Average Error: 0.2 → 0.4
Time: 5.5s
Precision: 64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\left(\left(x \cdot y + \frac{z \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}{\frac{16}{\sqrt[3]{t}}}\right) - \frac{a \cdot b}{4}\right) + c\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\left(\left(x \cdot y + \frac{z \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}{\frac{16}{\sqrt[3]{t}}}\right) - \frac{a \cdot b}{4}\right) + c
double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((double) (((double) (((double) (((double) (x * y)) + ((double) (((double) (z * t)) / 16.0)))) - ((double) (((double) (a * b)) / 4.0)))) + c));
}
↓
double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((double) (((double) (((double) (((double) (x * y)) + ((double) (((double) (z * ((double) (((double) cbrt(t)) * ((double) cbrt(t)))))) / ((double) (16.0 / ((double) cbrt(t)))))))) - ((double) (((double) (a * b)) / 4.0)))) + c));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

    \[\leadsto \left(\left(x \cdot y + \frac{z \cdot \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}}{16}\right) - \frac{a \cdot b}{4}\right) + c\]

  4. Applied associate-*r*0.5

    \[\leadsto \left(\left(x \cdot y + \frac{\color{blue}{\left(z \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t}}}{16}\right) - \frac{a \cdot b}{4}\right) + c\]

  5. Applied associate-/l*0.4

    \[\leadsto \left(\left(x \cdot y + \color{blue}{\frac{z \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}{\frac{16}{\sqrt[3]{t}}}}\right) - \frac{a \cdot b}{4}\right) + c\]

  6. Final simplification0.4

    \[\leadsto \left(\left(x \cdot y + \frac{z \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}{\frac{16}{\sqrt[3]{t}}}\right) - \frac{a \cdot b}{4}\right) + c\]

Reproduce

herbie shell --seed 2020113 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16)) (/ (* a b) 4)) c))