Average Error: 11.1 → 0.9
Time: 5.2s
Precision: binary64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -4063456.844976355 \lor \neg \left(t \leq -1.1735271166356401 \cdot 10^{-291}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;t \leq -4063456.844976355 \lor \neg \left(t \leq -1.1735271166356401 \cdot 10^{-291}\right):\\
\;\;\;\;x + t \cdot \frac{y - z}{a - z}\\

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

\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 (<= t -4063456.844976355) (not (<= t -1.1735271166356401e-291)))
   (+ x (* t (/ (- y z) (- a z))))
   (+ x (/ (* t (- y z)) (- a z)))))
double code(double x, double y, double z, double t, double a) {
	return x + (((y - z) * t) / (a - z));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4063456.844976355) || !(t <= -1.1735271166356401e-291)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = x + ((t * (y - z)) / (a - z));
	}
	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

Original11.1
Target0.6
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -4063456.84497635486 or -1.17352711663564e-291 < t

    1. Initial program 14.9

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

    2. Taylor expanded around 0 14.9

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

    3. Simplified1.1

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

    if -4063456.84497635486 < t < -1.17352711663564e-291

    1. Initial program 0.2

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4063456.844976355 \lor \neg \left(t \leq -1.1735271166356401 \cdot 10^{-291}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2021043 
(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))))