Details

Time bar (total: 2.7m)

sample520.0ms

Algorithm
intervals
Results
262.0ms77×body1280valid
108.0ms53×body640valid
79.0ms186×body80valid
36.0ms26×body320valid
9.0ms9×body160valid

simplify350.0ms

Calls
1 calls:
Slowest
349.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.5b

localize64.0ms

Local error

Found 4 expressions with local error:

14.6b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
10.9b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.3b
(/ t (* (/ l t) (/ l t)))
0.3b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite149.0ms

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/
Calls
4 calls:
Slowest
65.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
65.0ms
(/ (/ 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))

series1.2s

Calls
4 calls:
Slowest
836.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
249.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
61.0ms
(/ 2 (fma (/ k t) (/ k t) 2))
54.0ms
(/ t (* (/ l t) (/ l t)))

simplify1.0m

Calls
189 calls:
Slowest
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))))))
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) (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 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) (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))))))

prune3.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.8b

localize53.0ms

Local error

Found 4 expressions with local error:

14.6b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
3.7b
(/ (sin k) (/ l t))
3.7b
(/ (sin k) (/ l t))
0.3b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite100.0ms

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
50.0ms
(/ (/ 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))
6.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

series1.1s

Calls
4 calls:
Slowest
847.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
113.0ms
(/ (sin k) (/ l t))
107.0ms
(/ (sin k) (/ l t))
67.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

simplify1.5m

Calls
488 calls:
Slowest
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) (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))))
1.9s
(/ (/ (* (* 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))))
1.6s
(/ (* (* (/ 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))))

prune5.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.7b

localize38.0ms

Local error

Found 4 expressions with local error:

13.2b
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
13.2b
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
8.4b
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) t)
5.6b
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cos k)))

rewrite202.0ms

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/
Calls
4 calls:
Slowest
16.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
12.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) t)
2.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
2.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))

series845.0ms

Calls
4 calls:
Slowest
402.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
160.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
142.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) t)
141.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))