Details

Time bar (total: 2.7m)

sample392.0ms

Algorithm
intervals
Results
171.0ms75×body1280valid
115.0ms55×body640valid
53.0ms175×body80valid
19.0ms20×body320valid
10.0ms16×body160valid

simplify321.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
321.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.2b

localize64.0ms

Local error

Found 4 expressions with local error:

14.5b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
9.7b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.6b
(/ t (* (/ l t) (/ l t)))
0.3b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite137.0ms

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
59.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
59.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
10.0ms
(/ t (* (/ l t) (/ l t)))
4.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
952.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
234.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
61.0ms
(/ 2 (fma (/ k t) (/ k t) 2))
42.0ms
(/ t (* (/ l t) (/ l t)))

simplify59.4s

Counts
189 → 222
Calls
189 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 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))))))
1.9s
(/ (/ (* (* 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))))))
1.7s
(/ (* (* (/ 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))))))

prune3.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.9b

localize35.0ms

Local error

Found 4 expressions with local error:

14.5b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
1.9b
(/ (sin k) (/ l t))
1.9b
(/ (sin k) (/ l t))
0.3b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite86.0ms

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
56.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
10.0ms
(/ (sin k) (/ l t))
9.0ms
(/ (sin k) (/ l t))
4.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
772.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
89.0ms
(/ (sin k) (/ l t))
88.0ms
(/ (sin k) (/ l t))
66.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

simplify1.4m

Counts
488 → 370
Calls
488 calls:
Slowest
2.6s
(/ (* (* (/ 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))))
2.1s
(/ (* (* (/ 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))))
1.8s
(/ (/ (* (* 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))))
1.7s
(/ (/ (* (* 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))))

prune5.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.6b

localize74.0ms

Local error

Found 4 expressions with local error:

11.8b
(* (/ t (cbrt (cos k))) (sqrt (fma (/ k t) (/ k t) 2)))
7.7b
(/ (/ 2 (sqrt (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cbrt (cos k))))
7.5b
(sqrt (fma (/ k t) (/ k t) 2))
7.5b
(sqrt (fma (/ k t) (/ k t) 2))

rewrite665.0ms

Algorithm
rewrite-expression-head
Rules
25940×times-frac
10413×add-sqr-sqrt
10395×*-un-lft-identity add-cube-cbrt
3047×cbrt-prod
2433×sqrt-prod
846×div-inv
268×associate-/r*
139×associate-/r/
41×add-exp-log
34×add-cbrt-cube
25×cbrt-undiv div-exp
22×associate-*l* associate-/l*
8×pow1
6×associate-*r* unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 prod-exp cbrt-unprod
1×clear-num frac-2neg pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 6300
Calls
4 calls:
Slowest
48.0ms
(/ (/ 2 (sqrt (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cbrt (cos k))))
29.0ms
(* (/ t (cbrt (cos k))) (sqrt (fma (/ k t) (/ k t) 2)))
2.0ms
(sqrt (fma (/ k t) (/ k t) 2))
2.0ms
(sqrt (fma (/ k t) (/ k t) 2))

series871.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
484.0ms
(/ (/ 2 (sqrt (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cbrt (cos k))))
277.0ms
(* (/ t (cbrt (cos k))) (sqrt (fma (/ k t) (/ k t) 2)))
58.0ms
(sqrt (fma (/ k t) (/ k t) 2))
53.0ms
(sqrt (fma (/ k t) (/ k t) 2))