \left(x + \frac{y \cdot \left(z - t\right)}{a - t} \le -1.866487279816731 \cdot 10^{-197}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(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))))