Average Error: 2.2 → 1.9
Time: 9.1s
Precision: binary64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[x + \left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(\frac{\sqrt[3]{y - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\right)\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
x + \left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \left(\frac{\sqrt[3]{y - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\right)
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (y - x)) * (z / t)))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (((double) cbrt(((double) (y - x)))) * ((double) cbrt(((double) (y - x)))))) * ((double) ((((double) cbrt(((double) (y - x)))) / ((double) (((double) cbrt(t)) * ((double) cbrt(t))))) * (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

Original2.2
Target2.4
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program 2.2

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

  3. Applied add-cube-cbrt2.7

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

  4. Applied associate-*l*2.7

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

  6. Applied add-cube-cbrt2.8

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

  7. Applied *-un-lft-identity2.8

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

  8. Applied times-frac2.8

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

  9. Applied associate-*r*1.9

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

  10. Simplified1.9

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

  11. Final simplification1.9

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

Reproduce

herbie shell --seed 2020182 
(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))))