Details

Time bar (total: 2.7m)

sample445.0ms

Algorithm
intervals
Results
237.0ms84×body1280valid
90.0ms49×body640valid
61.0ms169×body80valid
25.0ms24×body320valid
11.0ms15×body160valid

simplify365.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
365.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.8b

localize58.0ms

Local error

Found 4 expressions with local error:

17.4b
(/ (/ 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))))
2.1b
(/ t (* (/ l t) (/ l t)))
0.3b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite182.0ms

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
82.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
76.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
15.0ms
(/ t (* (/ l t) (/ l t)))
4.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
899.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
243.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
85.0ms
(/ 2 (fma (/ k t) (/ k t) 2))
52.0ms
(/ t (* (/ l t) (/ l t)))

simplify59.4s

Counts
189 → 222
Calls
189 calls:
Slowest
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))))))
1.8s
(/ (/ (* (* 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 (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))))))
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) (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))))))
1.7s
(/ (* (* (/ 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))))))

prune3.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.7b

localize70.0ms

Local error

Found 4 expressions with local error:

17.4b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
3.4b
(/ (sin k) (/ l t))
3.4b
(/ (sin k) (/ l t))
0.3b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite84.0ms

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
54.0ms
(/ (/ 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))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
847.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
85.0ms
(/ (sin k) (/ l t))
81.0ms
(/ (sin k) (/ l t))
61.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

simplify1.5m

Counts
488 → 370
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))))
2.1s
(/ (/ (* (* 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))))
2.0s
(/ (* (* (/ 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 (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))))

prune5.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.4b

localize91.0ms

Local error

Found 4 expressions with local error:

13.2b
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) t)
9.6b
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
9.6b
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
8.2b
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cos k)))

rewrite567.0ms

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
31.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
13.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) t)
4.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
4.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))

series840.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
418.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
148.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
140.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) t)
134.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))