Average Error: 10.2 → 0.5
Time: 4.6s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -3.099128616291226 \cdot 10^{-118}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\ \mathbf{elif}\;y \leq 7.043274856239975 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{1}{\frac{z - a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -3.099128616291226 \cdot 10^{-118}:\\
\;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\

\mathbf{elif}\;y \leq 7.043274856239975 \cdot 10^{-34}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\

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

\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) (- z a))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.099128616291226e-118)
   (+ x (* y (- (/ z (- z a)) (/ t (- z a)))))
   (if (<= y 7.043274856239975e-34)
     (+ x (/ (* y (- z t)) (- z a)))
     (+ x (* y (/ 1.0 (/ (- z a) (- z t))))))))
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + (((double) (y * ((double) (z - t)))) / ((double) (z - a)))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.099128616291226e-118)) {
		tmp = ((double) (x + ((double) (y * ((double) ((z / ((double) (z - a))) - (t / ((double) (z - a)))))))));
	} else {
		double tmp_1;
		if ((y <= 7.043274856239975e-34)) {
			tmp_1 = ((double) (x + (((double) (y * ((double) (z - t)))) / ((double) (z - a)))));
		} else {
			tmp_1 = ((double) (x + ((double) (y * (1.0 / (((double) (z - a)) / ((double) (z - t))))))));
		}
		tmp = tmp_1;
	}
	return tmp;
}

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

Original10.2
Target1.2
Herbie0.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -3.09912861629122609e-118

    1. Initial program Error: 14.9 bits

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

    2. SimplifiedError: 0.6 bits

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

    4. Applied div-subError: 0.6 bits

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

    if -3.09912861629122609e-118 < y < 7.04327485623997529e-34

    1. Initial program Error: 0.5 bits

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

    if 7.04327485623997529e-34 < y

    1. Initial program Error: 20.1 bits

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

    2. SimplifiedError: 0.4 bits

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

    4. Applied clear-numError: 0.5 bits

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

  4. Final simplificationError: 0.5 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.099128616291226 \cdot 10^{-118}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\ \mathbf{elif}\;y \leq 7.043274856239975 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{1}{\frac{z - a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020203 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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