Details

Time bar (total: 10.0m)

sample473.0ms

Algorithm
intervals
Results
216.0ms67×body1280valid
100.0ms58×body640valid
61.0ms178×body80valid
49.0ms41×body320valid
17.0ms22×body160valid

simplify2.8s

Counts
1 → 1

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.9b

localize53.0ms

Local error

Found 4 expressions with local error:

13.2b
(/ (* (* (fma (/ k t) (/ k t) 2) t) (sin k)) (* (/ l t) (/ l t)))
3.4b
(/ (/ 2 (tan k)) (/ (* (* (fma (/ k t) (/ k t) 2) t) (sin k)) (* (/ l t) (/ l t))))
2.4b
(* (fma (/ k t) (/ k t) 2) t)
0.2b
(* (/ l t) (/ l t))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
275×add-cbrt-cube add-exp-log
249×times-frac
133×cbrt-undiv div-exp
126×add-sqr-sqrt
112×*-un-lft-identity add-cube-cbrt
86×prod-exp cbrt-unprod
58×associate-/r/
30×div-inv
17×frac-times associate-*l/ associate-*r/
16×associate-*r* associate-*l*
15×associate-/l*
13×pow1 swap-sqr
9×associate-/r* tan-quot
5×unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg pow-prod-down *-commutative
1×pow2 pow-plus pow-sqr pow-prod-up associate-/l/
Counts
4 → 353
Calls
4 calls:
Slowest
49.0ms
(/ (/ 2 (tan k)) (/ (* (* (fma (/ k t) (/ k t) 2) t) (sin k)) (* (/ l t) (/ l t))))
25.0ms
(/ (* (* (fma (/ k t) (/ k t) 2) t) (sin k)) (* (/ l t) (/ l t)))
12.0ms
(* (/ l t) (/ l t))
5.0ms
(* (fma (/ k t) (/ k t) 2) t)

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
917.0ms
(/ (/ 2 (tan k)) (/ (* (* (fma (/ k t) (/ k t) 2) t) (sin k)) (* (/ l t) (/ l t))))
217.0ms
(/ (* (* (fma (/ k t) (/ k t) 2) t) (sin k)) (* (/ l t) (/ l t)))
92.0ms
(* (fma (/ k t) (/ k t) 2) t)
49.0ms
(* (/ l t) (/ l t))

simplify1.3s

Counts
365 → 365

prune5.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.3b

localize50.0ms

Local error

Found 4 expressions with local error:

6.6b
(* (/ (* (/ (cbrt 2) (cbrt (tan k))) (/ (cbrt 2) (cbrt (tan k)))) (* t (fma (/ k t) (/ k t) 2))) (/ l t))
6.4b
(* (* (/ (* (/ (cbrt 2) (cbrt (tan k))) (/ (cbrt 2) (cbrt (tan k)))) (* t (fma (/ k t) (/ k t) 2))) (/ l t)) (/ (/ (cbrt 2) (cbrt (tan k))) (/ (sin k) (/ l t))))
3.1b
(/ (sin k) (/ l t))
2.4b
(* t (fma (/ k t) (/ k t) 2))

rewrite629.0ms

Algorithm
rewrite-expression-head
Rules
6180×times-frac
2599×add-sqr-sqrt
2592×*-un-lft-identity add-cube-cbrt
1825×associate-*r*
1584×cbrt-prod
1460×add-exp-log
1066×add-cbrt-cube
724×cbrt-undiv div-exp
546×prod-exp cbrt-unprod
216×div-inv
87×associate-/r/
44×cbrt-div tan-quot
13×pow1 associate-/r*
9×associate-*l*
6×frac-times associate-*l/
5×pow-prod-down
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative associate-/l* unswap-sqr
2×fma-udef
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in
Counts
4 → 2327
Calls
4 calls:
Slowest
322.0ms
(* (* (/ (* (/ (cbrt 2) (cbrt (tan k))) (/ (cbrt 2) (cbrt (tan k)))) (* t (fma (/ k t) (/ k t) 2))) (/ l t)) (/ (/ (cbrt 2) (cbrt (tan k))) (/ (sin k) (/ l t))))
88.0ms
(* (/ (* (/ (cbrt 2) (cbrt (tan k))) (/ (cbrt 2) (cbrt (tan k)))) (* t (fma (/ k t) (/ k t) 2))) (/ l t))
19.0ms
(/ (sin k) (/ l t))
9.0ms
(* t (fma (/ k t) (/ k t) 2))

