Average Error: 10.6 → 0.7
Time: 4.7s
Precision: binary64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -8.02507296804989 \cdot 10^{+199} \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 6.154305159463207 \cdot 10^{+278}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -8.02507296804989 \cdot 10^{+199} \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 6.154305159463207 \cdot 10^{+278}\right):\\
\;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\

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

\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y z) t) (- a z))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (/ (* (- y z) t) (- a z)) -8.02507296804989e+199)
         (not (<= (/ (* (- y z) t) (- a z)) 6.154305159463207e+278)))
   (+ x (* (- y z) (/ t (- a z))))
   (+ (/ (* (- y z) t) (- a z)) x)))
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + (((double) (((double) (y - z)) * t)) / ((double) (a - z)))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((((((double) (((double) (y - z)) * t)) / ((double) (a - z))) <= -8.02507296804989e+199) || !((((double) (((double) (y - z)) * t)) / ((double) (a - z))) <= 6.154305159463207e+278))) {
		tmp = ((double) (x + ((double) (((double) (y - z)) * (t / ((double) (a - z)))))));
	} else {
		tmp = ((double) ((((double) (((double) (y - z)) * t)) / ((double) (a - z))) + x));
	}
	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

Original10.6
Target0.5
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* (- y z) t) (- a z)) < -8.02507296804988997e199 or 6.1543051594632072e278 < (/ (* (- y z) t) (- a z))

    1. Initial program Error: 53.2 bits

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

    2. SimplifiedError: 2.5 bits

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

    if -8.02507296804988997e199 < (/ (* (- y z) t) (- a z)) < 6.1543051594632072e278

    1. Initial program Error: 0.2 bits

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

  4. Final simplificationError: 0.7 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -8.02507296804989 \cdot 10^{+199} \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 6.154305159463207 \cdot 10^{+278}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \end{array}\]

Reproduce

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

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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