Details

Time bar (total: 2.7m)

sample389.0ms

Algorithm
intervals
Results
159.0ms60×body1280valid
104.0ms61×body640valid
60.0ms186×body80valid
31.0ms26×body320valid
13.0ms16×body160valid

simplify334.0ms

Calls
1 calls:
Slowest
333.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.6b

localize43.0ms

Local error

Found 4 expressions with local error:

14.7b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
9.8b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
0.8b
(/ t (* (/ l t) (/ l t)))
0.2b
(* (sin k) (tan k))

rewrite200.0ms

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/
Calls
4 calls:
Slowest
86.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
61.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
23.0ms
(* (sin k) (tan k))
20.0ms
(/ t (* (/ l t) (/ l t)))

series1.2s

Calls
4 calls:
Slowest
860.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
263.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
47.0ms
(* (sin k) (tan k))
42.0ms
(/ t (* (/ l t) (/ l t)))

simplify58.9s

Calls
175 calls:
Slowest
2.2s
(/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 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))))))
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))))))
1.8s
(/ (/ (* (* 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))))))
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 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))))))

prune2.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.2b

localize38.0ms

Local error

Found 4 expressions with local error:

14.7b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
4.9b
(/ (sin k) (/ l t))
4.9b
(/ (sin k) (/ l t))
0.2b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite132.0ms

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/
Calls
4 calls:
Slowest
74.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
18.0ms
(/ (sin k) (/ l t))
18.0ms
(/ (sin k) (/ l t))
7.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

series1.1s

Calls
4 calls:
Slowest
843.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
79.0ms
(/ (sin k) (/ l t))
78.0ms
(/ (sin k) (/ l t))
64.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

simplify1.5m

Calls
488 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))))
1.9s
(/ (* (* (/ 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))))
1.8s
(/ (/ (* (* 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))) (/ (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))))
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))))

prune5.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.1b

localize64.0ms

Local error

Found 4 expressions with local error:

10.0b
(sqrt (fma (/ k t) (/ k t) 2))
10.0b
(sqrt (fma (/ k t) (/ k t) 2))
9.8b
(* (/ t (cbrt (cos k))) (sqrt (fma (/ k t) (/ k t) 2)))
7.4b
(/ (/ 2 (sqrt (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cbrt (cos k))))

rewrite612.0ms

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/
Calls
4 calls:
Slowest
25.0ms
(/ (/ 2 (sqrt (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cbrt (cos k))))
21.0ms
(* (/ t (cbrt (cos k))) (sqrt (fma (/ k t) (/ k t) 2)))
1.0ms
(sqrt (fma (/ k t) (/ k t) 2))
1.0ms
(sqrt (fma (/ k t) (/ k t) 2))

series811.0ms

Calls
4 calls:
Slowest
436.0ms
(/ (/ 2 (sqrt (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cbrt (cos k))))
262.0ms
(* (/ t (cbrt (cos k))) (sqrt (fma (/ k t) (/ k t) 2)))
66.0ms
(sqrt (fma (/ k t) (/ k t) 2))
47.0ms
(sqrt (fma (/ k t) (/ k t) 2))