series2.7s

Counts
4 → 12
Calls
4 calls:
Slowest
1.3s
(* (/ (* (/ (cbrt 2) (cbrt (tan k))) (/ (cbrt 2) (cbrt (tan k)))) (* t (fma (/ k t) (/ k t) 2))) (/ l t))
1.1s
(* (* (/ (* (/ (cbrt 2) (cbrt (tan k))) (/ (cbrt 2) (cbrt (tan k)))) (* t (fma (/ k t) (/ k t) 2))) (/ l t)) (/ (/ (cbrt 2) (cbrt (tan k))) (/ (sin k) (/ l t))))
105.0ms
(/ (sin k) (/ l t))
72.0ms
(* t (fma (/ k t) (/ k t) 2))

simplify33.6s

Counts
2339 → 2339

prune50.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.3b

localize90.0ms

Local error

Found 4 expressions with local error:

6.4b
(* (* (/ (/ (cbrt 2) (cbrt (tan k))) t) (* (/ (/ (cbrt 2) (cbrt (tan k))) (fma (/ k t) (/ k t) 2)) (/ l t))) (/ (/ (cbrt 2) (cbrt (tan k))) (/ (sin k) (/ l t))))
6.2b
(* (/ (/ (cbrt 2) (cbrt (tan k))) (fma (/ k t) (/ k t) 2)) (/ l t))
4.1b
(* (/ (/ (cbrt 2) (cbrt (tan k))) t) (* (/ (/ (cbrt 2) (cbrt (tan k))) (fma (/ k t) (/ k t) 2)) (/ l t)))
3.1b
(/ (sin k) (/ l t))

rewrite495.0ms

Algorithm
rewrite-expression-head
Rules
6664×times-frac
2871×add-sqr-sqrt
2823×*-un-lft-identity add-cube-cbrt
1823×associate-*r*
1808×cbrt-prod
1385×add-exp-log
1041×add-cbrt-cube
726×cbrt-undiv div-exp
472×prod-exp cbrt-unprod
255×associate-*l*
223×div-inv
93×associate-/r/
50×cbrt-div tan-quot
23×frac-times
20×pow1
17×associate-*l/ associate-*r/
13×associate-/r*
12×unswap-sqr
10×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative associate-/l*
1×clear-num frac-2neg
Counts
4 → 2589
Calls
4 calls:
Slowest
221.0ms
(* (* (/ (/ (cbrt 2) (cbrt (tan k))) t) (* (/ (/ (cbrt 2) (cbrt (tan k))) (fma (/ k t) (/ k t) 2)) (/ l t))) (/ (/ (cbrt 2) (cbrt (tan k))) (/ (sin k) (/ l t))))
65.0ms
(* (/ (/ (cbrt 2) (cbrt (tan k))) t) (* (/ (/ (cbrt 2) (cbrt (tan k))) (fma (/ k t) (/ k t) 2)) (/ l t)))
31.0ms
(* (/ (/ (cbrt 2) (cbrt (tan k))) (fma (/ k t) (/ k t) 2)) (/ l t))
18.0ms
(/ (sin k) (/ l t))

series3.1s

Counts
4 → 12
Calls
4 calls:
Slowest
1.3s
(* (/ (/ (cbrt 2) (cbrt (tan k))) t) (* (/ (/ (cbrt 2) (cbrt (tan k))) (fma (/ k t) (/ k t) 2)) (/ l t)))
995.0ms
(* (* (/ (/ (cbrt 2) (cbrt (tan k))) t) (* (/ (/ (cbrt 2) (cbrt (tan k))) (fma (/ k t) (/ k t) 2)) (/ l t))) (/ (/ (cbrt 2) (cbrt (tan k))) (/ (sin k) (/ l t))))
685.0ms
(* (/ (/ (cbrt 2) (cbrt (tan k))) (fma (/ k t) (/ k t) 2)) (/ l t))
103.0ms
(/ (sin k) (/ l t))

simplify38.1s

Counts
2601 → 2601

prune58.5s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 6.3b

localize106.0ms

Local error

Found 4 expressions with local error:

