Details

Time bar (total: 2.8m)

sample416.0ms

Algorithm
intervals
Results
193.0ms62×body1280valid
102.0ms65×body640valid
51.0ms156×body80valid
36.0ms32×body320valid
7.0ms10×body160valid

simplify667.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
667.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.4b

localize75.0ms

Local error

Found 4 expressions with local error:

12.7b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
10.0b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
0.9b
(/ t (* (/ l t) (/ l t)))
0.2b
(* (sin k) (tan k))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
233×add-cbrt-cube add-exp-log
102×cbrt-undiv div-exp
83×prod-exp cbrt-unprod
37×times-frac
26×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
16×associate-/l*
13×associate-*r*
11×pow1
9×associate-*r/ associate-/r/
5×tan-quot div-inv
4×expm1-log1p-u frac-times associate-*l* pow-prod-down associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
2×clear-num associate-/r* frac-2neg *-commutative
1×unswap-sqr associate-/l/
Counts
4 → 202
Calls
4 calls:
Slowest
66.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
56.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
13.0ms
(* (sin k) (tan k))
10.0ms
(/ t (* (/ l t) (/ l t)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
873.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
233.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
61.0ms
(/ t (* (/ l t) (/ l t)))
49.0ms
(* (sin k) (tan k))

simplify1.0m

Counts
175 → 214
Calls
175 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) (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))))))
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 t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l 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 t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t))))))

prune3.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.2b

localize41.0ms

Local error

Found 4 expressions with local error:

12.7b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
5.2b
(/ (sin k) (/ l t))
5.2b
(/ (sin k) (/ l t))
0.2b
(* t (/ (sin k) (/ l t)))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
424×times-frac
217×add-sqr-sqrt
208×*-un-lft-identity add-cube-cbrt
203×add-cbrt-cube add-exp-log
119×cbrt-undiv div-exp
45×prod-exp cbrt-unprod
44×associate-*r*
37×div-inv
33×associate-/r*
19×associate-/l*
6×pow1
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*l* unswap-sqr
1×pow-prod-down associate-*r/ *-commutative associate-/l/
Counts
4 → 397
Calls
4 calls:
Slowest
52.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
26.0ms
(* t (/ (sin k) (/ l t)))
19.0ms
(/ (sin k) (/ l t))
19.0ms
(/ (sin k) (/ l t))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
920.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
97.0ms
(/ (sin k) (/ l t))
79.0ms
(/ (sin k) (/ l t))
76.0ms
(* t (/ (sin k) (/ l t)))

simplify1.5m

Counts
522 → 409
Calls
522 calls:
Slowest
2.5s
(/ (* (* (/ 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))))
2.4s
(/ (* (* (/ 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) (/ 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 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))))
1.7s
(/ (/ (* (* 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 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))) (/ (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))))

prune6.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.5b

localize65.0ms

Local error

Found 4 expressions with local error:

11.2b
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
11.2b
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
8.9b
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) t)
6.2b
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cos k)))

rewrite185.0ms

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
16.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
14.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
8.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) t)
6.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))

series822.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
404.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
151.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) t)
150.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
117.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))