Average Error: 2.1 → 1.1
Time: 5.2s
Precision: binary64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[x + \left(\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(\sqrt[3]{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}} \cdot \left(\sqrt[3]{\sqrt[3]{y - x}} \cdot \frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)\right)\right) \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
x + \left(\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(\sqrt[3]{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}} \cdot \left(\sqrt[3]{\sqrt[3]{y - x}} \cdot \frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)\right)\right) \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{t}}
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (y - x)) * ((double) (z / t))))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (((double) (((double) cbrt(((double) (y - x)))) * ((double) cbrt(((double) (y - x)))))) * ((double) (((double) cbrt(((double) (((double) cbrt(((double) (y - x)))) * ((double) cbrt(((double) (y - x)))))))) * ((double) (((double) cbrt(((double) cbrt(((double) (y - x)))))) * ((double) (((double) (((double) cbrt(z)) * ((double) cbrt(z)))) / ((double) (((double) cbrt(t)) * ((double) cbrt(t)))))))))))) * ((double) (((double) cbrt(z)) / ((double) cbrt(t))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.1
Target2.3
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 2.1

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

  3. Applied add-cube-cbrt2.7

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

  4. Applied add-cube-cbrt2.8

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

  5. Applied times-frac2.8

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

  6. Applied associate-*r*1.0

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

  8. Applied add-cube-cbrt1.1

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

  9. Applied associate-*l*1.1

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

  11. Applied add-cube-cbrt1.1

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

  12. Applied cbrt-prod1.1

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

  13. Applied associate-*l*1.1

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

  14. Final simplification1.1

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

Reproduce

herbie shell --seed 2020177 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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