Details

Time bar (total: 2.6m)

sample404.0ms

Algorithm
intervals
Results
150.0ms57×body1280valid
126.0ms62×body640valid
61.0ms186×body80valid
32.0ms29×body320valid
8.0ms11×body160valid

simplify283.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
283.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.4b

localize35.0ms

Local error

Found 4 expressions with local error:

13.6b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
10.7b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.0b
(/ t (* (/ l t) (/ l t)))
0.2b
(* (/ k t) (/ k t))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
243×add-cbrt-cube add-exp-log
106×cbrt-undiv div-exp
86×prod-exp cbrt-unprod
79×times-frac
62×add-sqr-sqrt
50×*-un-lft-identity add-cube-cbrt
23×associate-*r*
18×associate-/l*
16×pow1
14×associate-*l*
13×swap-sqr associate-/r/
9×associate-*r/ div-inv
5×frac-times associate-*l/
4×pow-prod-down tan-quot insert-posit16 add-log-exp unswap-sqr
2×clear-num associate-/r* frac-2neg flip3-+ *-commutative flip-+
1×pow2 pow-plus pow-sqr pow-prod-up associate-/l/
Counts
4 → 246
Calls
4 calls:
Slowest
94.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
66.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
26.0ms
(* (/ k t) (/ k t))
13.0ms
(/ t (* (/ l t) (/ l t)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
870.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
255.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
61.0ms
(/ t (* (/ l t) (/ l t)))
28.0ms
(* (/ k t) (/ k t))

simplify48.5s

Counts
245 → 258
Calls
245 calls:
Slowest
1.9s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (* (/ l t) (/ l t))) (* (/ l t) (/ l t))))))
1.8s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t))))))
1.7s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (* (* (* (sin k) (tan k)) (* (sin k) (tan k))) (* (sin k) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (* (/ l t) (/ l t))) (* (/ l t) (/ l t))))))
1.7s
(/ (/ (* (* 2 2) 2) (* (* (+ (* (/ k t) (/ k t)) 2) (+ (* (/ k t) (/ k t)) 2)) (+ (* (/ k t) (/ k t)) 2))) (* (* (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))))
1.4s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (* (* (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))))

prune3.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.1b

localize67.0ms

Local error

Found 4 expressions with local error:

13.6b
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
3.1b
(/ (sin k) (/ l t))
3.1b
(/ (sin k) (/ l t))
0.2b
(* (/ k t) (/ k t))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
415×times-frac
216×add-sqr-sqrt
206×add-cbrt-cube add-exp-log
204×*-un-lft-identity add-cube-cbrt
120×cbrt-undiv div-exp
46×prod-exp cbrt-unprod
39×div-inv
33×associate-/r*
21×associate-/l*
19×associate-/r/
13×swap-sqr associate-*r* associate-*l*
11×pow1
8×flip3-+ flip-+
4×insert-posit16 add-log-exp unswap-sqr
3×clear-num frac-2neg
1×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up associate-/l/
Counts
4 → 406
Calls
4 calls:
Slowest
70.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
19.0ms
(* (/ k t) (/ k t))
9.0ms
(/ (sin k) (/ l t))
9.0ms
(/ (sin k) (/ l t))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
803.0ms
(/ (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
97.0ms
(/ (sin k) (/ l t))
91.0ms
(/ (sin k) (/ l t))
42.0ms
(* (/ k t) (/ k t))

simplify1.5m

Counts
568 → 418
Calls
568 calls:
Slowest
1.8s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ (* (* (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
1.7s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ (* (* (* (* t t) t) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
1.6s
(/ (* (* (/ 2 (+ (* (/ k t) (/ k t)) 2)) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ 2 (+ (* (/ k t) (/ k t)) 2))) (/ (* (* (* (* t (/ (sin k) (/ l t))) (* t (/ (sin k) (/ l t)))) (* t (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k))))
1.3s
(/ (/ (sqrt 2) (* (cbrt (+ (* (/ k t) (/ k t)) 2)) (cbrt (+ (* (/ k t) (/ k t)) 2)))) (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))))
905.0ms
(/ (/ (* (* 2 2) 2) (* (* (+ (* (/ k t) (/ k t)) 2) (+ (* (/ k t) (/ k t)) 2)) (+ (* (/ k t) (/ k t)) 2))) (* (* (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k))) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k))))

prune6.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.4b

localize67.0ms

Local error

Found 4 expressions with local error:

10.0b
(/ (/ 1 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
6.2b
(sqrt (+ (* (/ k t) (/ k t)) 2))
6.2b
(sqrt (+ (* (/ k t) (/ k t)) 2))
6.1b
(/ (/ 2 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))

rewrite406.0ms

Algorithm
rewrite-expression-head
Rules
14367×times-frac
5693×add-sqr-sqrt
5691×*-un-lft-identity add-cube-cbrt
1311×sqrt-prod
497×div-inv
367×associate-/r/
294×sqrt-div
181×add-exp-log
147×flip3-+ flip-+
143×associate-/r*
134×div-exp
81×add-cbrt-cube
53×cbrt-undiv
48×associate-/l*
25×1-exp
24×prod-exp
9×rec-exp
6×pow1 cbrt-unprod
4×insert-posit16 add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 3743
Calls
4 calls:
Slowest
68.0ms
(/ (/ 1 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
49.0ms
(/ (/ 2 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
29.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))
24.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))

series718.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
358.0ms
(/ (/ 2 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
232.0ms
(/ (/ 1 (sqrt (+ (* (/ k t) (/ k t)) 2))) (/ (* t (/ (sin k) (/ l t))) 1))
71.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))
57.0ms
(sqrt (+ (* (/ k t) (/ k t)) 2))