Details

Time bar (total: 12.8s)

sample249.0ms

Algorithm
intervals
Results
112.0ms46×body1280valid
23.0ms141×body80valid
20.0ms28×body640valid
13.0ms26×body320valid
5.0ms15×body160valid

simplify36.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0715
11315
22115
32615
43415
53615
done3615

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.1b
(- 1.0 (* (tan x) (tan x)))
0.2b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan x))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×pow1
12×times-frac
10×add-exp-log add-cbrt-cube
8×tan-quot
6×swap-sqr associate-*r* associate-*l* add-log-exp
5×difference-of-squares
4×associate-/l*
3×associate-/r*
2×pow2 frac-times flip3-- pow-plus associate-*r/ pow-prod-down associate-*l/ prod-exp associate-/r/ pow-sqr *-commutative pow-prod-up flip-- cbrt-unprod associate-/l/ unswap-sqr
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-sub div-exp clear-num flip-+ div-inv
Counts
4 → 105
Calls
4 calls:
20.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
12.0ms
(- 1.0 (* (tan x) (tan x)))
35.0ms
(* (tan x) (tan x))
21.0ms
(* (tan x) (tan x))

series311.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
65.0ms
(- 1.0 (* (tan x) (tan x)))
45.0ms
(* (tan x) (tan x))
65.0ms
(* (tan x) (tan x))

simplify2.1s

Counts
117 → 117
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01381632
13151486
28611368
326781346
done50011342

prune453.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (sqrt 1.0) (tan x))
0.2b
(- (sqrt 1.0) (tan x))
0.2b
(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.2b
(* (tan x) (tan x))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
18×*-un-lft-identity
13×pow1
10×add-cube-cbrt
9×associate-*r*
8×add-exp-log add-cbrt-cube add-log-exp
7×associate-*l*
5×frac-times
4×tan-quot flip3-- flip3-+ flip-- flip-+ difference-of-squares
3×sub-neg associate-*r/ swap-sqr associate-*l/
2×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp sqrt-prod *-commutative cbrt-unprod distribute-lft-out distribute-lft-out-- unswap-sqr
1×+-commutative pow2 pow-plus diff-log sum-log pow-sqr pow-prod-up
Counts
4 → 89
Calls
4 calls:
17.0ms
(+ (sqrt 1.0) (tan x))
18.0ms
(- (sqrt 1.0) (tan x))
76.0ms
(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
17.0ms
(* (tan x) (tan x))

series354.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(+ (sqrt 1.0) (tan x))
59.0ms
(- (sqrt 1.0) (tan x))
178.0ms
(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
66.0ms
(* (tan x) (tan x))

simplify1.5s

Counts
101 → 101
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01351238
13221033
21203955
done5000949

prune431.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(- 1.0 (* (tan x) (tan x)))
0.2b
(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
0.2b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan x))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
80×add-sqr-sqrt
63×add-cube-cbrt *-un-lft-identity
19×pow1 add-exp-log
18×associate-/r*
13×add-cbrt-cube difference-of-squares
9×associate-/r/
8×tan-quot
7×div-exp
6×swap-sqr associate-*r* associate-*l* add-log-exp
5×flip3-- flip-- div-inv
3×cbrt-undiv associate-/l*
2×pow2 frac-times rec-exp pow-plus 1-exp associate-*r/ pow-prod-down associate-*l/ prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
1×sub-neg pow-flip frac-2neg diff-log clear-num inv-pow
Counts
4 → 165
Calls
4 calls:
11.0ms
(- 1.0 (* (tan x) (tan x)))
41.0ms
(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
35.0ms
(* (tan x) (tan x))
15.0ms
(* (tan x) (tan x))

series362.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- 1.0 (* (tan x) (tan x)))
166.0ms
(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
69.0ms
(* (tan x) (tan x))
64.0ms
(* (tan x) (tan x))

simplify2.8s

Counts
177 → 177
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02493696
15323293
212433001
335292878
done50002874

prune363.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan x))
0.4b
(pow (tan x) 4)
0.6b
(pow (tan x) 6)

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
10×add-exp-log
8×tan-quot add-cbrt-cube
6×unpow-prod-down pow-unpow swap-sqr associate-*r* associate-*l*
4×add-log-exp
2×pow2 frac-times pow-to-exp pow-pow pow-plus associate-*r/ pow-prod-down associate-*l/ pow-exp prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr sqr-pow
Counts
4 → 90
Calls
4 calls:
32.0ms
(* (tan x) (tan x))
33.0ms
(* (tan x) (tan x))
8.0ms
(pow (tan x) 4)
6.0ms
(pow (tan x) 6)

series331.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (tan x) (tan x))
66.0ms
(* (tan x) (tan x))
102.0ms
(pow (tan x) 4)
100.0ms
(pow (tan x) 6)

simplify2.5s

Counts
102 → 102
Iterations

Useful iterations: 3 (729.0ms)

IterNodesCost
0113804
1236645
2536571
32188539
done5000539

prune462.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes5.0ms