Details

Time bar (total: 10.0m)

sample737.0ms

Algorithm
intervals
Results
293.0ms79×body2560valid
167.0ms29×body5120valid
134.0ms113×body1280valid
67.0ms81×body640valid
19.0ms32×body320valid
11.0ms61×body80valid
6.0ms17×body160valid

simplify3.1s

Counts
1 → 1
Iterations
IterNodes
done5000
43734
3704
2144
144
019

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 2.0 (pow (/ k t) 2.0))
6.9b
(/ (* l l) (* (sin k) (tan k)))
16.1b
(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
29.4b
(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

rewrite725.0ms

Algorithm
rewrite-expression-head
Rules
9211×times-frac
3212×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
2953×unpow-prod-down
656×div-inv
491×sqr-pow
467×add-exp-log
459×associate-/r/
401×tan-quot associate-*r/
331×div-exp
92×add-cbrt-cube
76×prod-exp
71×associate-/r*
66×associate-/l*
64×pow-exp
50×cbrt-undiv
47×pow-to-exp
16×cbrt-unprod
4×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
1×associate-/l/
Counts
4 → 2993
Calls
4 calls:
28.0ms
(/ 2.0 (pow (/ k t) 2.0))
24.0ms
(/ (* l l) (* (sin k) (tan k)))
35.0ms
(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
143.0ms
(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

series1.9s

Counts
4 → 12
Calls
4 calls:
260.0ms
(/ 2.0 (pow (/ k t) 2.0))
181.0ms
(/ (* l l) (* (sin k) (tan k)))
499.0ms
(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
926.0ms
(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

simplify6.6s

Counts
3005 → 3005
Iterations
IterNodes
done5069
05069

prune37.0s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 11.7b

localize75.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2)))
7.3b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) (/ l (sin k)))
13.6b
(/ (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (/ (pow (cbrt t) 3.0) (/ l (tan k))))
19.6b
(/ (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (/ l (sin k))))

rewrite6.3s

Algorithm
rewrite-expression-head
Rules
93306×times-frac
35497×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27410×unpow-prod-down
11121×sqrt-prod
4494×cbrt-prod
4212×sqr-pow
3355×div-inv
1287×associate-/r/
1070×tan-quot
351×add-exp-log
282×div-exp
245×associate-/r*
223×associate-/l*
68×pow-exp
53×add-cbrt-cube
39×pow-to-exp
34×cbrt-undiv
12×prod-exp
4×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
2×associate-/l/
Counts
4 → 23585
Calls
4 calls:
14.0ms
(/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2)))
12.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) (/ l (sin k)))
612.0ms
(/ (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (/ (pow (cbrt t) 3.0) (/ l (tan k))))
281.0ms
(/ (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (/ l (sin k))))

series2.1s

Counts
4 → 12
Calls
4 calls:
264.0ms
(/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2)))
359.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) (/ l (sin k)))
705.0ms
(/ (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (/ (pow (cbrt t) 3.0) (/ l (tan k))))
817.0ms
(/ (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (/ (pow (* (cbrt t) (cbrt t)) 3.0) (/ l (sin k))))

simplify44.5s

Counts
23597 → 23597
Iterations
IterNodes
done29661
029661

prune4.2m

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 5.8b

localize130.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2)))
3.5b
(/ (/ (sqrt (sqrt 2.0)) (pow (/ (cbrt k) (cbrt t)) (/ 2.0 2))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k)))))
6.6b
(/ (/ (sqrt (sqrt 2.0)) (pow (/ (* (cbrt k) (cbrt k)) (* (cbrt t) (cbrt t))) (/ 2.0 2))) (/ (pow (cbrt t) 3.0) (* (cbrt (/ l (sin k))) (cbrt (/ l (sin k))))))
13.6b
(/ (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (/ (pow (cbrt t) 3.0) (/ l (tan k))))

rewrite17.0s

Algorithm
rewrite-expression-head
Rules
352616×times-frac
138128×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
129914×cbrt-prod
120049×unpow-prod-down
74694×sqrt-prod
10539×sqr-pow
8547×div-inv
1839×associate-/r/
1070×tan-quot
745×cbrt-div
597×associate-/l*
477×add-exp-log
356×div-exp
344×associate-/r*
90×pow-exp
86×frac-times associate-*l/ associate-*r/
54×add-cbrt-cube
52×prod-exp
50×pow-to-exp
37×cbrt-undiv
4×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
3×associate-/l/
2×cbrt-unprod
Counts
4 → 84044
Calls
4 calls:
13.0ms
(/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2)))
1.3s
(/ (/ (sqrt (sqrt 2.0)) (pow (/ (cbrt k) (cbrt t)) (/ 2.0 2))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k)))))
71.0ms
(/ (/ (sqrt (sqrt 2.0)) (pow (/ (* (cbrt k) (cbrt k)) (* (cbrt t) (cbrt t))) (/ 2.0 2))) (/ (pow (cbrt t) 3.0) (* (cbrt (/ l (sin k))) (cbrt (/ l (sin k))))))
331.0ms
(/ (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (/ (pow (cbrt t) 3.0) (/ l (tan k))))

series1.8s

Counts
4 → 12
Calls
4 calls:
183.0ms
(/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2)))
582.0ms
(/ (/ (sqrt (sqrt 2.0)) (pow (/ (cbrt k) (cbrt t)) (/ 2.0 2))) (/ (pow (cbrt t) 3.0) (cbrt (/ l (sin k)))))
561.0ms
(/ (/ (sqrt (sqrt 2.0)) (pow (/ (* (cbrt k) (cbrt k)) (* (cbrt t) (cbrt t))) (/ 2.0 2))) (/ (pow (cbrt t) 3.0) (* (cbrt (/ l (sin k))) (cbrt (/ l (sin k))))))
473.0ms
(/ (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (/ (pow (cbrt t) 3.0) (/ l (tan k))))

simplify2.0m

Counts
84056 → 84056
Iterations
IterNodes
done84749
084749

prune1.8m