Average Error: 1.2 → 0.7
Time: 4.6s
Precision: binary64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -3.2104700123273477 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{elif}\;y \leq 4.588785361859496 \cdot 10^{-172}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -3.2104700123273477 \cdot 10^{-99}:\\
\;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\

\mathbf{elif}\;y \leq 4.588785361859496 \cdot 10^{-172}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\

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

\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 -3.2104700123273477e-99)
   (+ x (/ y (/ (- z a) (- z t))))
   (if (<= y 4.588785361859496e-172)
     (+ x (/ (* y (- z t)) (- z a)))
     (+ x (* y (/ (- z t) (- z a)))))))
double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (z - a)));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.2104700123273477e-99) {
		tmp = x + (y / ((z - a) / (z - t)));
	} else if (y <= 4.588785361859496e-172) {
		tmp = x + ((y * (z - t)) / (z - a));
	} else {
		tmp = x + (y * ((z - t) / (z - a)));
	}
	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

Original1.2
Target1.1
Herbie0.7
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -3.21047001232734775e-99

    1. Initial program 0.6

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

    3. Applied associate-*r/_binary64_1586016.7

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

    5. Applied associate-/l*_binary64_158630.6

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

    if -3.21047001232734775e-99 < y < 4.58878536185949592e-172

    1. Initial program 2.3

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

    3. Applied associate-*r/_binary64_158600.6

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

    if 4.58878536185949592e-172 < y

    1. Initial program 0.9

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2104700123273477 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{elif}\;y \leq 4.588785361859496 \cdot 10^{-172}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020292 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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