6.6b
(* (/ (/ (cbrt 2) (cbrt (tan k))) (/ (* (fma (/ k t) (/ k t) 2) t) (/ (cbrt 2) (cbrt (tan k))))) (/ l t))
6.1b
(* (* (* (/ (/ (cbrt 2) (cbrt (tan k))) (/ (* (fma (/ k t) (/ k t) 2) t) (/ (cbrt 2) (cbrt (tan k))))) (/ l t)) (/ (* (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k)))) (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k))))) (* (cbrt (sin k)) (cbrt (sin k))))) (/ (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k)))) (/ (cbrt (sin k)) (/ l t))))
2.4b
(* (fma (/ k t) (/ k t) 2) t)
2.0b
(* (* (/ (/ (cbrt 2) (cbrt (tan k))) (/ (* (fma (/ k t) (/ k t) 2) t) (/ (cbrt 2) (cbrt (tan k))))) (/ l t)) (/ (* (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k)))) (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k))))) (* (cbrt (sin k)) (cbrt (sin k)))))

rewrite3.7s

Algorithm
rewrite-expression-head
Rules
31946×times-frac
23830×add-exp-log
19940×cbrt-prod
13302×add-cbrt-cube
12907×cbrt-undiv div-exp
12781×add-sqr-sqrt
12731×*-un-lft-identity add-cube-cbrt
8865×prod-exp cbrt-unprod
7164×associate-*r*
1896×associate-*l*
817×div-inv
299×associate-/r/
253×cbrt-div
170×tan-quot
23×frac-times associate-*l/
22×pow1
13×unswap-sqr
11×pow-prod-down associate-*r/
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 13257
Calls
4 calls:
Slowest
1.0s
(* (* (* (/ (/ (cbrt 2) (cbrt (tan k))) (/ (* (fma (/ k t) (/ k t) 2) t) (/ (cbrt 2) (cbrt (tan k))))) (/ l t)) (/ (* (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k)))) (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k))))) (* (cbrt (sin k)) (cbrt (sin k))))) (/ (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k)))) (/ (cbrt (sin k)) (/ l t))))
238.0ms
(* (* (/ (/ (cbrt 2) (cbrt (tan k))) (/ (* (fma (/ k t) (/ k t) 2) t) (/ (cbrt 2) (cbrt (tan k))))) (/ l t)) (/ (* (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k)))) (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k))))) (* (cbrt (sin k)) (cbrt (sin k)))))
119.0ms
(* (/ (/ (cbrt 2) (cbrt (tan k))) (/ (* (fma (/ k t) (/ k t) 2) t) (/ (cbrt 2) (cbrt (tan k))))) (/ l t))
6.0ms
(* (fma (/ k t) (/ k t) 2) t)

series4.0s

Counts
4 → 12
Calls
4 calls:
Slowest
1.9s
(* (* (/ (/ (cbrt 2) (cbrt (tan k))) (/ (* (fma (/ k t) (/ k t) 2) t) (/ (cbrt 2) (cbrt (tan k))))) (/ l t)) (/ (* (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k)))) (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k))))) (* (cbrt (sin k)) (cbrt (sin k)))))
1.0s
(* (* (* (/ (/ (cbrt 2) (cbrt (tan k))) (/ (* (fma (/ k t) (/ k t) 2) t) (/ (cbrt 2) (cbrt (tan k))))) (/ l t)) (/ (* (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k)))) (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k))))) (* (cbrt (sin k)) (cbrt (sin k))))) (/ (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k)))) (/ (cbrt (sin k)) (/ l t))))
948.0ms
(* (/ (/ (cbrt 2) (cbrt (tan k))) (/ (* (fma (/ k t) (/ k t) 2) t) (/ (cbrt 2) (cbrt (tan k))))) (/ l t))
63.0ms
(* (fma (/ k t) (/ k t) 2) t)

simplify6.5m