Average Error: 0.1 → 0.2
Time: 5.2s
Precision: binary64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a}{{4}^{\frac{2}{3}}} \cdot \frac{b}{\sqrt[3]{4}}\right) + c\]
\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 t}{16}\right) - \frac{a}{{4}^{\frac{2}{3}}} \cdot \frac{b}{\sqrt[3]{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 * t)) / 16.0)))) - ((double) (((double) (a / ((double) pow(4.0, 0.6666666666666666)))) * ((double) (b / ((double) cbrt(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 0.1

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

  3. Applied add-cube-cbrt0.4

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

  4. Applied times-frac0.4

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

  6. Applied pow1/30.2

    \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a}{\sqrt[3]{4} \cdot \color{blue}{{4}^{\frac{1}{3}}}} \cdot \frac{b}{\sqrt[3]{4}}\right) + c\]

  7. Applied pow1/30.2

    \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a}{\color{blue}{{4}^{\frac{1}{3}}} \cdot {4}^{\frac{1}{3}}} \cdot \frac{b}{\sqrt[3]{4}}\right) + c\]

  8. Applied pow-prod-up0.2

    \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a}{\color{blue}{{4}^{\left(\frac{1}{3} + \frac{1}{3}\right)}}} \cdot \frac{b}{\sqrt[3]{4}}\right) + c\]

  9. Simplified0.2

    \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a}{{4}^{\color{blue}{\frac{2}{3}}}} \cdot \frac{b}{\sqrt[3]{4}}\right) + c\]

  10. Final simplification0.2

    \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a}{{4}^{\frac{2}{3}}} \cdot \frac{b}{\sqrt[3]{4}}\right) + c\]

Reproduce

herbie shell --seed 2020152 
(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) 16.0)) (/ (* a b) 4.0)) c))