Average Error: 16.3 → 7.1
Time: 13.5s
Precision: binary64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;\left(x + y\right) - \frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 2.9860019198064306 \cdot 10^{+294}:\\ \;\;\;\;\left(x + \left(y + \frac{y \cdot t}{a - t}\right)\right) - \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z - t}{\frac{a - t}{y}}\\ \end{array}\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -\infty:\\
\;\;\;\;\left(x + y\right) - \frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\\

\mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 2.9860019198064306 \cdot 10^{+294}:\\
\;\;\;\;\left(x + \left(y + \frac{y \cdot t}{a - t}\right)\right) - \frac{y \cdot z}{a - t}\\

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

\end{array}
(FPCore (x y z t a) :precision binary64 (- (+ x y) (/ (* (- z t) y) (- a t))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (<= (- (+ x y) (/ (* y (- z t)) (- a t))) (- INFINITY))
   (-
    (+ x y)
    (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
   (if (<= (- (+ x y) (/ (* y (- z t)) (- a t))) 2.9860019198064306e+294)
     (- (+ x (+ y (/ (* y t) (- a t)))) (/ (* y z) (- a t)))
     (- (+ x y) (/ (- z t) (/ (- a t) y))))))
double code(double x, double y, double z, double t, double a) {
	return (x + y) - (((z - t) * y) / (a - t));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x + y) - ((y * (z - t)) / (a - t))) <= -((double) INFINITY)) {
		tmp = (x + y) - (((z - t) / (cbrt(a - t) * cbrt(a - t))) * (y / cbrt(a - t)));
	} else if (((x + y) - ((y * (z - t)) / (a - t))) <= 2.9860019198064306e+294) {
		tmp = (x + (y + ((y * t) / (a - t)))) - ((y * z) / (a - t));
	} else {
		tmp = (x + y) - ((z - t) / ((a - t) / y));
	}
	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

Original16.3
Target8.4
Herbie7.1
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} < -1.3664970889390727 \cdot 10^{-07}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0

    1. Initial program 64.0

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

    3. Applied add-cube-cbrt_binary64_1443564.0

      \[\leadsto \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}\]

    4. Applied times-frac_binary64_1440628.7

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}}\]

    if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 2.9860019198064306e294

    1. Initial program 7.0

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

    2. Taylor expanded around 0 2.8

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

    if 2.9860019198064306e294 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

    1. Initial program 54.3

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

    3. Applied associate-/l*_binary64_1434525.0

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

  4. Final simplification7.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;\left(x + y\right) - \frac{z - t}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{y}{\sqrt[3]{a - t}}\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 2.9860019198064306 \cdot 10^{+294}:\\ \;\;\;\;\left(x + \left(y + \frac{y \cdot t}{a - t}\right)\right) - \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z - t}{\frac{a - t}{y}}\\ \end{array}\]

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, B"
  :precision binary64

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-07) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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