Details

Time bar (total: 2.7m)

sample456.0ms

Algorithm
intervals
Results
214.0ms66×body1280valid
84.0ms51×body640valid
75.0ms195×body80valid
42.0ms29×body320valid
14.0ms15×body160valid

simplify369.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
369.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.9b

localize42.0ms

Local error

Found 4 expressions with local error:

12.9b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
8.8b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.9b
(/ t (* (/ l t) (/ l t)))
0.3b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite176.0ms

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
72.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
67.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
21.0ms
(/ t (* (/ l t) (/ l t)))
7.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
870.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
251.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
72.0ms
(/ 2 (fma (/ k t) (/ k t) 2))
53.0ms
(/ t (* (/ l t) (/ l t)))

simplify58.2s

Counts
189 → 222
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))))))
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))))))
1.8s
(/ (* (* (/ 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))))))

prune3.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.9b

localize49.0ms

Local error

Found 4 expressions with local error:

12.9b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
3.0b
(/ (sin k) (/ l t))
3.0b
(/ (sin k) (/ l t))
0.3b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite101.0ms

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
41.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
19.0ms
(/ (sin k) (/ l t))
15.0ms
(/ (sin k) (/ l t))
7.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
934.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
94.0ms
(/ (sin k) (/ l t))
75.0ms
(/ (sin k) (/ l t))
74.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

simplify1.5m

Counts
488 → 370
Calls
488 calls:
Slowest
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) (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))))
2.0s
(/ (/ (* (* 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 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 (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))))
1.6s
(/ (/ (* (* 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))))

prune5.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.3b

localize70.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
10.8b
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
6.9b
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) t)
5.2b
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cos k)))

rewrite275.0ms

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)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
521.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))
422.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) (/ (/ (sin k) (/ l t)) (cos k)))
129.0ms
(/ (sqrt (/ 2 (fma (/ k t) (/ k t) 2))) t)
126.0ms
(sqrt (/ 2 (fma (/ k t) (/ k t) 2)))