Details

sample419.0ms

Algorithm

intervals

Results

156.0ms	71×	body	640	valid
147.0ms	72×	body	1280	valid
59.0ms	187×	body	80	valid
29.0ms	27×	body	320	valid
5.0ms	7×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	2003
4	2003
3	1174
2	189
1	54
0	19

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.2b

localize53.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
1.9b	(/ t (* (/ l t) (/ l t)))
3.7b	(* (/ t (* (/ l t) (/ l t))) (sin k))
13.1b	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

rewrite831.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 146

Calls

4 calls:

146.0ms	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
11.0ms	(/ t (* (/ l t) (/ l t)))
46.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
623.0ms	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

series764.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
47.0ms	(/ t (* (/ l t) (/ l t)))
92.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
402.0ms	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

simplify1.1s

Counts

158 → 158

Iterations

Iter	Nodes
done	2001
2	2001
1	672
0	235

prune2.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (/ l t))
1.8b	(* (* (/ 1 (/ l t)) (* (/ t (/ l t)) (sin k))) (tan k))
3.0b	(* (/ t (/ l t)) (sin k))
13.1b	(* (* (* (/ 1 (/ l t)) (* (/ t (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

rewrite990.0ms

Algorithm

rewrite-expression-head

Rules

351×	`add-exp-log`
189×	`prod-exp`
169×	`add-cbrt-cube`
144×	`times-frac`
108×	`div-exp`
93×	`add-sqr-sqrt`
85×	`cbrt-unprod`
84×	`*-un-lft-identity` `add-cube-cbrt`
48×	`cbrt-undiv`
46×	`associate-l`
30×	`pow1`
26×	`associate-*l/`
18×	`rec-exp` `1-exp`
17×	`pow-prod-down`
13×	`associate-/r*`
10×	`frac-times`
9×	`associate-r` `div-inv`
8×	`tan-quot`
6×	`associate-*r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`-commutative` `associate-/l` `unswap-sqr`
2×	`associate-/r/` `fma-udef`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `pow-flip` `inv-pow`

Counts

4 → 287

Calls

4 calls:

14.0ms	(/ 1 (/ l t))
198.0ms	(* (* (/ 1 (/ l t)) (* (/ t (/ l t)) (sin k))) (tan k))
22.0ms	(* (/ t (/ l t)) (sin k))
743.0ms	(* (* (* (/ 1 (/ l t)) (* (/ t (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

series862.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 1 (/ l t))
254.0ms	(* (* (/ 1 (/ l t)) (* (/ t (/ l t)) (sin k))) (tan k))
97.0ms	(* (/ t (/ l t)) (sin k))
495.0ms	(* (* (* (/ 1 (/ l t)) (* (/ t (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

simplify1.7s

Counts

299 → 299

Iterations

Iter	Nodes
done	2000
2	2000
1	1409
0	490

prune4.9s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.1b

localize46.0ms

Local error

Found 4 expressions with local error:

1.2b	(/ (* (sin k) t) (/ l t))
2.7b	(* (tan k) (/ (* (sin k) t) (/ l t)))
7.1b	(/ (* (fma (/ k t) (/ k t) 2) (* (tan k) (/ (* (sin k) t) (/ l t)))) (/ l t))
9.9b	(* (fma (/ k t) (/ k t) 2) (* (tan k) (/ (* (sin k) t) (/ l t))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

132×	`add-cbrt-cube` `add-exp-log`
84×	`times-frac`
51×	`cbrt-undiv` `div-exp`
48×	`prod-exp` `cbrt-unprod`
44×	`add-sqr-sqrt`
42×	`*-un-lft-identity` `add-cube-cbrt`
26×	`associate-/r*`
19×	`associate-r`
11×	`pow1`
9×	`associate-*r/`
8×	`div-inv`
6×	`associate-l` `tan-quot`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-*l/` `associate-/r/` `associate-/l/`
2×	`clear-num` `frac-2neg` `-commutative` `associate-/l`
1×	`unswap-sqr`

Counts

4 → 200

Calls

4 calls:

23.0ms	(/ (* (sin k) t) (/ l t))
22.0ms	(* (tan k) (/ (* (sin k) t) (/ l t)))
69.0ms	(/ (* (fma (/ k t) (/ k t) 2) (* (tan k) (/ (* (sin k) t) (/ l t)))) (/ l t))
62.0ms	(* (fma (/ k t) (/ k t) 2) (* (tan k) (/ (* (sin k) t) (/ l t))))

series951.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (* (sin k) t) (/ l t))
188.0ms	(* (tan k) (/ (* (sin k) t) (/ l t)))
368.0ms	(/ (* (fma (/ k t) (/ k t) 2) (* (tan k) (/ (* (sin k) t) (/ l t)))) (/ l t))
310.0ms	(* (fma (/ k t) (/ k t) 2) (* (tan k) (/ (* (sin k) t) (/ l t))))

simplify1.3s

Counts

212 → 212

Iterations

Iter	Nodes
done	2000
2	2000
1	1040
0	342

prune3.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.3b

localize72.0ms

Local error

Found 4 expressions with local error:

9.9b	(* (fma (/ k t) (/ k t) 2) (* (tan k) (/ (/ (* (sin k) t) (* (cbrt (/ l t)) (cbrt (/ l t)))) (cbrt (/ l t)))))
12.0b	(cbrt (/ l t))
12.0b	(cbrt (/ l t))
12.0b	(cbrt (/ l t))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
37×	`add-exp-log`
28×	`add-cbrt-cube`
27×	`times-frac`
26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
17×	`prod-exp` `cbrt-unprod`
9×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `associate-l` `pow-prod-down` `div-inv`
2×	`tan-quot`
1×	`frac-times` `associate-r` `associate-l/` `-commutative`

Counts

4 → 109

Calls

4 calls:

135.0ms	(* (fma (/ k t) (/ k t) 2) (* (tan k) (/ (/ (* (sin k) t) (* (cbrt (/ l t)) (cbrt (/ l t)))) (cbrt (/ l t)))))
3.0ms	(cbrt (/ l t))
2.0ms	(cbrt (/ l t))
1.0ms	(cbrt (/ l t))

series639.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(* (fma (/ k t) (/ k t) 2) (* (tan k) (/ (/ (* (sin k) t) (* (cbrt (/ l t)) (cbrt (/ l t)))) (cbrt (/ l t)))))
102.0ms	(cbrt (/ l t))
103.0ms	(cbrt (/ l t))
112.0ms	(cbrt (/ l t))

simplify1.3s

Counts

121 → 121

Iterations

Iter	Nodes
done	2000
2	2000
1	544
0	210

prune2.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.3b

regimes645.0ms

Accuracy

66.1% (2.6b remaining)

Error of 9.3b against oracle of 6.6b and baseline of 14.4b

bsearch505.0ms

Steps

Iters	Range		Point
6	4.910198032679751e-35	2.124739062182176e-34	2.030695630825502e-34
9	-5.797751540880335e-18	-2.482857645479789e-25	-7.451781871449174e-25

simplify8.0ms

Iterations

Iter	Nodes
done	43
1	43
0	36

end0.0ms

sample15.5s

Algorithm

intervals

Results

6.2s	2126×	body	1280	valid
3.3s	1770×	body	640	valid
2.8s	5859×	body	80	valid
2.3s	882×	body	320	valid
483.0ms	394×	body	160	valid