Average Error: 1.5 → 0.5
Time: 5.6s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + \frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}} \cdot \frac{1}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}\]
x + y \cdot \frac{z - t}{z - a}
↓
x + \frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}} \cdot \frac{1}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}
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) {
	return (x + ((y / ((cbrt((z - a)) * cbrt((z - a))) / (cbrt((z - t)) * cbrt((z - t))))) * (1.0 / (cbrt((z - a)) / cbrt((z - 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
Target1.4
Herbie0.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.5

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

  3. Applied clear-num1.6

    \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{z - a}{z - t}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt2.1

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

  6. Applied add-cube-cbrt1.9

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

  7. Applied times-frac1.9

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

  8. Applied *-un-lft-identity1.9

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

  9. Applied times-frac1.8

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

  10. Applied associate-*r*0.5

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

  11. Simplified0.5

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

  12. Final simplification0.5

    \[\leadsto x + \frac{y}{\frac{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}}{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}} \cdot \frac{1}{\frac{\sqrt[3]{z - a}}{\sqrt[3]{z - t}}}\]

Reproduce

herbie shell --seed 2020075 
(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)))))