Average Error: 0.1 → 0.1
Time: 24.1s
Precision: binary64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[\left(x \cdot y + \left(z \cdot \frac{t}{16} - \frac{a \cdot b}{4}\right)\right) + c\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
\left(x \cdot y + \left(z \cdot \frac{t}{16} - \frac{a \cdot b}{4}\right)\right) + c
(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))
↓
(FPCore (x y z t a b c)
 :precision binary64
 (+ (+ (* x y) (- (* z (/ t 16.0)) (/ (* a b) 4.0))) c))
double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}
↓
double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((x * y) + ((z * (t / 16.0)) - ((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 0.1

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

  3. Applied *-un-lft-identity_binary64_75800.1

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

  4. Applied times-frac_binary64_75860.1

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

  5. Simplified0.1

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

  7. Applied associate--l+_binary64_75170.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2021076 
(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))