Details

Time bar (total: 5.5s)

sample28.0ms

Algorithm
intervals
Results
8.0ms256×body80valid
8.0ms272×body80nan

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
056
176
2116
done116

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b
(sqrt (- 1.0 (* x x)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt sqrt-prod
2×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
1×add-exp-log rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- add-log-exp difference-of-squares
Counts
1 → 16
Calls
1 calls:
3.0ms
(sqrt (- 1.0 (* x x)))

series62.0ms

Counts
1 → 3
Calls
1 calls:
62.0ms
(sqrt (- 1.0 (* x x)))

simplify1.0s

Counts
19 → 19
Iterations

Useful iterations: 3 (261.0ms)

IterNodesCost
067246
1155220
2454206
31812202
done5000202

prune50.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 1 expressions with local error:

0.0b
(/ (sqrt (- (pow 1.0 3) (pow x 6))) (sqrt (+ (pow x 4) (* (+ 1.0 (* x x)) 1.0))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
174×add-sqr-sqrt
172×sqrt-prod
114×times-frac
84×difference-of-squares
69×*-un-lft-identity
55×add-cube-cbrt
49×unpow-prod-down sqr-pow
21×cube-prod
19×associate-/l*
7×distribute-lft-out--
6×associate-/r*
4×sqrt-div
3×add-exp-log add-cbrt-cube
2×associate-/r/ associate-/l/
1×pow1 cbrt-undiv sqrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num flip-- flip-+ div-inv add-log-exp
Counts
1 → 156
Calls
1 calls:
40.0ms
(/ (sqrt (- (pow 1.0 3) (pow x 6))) (sqrt (+ (pow x 4) (* (+ 1.0 (* x x)) 1.0))))

series142.0ms

Counts
1 → 3
Calls
1 calls:
142.0ms
(/ (sqrt (- (pow 1.0 3) (pow x 6))) (sqrt (+ (pow x 4) (* (+ 1.0 (* x x)) 1.0))))

simplify1.6s

Counts
159 → 159
Iterations

Useful iterations: 3 (877.0ms)

IterNodesCost
02776618
14705973
210505903
335445849
done50015849

prune346.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* (+ 1.0 (* x x)) 1.0)))
0.0b
(sqrt (/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* (+ 1.0 (* x x)) 1.0))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
165×add-sqr-sqrt
97×times-frac
84×difference-of-squares
57×*-un-lft-identity
54×sqrt-prod
49×unpow-prod-down sqr-pow
43×add-cube-cbrt
21×cube-prod
16×associate-/l*
7×distribute-lft-out--
4×add-exp-log associate-/r/ add-cbrt-cube
3×pow1 associate-/r*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/ add-log-exp
1×cbrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num flip--
Counts
2 → 150
Calls
2 calls:
41.0ms
(/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* (+ 1.0 (* x x)) 1.0)))
33.0ms
(sqrt (/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* (+ 1.0 (* x x)) 1.0))))

series329.0ms

Counts
2 → 6
Calls
2 calls:
196.0ms
(/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* (+ 1.0 (* x x)) 1.0)))
133.0ms
(sqrt (/ (- (pow 1.0 3) (pow x 6)) (+ (pow x 4) (* (+ 1.0 (* x x)) 1.0))))

simplify716.0ms

Counts
156 → 156
Iterations

Useful iterations: 2 (345.0ms)

IterNodesCost
02855792
15755467
214955330
done50015330

prune513.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01520
11820
done1820

end0.0ms

sample429.0ms

Algorithm
intervals
Results
135.0ms8000×body80valid
127.0ms8067×body80nan