Details

Time bar (total: 2.8m)

sample411.0ms

Algorithm
intervals
Results
150.0ms58×body1280valid
148.0ms72×body640valid
63.0ms207×body80valid
22.0ms22×body320valid
8.0ms10×body160valid

simplify292.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
292.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.2b

localize75.0ms

Local error

Found 4 expressions with local error:

14.8b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
10.3b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.7b
(/ t (* (/ l t) (/ l t)))
0.2b
(* (/ l t) (/ l t))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
243×add-cbrt-cube add-exp-log
106×cbrt-undiv div-exp
86×prod-exp cbrt-unprod
77×times-frac
62×add-sqr-sqrt
50×*-un-lft-identity add-cube-cbrt
23×associate-*r*
16×pow1 associate-/l*
14×associate-*l*
13×swap-sqr
9×associate-*r/ associate-/r/ div-inv
5×frac-times associate-*l/
4×expm1-log1p-u pow-prod-down tan-quot insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×clear-num associate-/r* frac-2neg *-commutative
1×pow2 pow-plus pow-sqr pow-prod-up associate-/l/
Counts
4 → 250
Calls
4 calls:
Slowest
85.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
59.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
20.0ms
(/ t (* (/ l t) (/ l t)))
16.0ms
(* (/ l t) (/ l t))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
893.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
295.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
38.0ms
(/ t (* (/ l t) (/ l t)))
36.0ms
(* (/ l t) (/ l t))

simplify1.1m

Counts
239 → 262
Calls
239 calls:
Slowest
2.2s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ 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))))))
2.0s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (tan k)) (* (sin k) (tan k))) (* (sin k) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))
1.9s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))
1.8s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t))))))
1.8s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ 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))))))

prune3.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.8b

localize58.0ms

Local error

Found 4 expressions with local error:

14.8b
(/ (/ 2 (fma (/ 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
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
364×times-frac
196×add-cbrt-cube add-exp-log
180×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
117×cbrt-undiv div-exp
42×prod-exp cbrt-unprod
36×associate-/r*
34×div-inv
22×associate-/l*
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r/
1×associate-/l/
Counts
4 → 358
Calls
4 calls:
Slowest
49.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
20.0ms
(/ (sin k) (/ l t))
19.0ms
(/ (sin k) (/ l t))
6.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
842.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
92.0ms
(/ (sin k) (/ l t))
70.0ms
(/ (sin k) (/ l t))
61.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

simplify1.5m

Counts
488 → 370
Calls
488 calls:
Slowest
2.4s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (* (* (cos k) (cos k)) (cos k))))
2.0s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ 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))))
1.9s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ 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))))
1.8s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ 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))))
1.7s
(/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ 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))))

prune5.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.5b

localize68.0ms

Local error

Found 4 expressions with local error:

11.4b
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) t)
8.7b
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
8.7b
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
8.2b
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cos k)))

rewrite271.0ms

Algorithm
rewrite-expression-head
Rules
9123×times-frac
3719×add-sqr-sqrt
3713×*-un-lft-identity add-cube-cbrt
1859×sqrt-prod
366×div-inv
139×associate-/r*
52×associate-/r/
32×associate-/l*
20×add-cbrt-cube add-exp-log
11×cbrt-undiv div-exp
6×pow1
4×expm1-log1p-u rem-sqrt-square sqrt-div insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 2490
Calls
4 calls:
Slowest
40.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
12.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) t)
4.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
4.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))

series829.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
417.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
160.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) t)
132.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
120.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))