Details

Time bar (total: 7.4s)

sample112.0ms

Algorithm
intervals
Results
81.0ms678×body80valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
019696
155686
2177661
3551661
41809661
done5000661

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
0.1b
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.3b
(pow (fma a a (* b b)) 2.0)
1.2b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt pow1 add-exp-log
9×*-un-lft-identity add-cbrt-cube add-cube-cbrt
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow unpow-prod-down associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/ fma-udef
1×pow-to-exp pow-pow flip3-- associate-*l* pow-exp *-commutative flip-- unswap-sqr sqr-pow
Counts
4 → 72
Calls
4 calls:
0.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
0.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
2.0ms
(pow (fma a a (* b b)) 2.0)
30.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series420.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0))
92.0ms
(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
159.0ms
(pow (fma a a (* b b)) 2.0)
58.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.8s

Counts
84 → 84
Iterations

Useful iterations: done (1.8s)

IterNodesCost
015833861
140629194
2128928352
done500028252

prune594.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize440.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (* b b) (- 1.0 (* 3.0 a)))
1.2b
(* (* b b) (- 1.0 (* 3.0 a)))
10.4b
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
10.4b
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt pow1
14×add-cbrt-cube add-exp-log
12×*-un-lft-identity prod-diff add-cube-cbrt
10×distribute-rgt-in distribute-lft-in
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×expm1-log1p-u sub-neg associate-*r/ log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 96
Calls
4 calls:
33.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
32.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
1.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

series730.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
70.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
301.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))
278.0ms
(sqrt (fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (pow (fma a a (* b b)) 2.0)))

simplify102.0ms

Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
013144722