Details

sample428.0ms

Algorithm

intervals

Results

209.0ms	72×	body	1280	valid
108.0ms	65×	body	640	valid
58.0ms	169×	body	80	valid
22.0ms	18×	body	320	valid
7.0ms	10×	body	160	valid

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
4	6637
3	1079
2	183
1	52
0	19

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (tan k) (fma (/ k t) (/ k t) 2))
1.6b	(/ t (* (/ l t) (/ l t)))
3.9b	(* (/ t (* (/ l t) (/ l t))) (sin k))
16.8b	(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

141×	`add-cbrt-cube` `add-exp-log`
66×	`cbrt-undiv` `div-exp`
43×	`prod-exp` `cbrt-unprod`
21×	`add-sqr-sqrt` `times-frac`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-l`
11×	`associate-/l*`
9×	`associate-/r/`
8×	`pow1`
7×	`associate-*l/`
6×	`associate-r`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `tan-quot` `associate-r/` `*-commutative` `fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-/l/`

Counts

4 → 161

Calls

4 calls:

10.0ms	(* (tan k) (fma (/ k t) (/ k t) 2))
19.0ms	(/ t (* (/ l t) (/ l t)))
40.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
91.0ms	(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (tan k) (fma (/ k t) (/ k t) 2))
62.0ms	(/ t (* (/ l t) (/ l t)))
115.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
307.0ms	(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

simplify1.7s

Counts

173 → 173

Iterations

Iter	Nodes
2	3709
1	856
0	303

prune2.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.6b

localize75.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt t)
0.6b	(* (tan k) (fma (/ k t) (/ k t) 2))
2.4b	(* (/ (cbrt t) (/ l t)) (sin k))
16.8b	(/ (/ 2 (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k)))) (* (tan k) (fma (/ k t) (/ k t) 2)))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

331×	`add-exp-log`
277×	`add-cbrt-cube`
167×	`cbrt-undiv` `div-exp`
154×	`times-frac`
112×	`prod-exp` `cbrt-unprod`
99×	`add-sqr-sqrt`
86×	`associate-l`
81×	`*-un-lft-identity` `add-cube-cbrt`
44×	`cbrt-prod`
10×	`div-inv` `associate-/l*`
9×	`associate-*l/`
8×	`pow1` `associate-/r/`
6×	`associate-r` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `pow-prod-down` `tan-quot` `associate-r/` `-commutative` `fma-udef`
1×	`distribute-rgt-in` `clear-num` `associate-/r*` `frac-2neg` `distribute-lft-in` `pow1/3` `associate-/l/`

Counts

4 → 272

Calls

4 calls:

1.0ms	(cbrt t)
16.0ms	(* (tan k) (fma (/ k t) (/ k t) 2))
36.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
140.0ms	(/ (/ 2 (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k)))) (* (tan k) (fma (/ k t) (/ k t) 2)))

series942.0ms

Counts

4 → 12

Calls

4 calls:

263.0ms	(cbrt t)
116.0ms	(* (tan k) (fma (/ k t) (/ k t) 2))
194.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
369.0ms	(/ (/ 2 (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k)))) (* (tan k) (fma (/ k t) (/ k t) 2)))

simplify3.3s

Counts

284 → 284

Iterations

Iter	Nodes
2	7413
1	1673
0	545

prune5.4s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 11.2b

localize87.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (/ (cbrt t) (/ l t)) (sin k))
3.0b	(/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k))
7.8b	(/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2))
9.3b	(* (/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k)) (/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2)))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

2650×	`times-frac`
1028×	`add-sqr-sqrt`
942×	`*-un-lft-identity` `add-cube-cbrt`
427×	`associate-l`
405×	`sqrt-prod`
361×	`add-exp-log`
315×	`add-cbrt-cube`
218×	`cbrt-undiv` `div-exp`
124×	`associate-/l*`
109×	`div-inv`
83×	`prod-exp` `cbrt-unprod`
59×	`associate-/r/`
41×	`cbrt-prod`
40×	`associate-r`
21×	`unswap-sqr`
9×	`associate-*l/`
8×	`pow1`
6×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `tan-quot` `*-commutative` `associate-/l/`
1×	`frac-times` `associate-*r/`

Counts

4 → 1159

Calls

4 calls:

35.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
34.0ms	(/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k))
30.0ms	(/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2))
109.0ms	(* (/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k)) (/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2)))

series1.9s

Counts

4 → 12

Calls

4 calls:

219.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
444.0ms	(/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k))
607.0ms	(/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2))
632.0ms	(* (/ (/ (sqrt 2) (/ (* (cbrt t) (cbrt t)) (/ l t))) (tan k)) (/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2)))

simplify3.5s

Counts

1171 → 1171

Iterations

Iter	Nodes
1	4992
0	1569

prune23.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.0b

localize86.0ms

Local error

Found 4 expressions with local error:

1.8b	(/ (tan k) (/ (sqrt (sqrt 2)) (/ (cbrt t) (/ l t))))
2.4b	(* (/ (cbrt t) (/ l t)) (sin k))
7.8b	(/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2))
9.3b	(* (/ (/ (sqrt (sqrt 2)) (/ (cbrt t) 1)) (/ (tan k) (/ (sqrt (sqrt 2)) (/ (cbrt t) (/ l t))))) (/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2)))

rewrite2.2m

Algorithm

rewrite-expression-head

Rules

2922871×	`times-frac`
1107886×	`add-sqr-sqrt`
1103883×	`*-un-lft-identity`
1103679×	`add-cube-cbrt`
906600×	`sqrt-prod`
459071×	`associate-l`
398741×	`cbrt-prod`
62063×	`div-inv`
8604×	`associate-/r/`
1094×	`add-exp-log`
787×	`div-exp`
755×	`associate-/r*`
735×	`add-cbrt-cube`
577×	`cbrt-undiv`
551×	`unswap-sqr`
195×	`prod-exp`
150×	`cbrt-unprod`
40×	`associate-r`
30×	`1-exp`
14×	`associate-/l*`
9×	`associate-*l/`
8×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `*-commutative` `associate-/l/`
1×	`frac-times` `tan-quot` `associate-*r/`

Counts

4 → 463023

Calls

4 calls:

40.0ms	(/ (tan k) (/ (sqrt (sqrt 2)) (/ (cbrt t) (/ l t))))
25.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
31.0ms	(/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2))
35.0s	(* (/ (/ (sqrt (sqrt 2)) (/ (cbrt t) 1)) (/ (tan k) (/ (sqrt (sqrt 2)) (/ (cbrt t) (/ l t))))) (/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2)))

series2.4s

Counts

4 → 12

Calls

4 calls:

497.0ms	(/ (tan k) (/ (sqrt (sqrt 2)) (/ (cbrt t) (/ l t))))
224.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
679.0ms	(/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2))
994.0ms	(* (/ (/ (sqrt (sqrt 2)) (/ (cbrt t) 1)) (/ (tan k) (/ (sqrt (sqrt 2)) (/ (cbrt t) (/ l t))))) (/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2)))

Details

sample428.0ms

simplify3.4s

prune22.0ms

localize57.0ms

rewrite164.0ms

series616.0ms

simplify1.7s

prune2.4s

localize75.0ms

rewrite201.0ms

series942.0ms

simplify3.3s

prune5.4s

localize87.0ms

rewrite267.0ms

series1.9s

simplify3.5s

prune23.1s

localize86.0ms

rewrite2.2m

series2.4s

simplify7.0m