Details

Time bar (total: 19.4s)

sample80.0ms

Algorithm
intervals
Results
55.0ms650×body80valid

simplify6.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01931
15331
216031
345131
4122331
5246931
6461831
done500131

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* a a) (* b b))
0.1b
(* (* a a) (+ 1.0 a))
0.2b
(* (* b b) (- 1.0 (* 3.0 a)))
0.4b
(pow (+ (* a a) (* b b)) 2.0)

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×associate-*r/
3×distribute-rgt-in unpow-prod-down pow-unpow distribute-lft-in
2×sub-neg flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out sqr-pow
Counts
4 → 77
Calls
4 calls:
8.0ms
(+ (* a a) (* b b))
46.0ms
(* (* a a) (+ 1.0 a))
49.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
21.0ms
(pow (+ (* a a) (* b b)) 2.0)

series393.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ (* a a) (* b b))
103.0ms
(* (* a a) (+ 1.0 a))
102.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
148.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify1.6s

Counts
89 → 89
Iterations

Useful iterations: 2 (564.0ms)

IterNodesCost
01551076
1426997
21606887
done5001887

prune448.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
9.3b
(cbrt (+ (* a a) (* b b)))
9.3b
(cbrt (+ (* a a) (* b b)))
9.3b
(cbrt (+ (* a a) (* b b)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
44.0ms
(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
5.0ms
(cbrt (+ (* a a) (* b b)))
13.0ms
(cbrt (+ (* a a) (* b b)))
5.0ms
(cbrt (+ (* a a) (* b b)))

series497.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
125.0ms
(cbrt (+ (* a a) (* b b)))
132.0ms
(cbrt (+ (* a a) (* b b)))
112.0ms
(cbrt (+ (* a a) (* b b)))

simplify3.0s

Counts
99 → 99
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01021926
12211757
25551543
312051394
432241384
done50011329

prune712.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize90.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (+ (* a a) (* b b)))
8.6b
(sqrt (+ (* a a) (* b b)))
9.3b
(cbrt (+ (* a a) (* b b)))
9.3b
(cbrt (+ (* a a) (* b b)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log cbrt-div flip3-+ sqrt-div add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
17.0ms
(sqrt (+ (* a a) (* b b)))
17.0ms
(sqrt (+ (* a a) (* b b)))
11.0ms
(cbrt (+ (* a a) (* b b)))
11.0ms
(cbrt (+ (* a a) (* b b)))

series889.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(sqrt (+ (* a a) (* b b)))
56.0ms
(sqrt (+ (* a a) (* b b)))
156.0ms
(cbrt (+ (* a a) (* b b)))
607.0ms
(cbrt (+ (* a a) (* b b)))

simplify1.8s

Counts
68 → 68
Iterations

Useful iterations: 3 (257.0ms)

IterNodesCost
065890
1144824
2313716
3670710
41768710
done5001710

prune723.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (+ (* a a) (* b b)))
8.6b
(sqrt (+ (* a a) (* b b)))
9.3b
(cbrt (+ (* a a) (* b b)))
9.3b
(cbrt (+ (* a a) (* b b)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log cbrt-div flip3-+ sqrt-div add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
8.0ms
(sqrt (+ (* a a) (* b b)))
9.0ms
(sqrt (+ (* a a) (* b b)))
6.0ms
(cbrt (+ (* a a) (* b b)))
6.0ms
(cbrt (+ (* a a) (* b b)))

series413.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(sqrt (+ (* a a) (* b b)))
53.0ms
(sqrt (+ (* a a) (* b b)))
161.0ms
(cbrt (+ (* a a) (* b b)))
150.0ms
(cbrt (+ (* a a) (* b b)))

simplify1.8s

Counts
68 → 68
Iterations

Useful iterations: 3 (263.0ms)

IterNodesCost
065890
1144824
2313716
3670710
41768710
done5001710

prune448.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes12.0ms