Average Error: 2.0 → 1.9
Time: 4.7s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[x + \sqrt[3]{1} \cdot \frac{y - x}{\frac{t}{z}}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
x + \sqrt[3]{1} \cdot \frac{y - x}{\frac{t}{z}}
double code(double x, double y, double z, double t) {
	return (x + ((y - x) * (z / t)));
}
↓
double code(double x, double y, double z, double t) {
	return (x + (cbrt(1.0) * ((y - x) / (t / z))));
}

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

Original2.0
Target2.2
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 2.0

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

  3. Applied add-cube-cbrt2.5

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

  4. Applied associate-*l*2.5

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

  6. Applied associate-*l*2.5

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

  8. Applied associate-*r/2.9

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

  10. Applied *-un-lft-identity2.9

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

  11. Applied cbrt-prod2.9

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

  12. Applied associate-*l*2.9

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

  13. Simplified1.9

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

  14. Final simplification1.9

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

Reproduce

herbie shell --seed 2020058 
(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)) -1013646692435.887) (+ 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))))