Average Error: 1.5 → 1.8
Time: 5.1s
Precision: binary64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[x + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\left(z - t\right) \cdot \frac{\sqrt[3]{y}}{a - t}\right)\]
x + y \cdot \frac{z - t}{a - t}
↓
x + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\left(z - t\right) \cdot \frac{\sqrt[3]{y}}{a - t}\right)
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (y * (((double) (z - t)) / ((double) (a - t)))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (((double) cbrt(y)) * ((double) cbrt(y)))) * ((double) (((double) (z - t)) * (((double) cbrt(y)) / ((double) (a - t)))))))));
}

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

Original1.5
Target0.5
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.5

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

  3. Applied add-cube-cbrt2.0

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

  4. Applied associate-*l*2.0

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

  5. Simplified2.0

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

  7. Applied div-inv2.0

    \[\leadsto x + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(\color{blue}{\left(\left(z - t\right) \cdot \frac{1}{a - t}\right)} \cdot \sqrt[3]{y}\right)\]

  8. Applied associate-*l*1.8

    \[\leadsto x + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \color{blue}{\left(\left(z - t\right) \cdot \left(\frac{1}{a - t} \cdot \sqrt[3]{y}\right)\right)}\]

  9. Simplified1.8

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

  10. Final simplification1.8

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

Reproduce

herbie shell --seed 2020196 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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