Details

sample293.0ms

Algorithm

intervals

Results

112.0ms	68×	body	1280	valid
59.0ms	54×	body	640	valid
53.0ms	29×	body	320	valid
35.0ms	160×	body	80	valid
11.0ms	20×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.8b

localize68.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
1.9b	(/ (tan k) (/ l t))
3.9b	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
11.5b	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

rewrite628.0ms

Algorithm

rewrite-expression-head

Rules

225×	`times-frac`
154×	`add-sqr-sqrt`
151×	`add-cbrt-cube` `add-exp-log`
118×	`*-un-lft-identity` `add-cube-cbrt`
58×	`prod-exp` `cbrt-unprod`
57×	`cbrt-undiv` `div-exp`
50×	`associate-r`
46×	`associate-l`
20×	`pow1`
13×	`associate-/r*` `div-inv`
12×	`associate-*l/`
10×	`pow-prod-down`
9×	`unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `associate-/r/` `-commutative` `associate-/l*`
2×	`fma-udef`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `tan-quot` `associate-/l/`

Counts

4 → 289

Calls

4 calls:

63.0ms	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
16.0ms	(/ (tan k) (/ l t))
139.0ms	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
382.0ms	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

series965.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
149.0ms	(/ (tan k) (/ l t))
201.0ms	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
436.0ms	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

simplify1.7s

Counts

301 → 301

Iterations

Iter	Nodes
done	5002
1	1545
0	465

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize64.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (* t (/ (tan k) (/ l t))) (sin k))
1.9b	(/ (tan k) (/ l t))
5.8b	(/ (* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2)) (/ l t))
8.9b	(* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

rewrite579.0ms

Algorithm

rewrite-expression-head

Rules

106×	`times-frac`
103×	`add-cbrt-cube` `add-exp-log`
62×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
43×	`prod-exp` `cbrt-unprod`
33×	`cbrt-undiv` `div-exp`
26×	`associate-/r*`
18×	`pow1`
9×	`pow-prod-down`
8×	`div-inv`
6×	`associate-r`
5×	`associate-*l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-*r/`
2×	`clear-num` `frac-2neg` `associate-l` `associate-/r/` `*-commutative` `fma-udef` `associate-/l/`
1×	`distribute-rgt-in` `distribute-lft-in` `tan-quot`

Counts

4 → 197

Calls

4 calls:

89.0ms	(* (* t (/ (tan k) (/ l t))) (sin k))
12.0ms	(/ (tan k) (/ l t))
241.0ms	(/ (* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2)) (/ l t))
225.0ms	(* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

series1.1s

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (* t (/ (tan k) (/ l t))) (sin k))
184.0ms	(/ (tan k) (/ l t))
363.0ms	(/ (* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2)) (/ l t))
385.0ms	(* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

simplify2.8s

Counts

209 → 209

Iterations

Iter	Nodes
done	5002
2	4720
1	1073
0	367

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.6b

localize39.0ms

Local error

Found 4 expressions with local error:

1.9b	(/ (tan k) (/ l t))
2.2b	(* t (* (fma (/ k t) (/ k t) 2) (sin k)))
4.4b	(* (/ (tan k) (/ l t)) (* t (* (fma (/ k t) (/ k t) 2) (sin k))))
5.8b	(/ (* (/ (tan k) (/ l t)) (* t (* (fma (/ k t) (/ k t) 2) (sin k)))) (/ l t))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

172×	`times-frac`
154×	`add-cbrt-cube` `add-exp-log`
96×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
60×	`cbrt-undiv` `div-exp`
57×	`prod-exp` `cbrt-unprod`
47×	`associate-l`
26×	`associate-/r*`
18×	`pow1`
12×	`div-inv`
9×	`pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-/r/`
2×	`clear-num` `frac-2neg` `associate-r` `associate-l/` `-commutative` `associate-/l/`
1×	`tan-quot`

Counts

4 → 255

Calls

4 calls:

10.0ms	(/ (tan k) (/ l t))
31.0ms	(* t (* (fma (/ k t) (/ k t) 2) (sin k)))
119.0ms	(* (/ (tan k) (/ l t)) (* t (* (fma (/ k t) (/ k t) 2) (sin k))))
74.0ms	(/ (* (/ (tan k) (/ l t)) (* t (* (fma (/ k t) (/ k t) 2) (sin k)))) (/ l t))

series1.1s

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (tan k) (/ l t))
113.0ms	(* t (* (fma (/ k t) (/ k t) 2) (sin k)))
447.0ms	(* (/ (tan k) (/ l t)) (* t (* (fma (/ k t) (/ k t) 2) (sin k))))
398.0ms	(/ (* (/ (tan k) (/ l t)) (* t (* (fma (/ k t) (/ k t) 2) (sin k)))) (/ l t))

simplify1.9s

Counts

267 → 267

Iterations

Iter	Nodes
done	5001
1	1268
0	399

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.6b

localize48.0ms

Local error

Found 4 expressions with local error:

1.9b	(/ (tan k) (/ l t))
4.4b	(* (/ (tan k) (/ l t)) (fma 2 (* t (sin k)) (/ (sin k) (/ t (* k k)))))
5.8b	(/ (* (/ (tan k) (/ l t)) (fma 2 (* t (sin k)) (/ (sin k) (/ t (* k k))))) (/ l t))
6.3b	(/ t (* k k))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
107×	`add-sqr-sqrt`
98×	`*-un-lft-identity` `add-cube-cbrt`
55×	`add-cbrt-cube` `add-exp-log`
44×	`associate-l`
27×	`associate-/r*`
26×	`cbrt-undiv` `div-exp`
13×	`div-inv`
10×	`prod-exp` `cbrt-unprod`
7×	`associate-/l*`
6×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `associate-/r/` `unswap-sqr`
2×	`associate-*l/` `fma-udef` `associate-/l/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `tan-quot` `*-commutative`

Counts

4 → 227

Calls

4 calls:

10.0ms	(/ (tan k) (/ l t))
50.0ms	(* (/ (tan k) (/ l t)) (fma 2 (* t (sin k)) (/ (sin k) (/ t (* k k)))))
46.0ms	(/ (* (/ (tan k) (/ l t)) (fma 2 (* t (sin k)) (/ (sin k) (/ t (* k k))))) (/ l t))
17.0ms	(/ t (* k k))

series1.1s

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (tan k) (/ l t))
482.0ms	(* (/ (tan k) (/ l t)) (fma 2 (* t (sin k)) (/ (sin k) (/ t (* k k)))))
455.0ms	(/ (* (/ (tan k) (/ l t)) (fma 2 (* t (sin k)) (/ (sin k) (/ t (* k k))))) (/ l t))
47.0ms	(/ t (* k k))

simplify2.8s

Counts

239 → 239

Iterations

Iter	Nodes
done	5000
2	4561
1	1101
0	379

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.6b

regimes533.0ms

Accuracy

55.4% (3.0b remaining)

Error of 9.0b against oracle of 6.0b and baseline of 12.7b

bsearch1.1s

Steps

Iters	Range		Point
9	1.100684037778415e-69	4.5468638315011444e-64	3.5056626454071755e-65
9	-1.8897009332101446e-61	-5.146057068734745e-67	-5.032269741332676e-63

simplify21.0ms

Iterations

Iter	Nodes
done	54
1	54
0	45

end0.0ms

sample10.7s

Algorithm

intervals

Results

4.1s	2057×	body	1280	valid
2.6s	5938×	body	80	valid
2.3s	1715×	body	640	valid
1.1s	823×	body	320	valid
228.0ms	463×	body	160	valid