Average Error: 17.0 → 7.7
Time: 4.7s
Precision: binary64
\[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\]
↓
\[x + \left(y + \left(y \cdot \left(\sqrt[3]{z - t} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{t - a} \cdot \sqrt[3]{t - a}}\right)\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{t - a}}\right)\]
\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}
↓
x + \left(y + \left(y \cdot \left(\sqrt[3]{z - t} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{t - a} \cdot \sqrt[3]{t - a}}\right)\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{t - a}}\right)
double code(double x, double y, double z, double t, double a) {
	return ((double) (((double) (x + y)) - (((double) (((double) (z - t)) * y)) / ((double) (a - t)))));
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (y + ((double) (((double) (y * ((double) (((double) cbrt(((double) (z - t)))) * (((double) cbrt(((double) (z - t)))) / ((double) (((double) cbrt(((double) (t - a)))) * ((double) cbrt(((double) (t - a))))))))))) * (((double) cbrt(((double) (z - t)))) / ((double) cbrt(((double) (t - a)))))))))));
}

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

Original17.0
Target8.4
Herbie7.7
\[\begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} < -1.3664970889390727 \cdot 10^{-07}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ \end{array}\]

Derivation

  1. Initial program 17.0

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

  2. Simplified7.5

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

  4. Applied add-cube-cbrt11.1

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

  5. Applied add-cube-cbrt7.7

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

  6. Applied times-frac7.7

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

  7. Applied associate-*r*6.7

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

  8. Simplified7.7

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

  9. Final simplification7.7

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

Reproduce

herbie shell --seed 2020196 
(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))))