Details

Time bar (total: 2.7m)

sample342.0ms

Algorithm
intervals
Results
102.0ms51×body640valid
101.0ms56×body1280valid
86.0ms204×body80valid
23.0ms25×body320valid
11.0ms18×body160valid

simplify604.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
604.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.6b

localize33.0ms

Local error

Found 4 expressions with local error:

15.4b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
10.2b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.0b
(/ t (* (/ l t) (/ l t)))
0.3b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
233×add-cbrt-cube add-exp-log
103×cbrt-undiv div-exp
82×prod-exp cbrt-unprod
46×times-frac
30×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
19×associate-/l*
10×associate-*r*
9×pow1 associate-/r/
8×associate-*r/
6×div-inv
5×associate-/r*
4×expm1-log1p-u frac-times associate-*l/ tan-quot insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down
1×associate-*l* *-commutative associate-/l/
Counts
4 → 210
Calls
4 calls:
Slowest
52.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
46.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
11.0ms
(/ t (* (/ l t) (/ l t)))
4.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
950.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
272.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
83.0ms
(/ 2 (fma (/ k t) (/ k t) 2))
62.0ms
(/ t (* (/ l t) (/ l t)))

simplify58.3s

Counts
189 → 222
Calls
189 calls:
Slowest
2.1s
(/ (* (* (/ 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 t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l 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))))))
1.9s
(/ (* (* (/ 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 t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l 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))))))

prune3.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.0b

localize50.0ms

Local error

Found 4 expressions with local error:

15.4b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
3.9b
(/ (sin k) (/ l t))
3.9b
(/ (sin k) (/ l t))
0.3b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite107.0ms

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
42.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
23.0ms
(/ (sin k) (/ l t))
18.0ms
(/ (sin k) (/ l t))
8.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
897.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
100.0ms
(/ (sin k) (/ l t))
93.0ms
(/ (sin k) (/ l t))
89.0ms
(/ 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))))
2.3s
(/ (* (* (/ 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))))
2.0s
(/ (/ (* (* 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))))

prune5.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.3b

localize124.0ms

Local error

Found 4 expressions with local error:

16.8b
(cbrt (fma (/ k t) (/ k t) 2))
16.8b
(cbrt (fma (/ k t) (/ k t) 2))
16.8b
(cbrt (fma (/ k t) (/ k t) 2))
6.5b
(* (/ (/ (cbrt 2) (cbrt (fma (/ k t) (/ k t) 2))) (/ t (/ (cbrt 2) (cbrt (fma (/ k t) (/ k t) 2))))) (/ l (* t (sin k))))

rewrite686.0ms

Algorithm
rewrite-expression-head
Rules
18722×times-frac
8873×cbrt-prod
7936×add-sqr-sqrt
7775×*-un-lft-identity add-cube-cbrt
5005×associate-*l*
287×div-inv
112×add-exp-log
82×add-cbrt-cube
59×cbrt-undiv div-exp
41×associate-/r/
31×unswap-sqr
28×prod-exp cbrt-unprod
7×associate-*r*
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 5142
Calls
4 calls:
Slowest
171.0ms
(* (/ (/ (cbrt 2) (cbrt (fma (/ k t) (/ k t) 2))) (/ t (/ (cbrt 2) (cbrt (fma (/ k t) (/ k t) 2))))) (/ l (* t (sin k))))
2.0ms
(cbrt (fma (/ k t) (/ k t) 2))
1.0ms
(cbrt (fma (/ k t) (/ k t) 2))
1.0ms
(cbrt (fma (/ k t) (/ k t) 2))

series1.9s

Counts
4 → 12
Calls
4 calls:
Slowest
847.0ms
(* (/ (/ (cbrt 2) (cbrt (fma (/ k t) (/ k t) 2))) (/ t (/ (cbrt 2) (cbrt (fma (/ k t) (/ k t) 2))))) (/ l (* t (sin k))))
718.0ms
(cbrt (fma (/ k t) (/ k t) 2))
190.0ms
(cbrt (fma (/ k t) (/ k t) 2))
181.0ms
(cbrt (fma (/ k t) (/ k t) 2))