Average Error: 10.5 → 2.4
Time: 3.7s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{z - t}{\sqrt[3]{a - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{z - t}{\sqrt[3]{a - t}}
double code(double x, double y, double z, double t, double a) {
	return (x + ((y * (z - t)) / (a - t)));
}
↓
double code(double x, double y, double z, double t, double a) {
	return (x + ((y / (cbrt((a - t)) * cbrt((a - t)))) * ((z - t) / cbrt((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

Original10.5
Target1.3
Herbie2.4
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.5

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

  3. Applied add-cube-cbrt10.9

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

  4. Applied times-frac2.4

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

  5. Final simplification2.4

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

Reproduce

herbie shell --seed 2020079 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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