Average Error: 0.0 → 0.2
Time: 6.4s
Precision: binary64
\[\left(x \cdot y + z \cdot t\right) + a \cdot b\]
↓
\[\frac{x \cdot y + z \cdot t}{1 - \frac{a \cdot b}{x \cdot y + z \cdot t}} - a \cdot \frac{b}{\frac{x \cdot y + z \cdot t}{a \cdot b} - 1}\]
\left(x \cdot y + z \cdot t\right) + a \cdot b
↓
\frac{x \cdot y + z \cdot t}{1 - \frac{a \cdot b}{x \cdot y + z \cdot t}} - a \cdot \frac{b}{\frac{x \cdot y + z \cdot t}{a \cdot b} - 1}
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (((double) (x * y)) + ((double) (z * t)))) + ((double) (a * b))));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (((double) (((double) (x * y)) + ((double) (z * t)))) / ((double) (1.0 - ((double) (((double) (a * b)) / ((double) (((double) (x * y)) + ((double) (z * t)))))))))) - ((double) (a * ((double) (b / ((double) (((double) (((double) (((double) (x * y)) + ((double) (z * t)))) / ((double) (a * b)))) - 1.0))))))));
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(x \cdot y + z \cdot t\right) + a \cdot b\]
  2. Using strategy rm

  3. Applied add-cbrt-cube30.8

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

  4. Simplified30.8

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

  6. Applied flip-+37.7

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

  7. Simplified43.2

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

  8. Simplified36.3

    \[\leadsto \frac{{\left(x \cdot y + z \cdot t\right)}^{2} - a \cdot \left(a \cdot \left(b \cdot b\right)\right)}{\color{blue}{x \cdot y + \left(z \cdot t - a \cdot b\right)}}\]
  9. Using strategy rm

  10. Applied div-sub36.3

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

  11. Simplified20.2

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

  12. Simplified0.2

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

  13. Final simplification0.2

    \[\leadsto \frac{x \cdot y + z \cdot t}{1 - \frac{a \cdot b}{x \cdot y + z \cdot t}} - a \cdot \frac{b}{\frac{x \cdot y + z \cdot t}{a \cdot b} - 1}\]

Reproduce

herbie shell --seed 2020181 
(FPCore (x y z t a b)
  :name "Linear.V3:$cdot from linear-1.19.1.3, B"
  :precision binary64
  (+ (+ (* x y) (* z t)) (* a b)))