Details

Time bar (total: 2.7m)

sample417.0ms

Algorithm
intervals
Results
130.0ms57×body1280valid
117.0ms186×body80valid
98.0ms62×body640valid
34.0ms29×body320valid
9.0ms11×body160valid

simplify326.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
326.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.4b

localize46.0ms

Local error

Found 4 expressions with local error:

13.6b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
10.7b
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
1.0b
(/ t (* (/ l t) (/ l t)))
0.2b
(* (sin k) (tan k))

rewrite164.0ms

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/
Counts
4 → 202
Calls
4 calls:
Slowest
68.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
65.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
15.0ms
(/ t (* (/ l t) (/ l t)))
12.0ms
(* (sin k) (tan k))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
946.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t)))))
255.0ms
(* (* (sin k) (tan k)) (/ t (* (/ l t) (/ l t))))
70.0ms
(* (sin k) (tan k))
58.0ms
(/ t (* (/ l t) (/ l t)))

simplify1.0m

Counts
175 → 214
Calls
175 calls:
Slowest
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))))))
1.9s
(/ (* (* (/ 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 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 (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))))))
1.8s
(/ (* (* (/ 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))))))

prune3.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.1b

localize37.0ms

Local error

Found 4 expressions with local error:

13.6b
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
3.1b
(/ (sin k) (/ l t))
3.1b
(/ (sin k) (/ l t))
0.2b
(/ 2 (fma (/ k t) (/ k t) 2))

rewrite93.0ms

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)))
18.0ms
(/ (sin k) (/ l t))
9.0ms
(/ (sin k) (/ l t))
4.0ms
(/ 2 (fma (/ k t) (/ k t) 2))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
890.0ms
(/ (/ 2 (fma (/ k t) (/ k t) 2)) (/ (* (* t (/ (sin k) (/ l t))) (/ (sin k) (/ l t))) (cos k)))
120.0ms
(/ (sin k) (/ l t))
90.0ms
(/ 2 (fma (/ k t) (/ k t) 2))
69.0ms
(/ (sin k) (/ l t))

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))))
2.1s
(/ (* (* (/ 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))))
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))))
1.8s
(/ (/ (* (* 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))))
1.7s
(/ (/ (* (* 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))))

prune5.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.4b

localize87.0ms

Local error

Found 4 expressions with local error:

13.6b
(cbrt (fma (/ k t) (/ k t) 2))
13.6b
(cbrt (fma (/ k t) (/ k t) 2))
13.6b
(cbrt (fma (/ k t) (/ k t) 2))
5.0b
(* (/ (/ (cbrt 2) (cbrt (fma (/ k t) (/ k t) 2))) (/ t (/ (cbrt 2) (cbrt (fma (/ k t) (/ k t) 2))))) (/ l (* t (sin k))))

rewrite733.0ms

Algorithm
rewrite-expression-head
Rules
18722×times-frac
8873×cbrt-prod
7936×add-sqr-sqrt
7775×*-un-lft-identity add-cube-cbrt
5005×associate-*l*
287×div-inv
112×add-exp-log
82×add-cbrt-cube
59×cbrt-undiv div-exp
41×associate-/r/
31×unswap-sqr
28×prod-exp cbrt-unprod
7×associate-*r*
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 5142
Calls
4 calls:
Slowest
223.0ms
(* (/ (/ (cbrt 2) (cbrt (fma (/ k t) (/ k t) 2))) (/ t (/ (cbrt 2) (cbrt (fma (/ k t) (/ k t) 2))))) (/ l (* t (sin k))))
1.0ms
(cbrt (fma (/ k t) (/ k t) 2))
1.0ms
(cbrt (fma (/ k t) (/ k t) 2))
1.0ms
(cbrt (fma (/ k t) (/ k t) 2))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
825.0ms
(* (/ (/ (cbrt 2) (cbrt (fma (/ k t) (/ k t) 2))) (/ t (/ (cbrt 2) (cbrt (fma (/ k t) (/ k t) 2))))) (/ l (* t (sin k))))
520.0ms
(cbrt (fma (/ k t) (/ k t) 2))
197.0ms
(cbrt (fma (/ k t) (/ k t) 2))
191.0ms
(cbrt (fma (/ k t) (/ k t) 2))