Details

sample476.0ms

Algorithm

intervals

Results

222.0ms	64×	body	1280	valid
112.0ms	59×	body	640	valid
78.0ms	193×	body	80	valid
24.0ms	19×	body	320	valid
11.0ms	12×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	1174
2	189
1	54
0	19

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.8b

localize38.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
3.2b	(/ (tan k) (/ l t))
3.4b	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
11.7b	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

rewrite3.6s

Algorithm

rewrite-expression-head

Rules

1704×	`times-frac`
1633×	`associate-/r*`
1587×	`add-sqr-sqrt`
1320×	`associate-*l/`
1263×	`*-un-lft-identity`
1260×	`add-cube-cbrt`
1140×	`frac-times`
540×	`associate-l`
414×	`associate-/l*`
165×	`associate-r`
152×	`div-inv`
151×	`add-cbrt-cube` `add-exp-log`
134×	`clear-num`
131×	`frac-2neg`
125×	`unswap-sqr`
81×	`associate-/r/`
61×	`tan-quot` `associate-/l/`
60×	`associate-*r/`
58×	`prod-exp` `cbrt-unprod`
57×	`cbrt-undiv` `div-exp`
20×	`pow1`
10×	`pow-prod-down`
6×	`un-div-inv` `*-commutative`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 1858

Calls

4 calls:

163.0ms	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
28.0ms	(/ (tan k) (/ l t))
664.0ms	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
2.6s	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

series1.0s

Counts

4 → 12

Calls

4 calls:

185.0ms	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
152.0ms	(/ (tan k) (/ l t))
214.0ms	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
475.0ms	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

simplify2.6s

Counts

1870 → 1870

Iterations

Iter	Nodes
done	5000
0	2134

prune13.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize56.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 2 (/ (* (/ t l) (* (sin k) (fma (/ k t) (/ k t) 2))) (* (/ 1 t) (/ (/ l t) (tan k)))))
3.2b	(/ (/ l t) (tan k))
5.7b	(* (/ t l) (* (sin k) (fma (/ k t) (/ k t) 2)))
8.8b	(/ (* (/ t l) (* (sin k) (fma (/ k t) (/ k t) 2))) (* (/ 1 t) (/ (/ l t) (tan k))))

rewrite3.8s

Algorithm

rewrite-expression-head

Rules

40146×	`times-frac`
25065×	`add-sqr-sqrt`
15419×	`*-un-lft-identity`
14893×	`add-cube-cbrt`
12938×	`associate-r`
7964×	`associate-l`
4054×	`unswap-sqr`
3603×	`associate-/r*`
1755×	`associate-/r/`
1341×	`associate-/l*`
1279×	`div-inv`
1260×	`frac-times`
888×	`*-commutative`
826×	`add-exp-log`
487×	`associate-/l/`
460×	`add-cbrt-cube`
433×	`div-exp`
282×	`prod-exp`
263×	`clear-num`
253×	`frac-2neg`
229×	`cbrt-undiv`
173×	`tan-quot`
150×	`cbrt-unprod`
140×	`associate-*r/`
72×	`associate-*l/`
30×	`rec-exp` `1-exp`
20×	`un-div-inv`
9×	`pow1`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`

Counts

4 → 14158

Calls

4 calls:

976.0ms	(/ 2 (/ (* (/ t l) (* (sin k) (fma (/ k t) (/ k t) 2))) (* (/ 1 t) (/ (/ l t) (tan k)))))
26.0ms	(/ (/ l t) (tan k))
97.0ms	(* (/ t l) (* (sin k) (fma (/ k t) (/ k t) 2)))
330.0ms	(/ (* (/ t l) (* (sin k) (fma (/ k t) (/ k t) 2))) (* (/ 1 t) (/ (/ l t) (tan k))))

series1.3s

Counts

4 → 12

Calls

4 calls:

343.0ms	(/ 2 (/ (* (/ t l) (* (sin k) (fma (/ k t) (/ k t) 2))) (* (/ 1 t) (/ (/ l t) (tan k)))))
238.0ms	(/ (/ l t) (tan k))
272.0ms	(* (/ t l) (* (sin k) (fma (/ k t) (/ k t) 2)))
492.0ms	(/ (* (/ t l) (* (sin k) (fma (/ k t) (/ k t) 2))) (* (/ 1 t) (/ (/ l t) (tan k))))

simplify25.3s

Counts

14170 → 14170

Iterations

Iter	Nodes
done	20911
0	20911

prune2.1m

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.0b

localize62.0ms

Local error

Found 4 expressions with local error:

5.6b	(/ (sqrt (fma (/ k t) (/ k t) 2)) (/ (/ l t) (tan k)))
8.6b	(* (/ t l) (* (sin k) (sqrt (fma (/ k t) (/ k t) 2))))
8.9b	(sqrt (fma (/ k t) (/ k t) 2))
8.9b	(sqrt (fma (/ k t) (/ k t) 2))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

747×	`times-frac`
389×	`add-sqr-sqrt`
364×	`*-un-lft-identity` `add-cube-cbrt`
147×	`sqrt-prod`
53×	`associate-/r*`
35×	`associate-/r/`
31×	`div-inv`
25×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
22×	`associate-r`
16×	`associate-l`
12×	`unswap-sqr`
11×	`pow1`
9×	`associate-*l/` `associate-/l/`
8×	`cbrt-undiv` `div-exp`
7×	`tan-quot`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative`

Counts

4 → 458

Calls

4 calls:

59.0ms	(/ (sqrt (fma (/ k t) (/ k t) 2)) (/ (/ l t) (tan k)))
78.0ms	(* (/ t l) (* (sin k) (sqrt (fma (/ k t) (/ k t) 2))))
3.0ms	(sqrt (fma (/ k t) (/ k t) 2))
3.0ms	(sqrt (fma (/ k t) (/ k t) 2))

series667.0ms

Counts

4 → 12

Calls

4 calls:

295.0ms	(/ (sqrt (fma (/ k t) (/ k t) 2)) (/ (/ l t) (tan k)))
244.0ms	(* (/ t l) (* (sin k) (sqrt (fma (/ k t) (/ k t) 2))))
63.0ms	(sqrt (fma (/ k t) (/ k t) 2))
65.0ms	(sqrt (fma (/ k t) (/ k t) 2))

simplify2.2s

Counts

470 → 470

Iterations

Iter	Nodes
done	5000
1	2075
0	734

prune3.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.0b

localize85.0ms

Local error

Found 4 expressions with local error:

8.9b	(sqrt (fma (/ k t) (/ k t) 2))
8.9b	(sqrt (fma (/ k t) (/ k t) 2))
10.0b	(sqrt (sqrt (fma (/ k t) (/ k t) 2)))
10.0b	(sqrt (sqrt (fma (/ k t) (/ k t) 2)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `sqrt-pow1` `add-cube-cbrt`
6×	`rem-sqrt-square` `pow1/2`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

8.0ms	(sqrt (fma (/ k t) (/ k t) 2))
1.0ms	(sqrt (fma (/ k t) (/ k t) 2))
2.0ms	(sqrt (sqrt (fma (/ k t) (/ k t) 2)))
2.0ms	(sqrt (sqrt (fma (/ k t) (/ k t) 2)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt (fma (/ k t) (/ k t) 2))
47.0ms	(sqrt (fma (/ k t) (/ k t) 2))
163.0ms	(sqrt (sqrt (fma (/ k t) (/ k t) 2)))
201.0ms	(sqrt (sqrt (fma (/ k t) (/ k t) 2)))

simplify2.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
4	2669
3	648
2	225
1	110
0	63

prune743.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.0b

regimes479.0ms

Accuracy

-5.1% (4.3b remaining)

Error of 11.2b against oracle of 6.8b and baseline of 11.0b

bsearch8.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	58
1	58
0	48

end0.0ms

sample15.7s

Algorithm

intervals

Results

6.5s	2075×	body	1280	valid
4.2s	1684×	body	640	valid
3.0s	6010×	body	80	valid
1.2s	826×	body	320	valid
468.0ms	457×	body	160	valid