Details

sample393.0ms

Algorithm

intervals

Results

134.0ms	63×	body	1280	valid
95.0ms	52×	body	640	valid
93.0ms	180×	body	80	valid
41.0ms	40×	body	320	valid
10.0ms	16×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

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

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.8b

localize46.0ms

Local error

Found 4 expressions with local error:

1.3b	(/ t (* (/ l t) (/ l t)))
2.5b	(* (/ t (* (/ l t) (/ l t))) (sin k))
3.1b	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
17.7b	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

rewrite729.0ms

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:

18.0ms	(/ t (* (/ l t) (/ l t)))
60.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
133.0ms	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
515.0ms	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

series946.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ t (* (/ l t) (/ l t)))
121.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
226.0ms	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
544.0ms	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

simplify1.2s

Counts

158 → 158

Iterations

Iter	Nodes
done	2000
2	2000
1	672
0	235

prune2.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 1 (/ l t))
2.9b	(* (/ t (/ l t)) (sin k))
3.1b	(* (* (/ 1 (/ l t)) (* (/ t (/ l t)) (sin k))) (tan k))
17.7b	(* (* (* (/ 1 (/ l t)) (* (/ t (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

rewrite894.0ms

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:

7.0ms	(/ 1 (/ l t))
19.0ms	(* (/ t (/ l t)) (sin k))
169.0ms	(* (* (/ 1 (/ l t)) (* (/ t (/ l t)) (sin k))) (tan k))
693.0ms	(* (* (* (/ 1 (/ l t)) (* (/ t (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

series763.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ 1 (/ l t))
119.0ms	(* (/ t (/ l t)) (sin k))
221.0ms	(* (* (/ 1 (/ l t)) (* (/ t (/ l t)) (sin k))) (tan k))
410.0ms	(* (* (* (/ 1 (/ l t)) (* (/ t (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

simplify1.5s

Counts

299 → 299

Iterations

Iter	Nodes
done	2001
2	2001
1	1408
0	490

prune4.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2 (/ (* (/ (* (sin k) t) (/ l t)) (* (fma (/ k t) (/ k t) 2) (tan k))) (/ l t)))
1.0b	(/ (* (sin k) t) (/ l t))
7.2b	(/ (* (/ (* (sin k) t) (/ l t)) (* (fma (/ k t) (/ k t) 2) (tan k))) (/ l t))
15.6b	(* (/ (* (sin k) t) (/ l t)) (* (fma (/ k t) (/ k t) 2) (tan k)))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

315×	`add-cbrt-cube` `add-exp-log`
226×	`times-frac`
155×	`cbrt-undiv` `div-exp`
97×	`prod-exp` `cbrt-unprod`
91×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
44×	`associate-/r*`
18×	`associate-l`
17×	`div-inv`
9×	`pow1`
8×	`associate-/r/`
6×	`associate-*r/`
5×	`associate-/l*`
4×	`expm1-log1p-u` `tan-quot` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `associate-/l/`
2×	`frac-times` `associate-*l/`
1×	`associate-r` `*-commutative`

Counts

4 → 327

Calls

4 calls:

40.0ms	(/ 2 (/ (* (/ (* (sin k) t) (/ l t)) (* (fma (/ k t) (/ k t) 2) (tan k))) (/ l t)))
28.0ms	(/ (* (sin k) t) (/ l t))
64.0ms	(/ (* (/ (* (sin k) t) (/ l t)) (* (fma (/ k t) (/ k t) 2) (tan k))) (/ l t))
61.0ms	(* (/ (* (sin k) t) (/ l t)) (* (fma (/ k t) (/ k t) 2) (tan k)))

series1.6s

Counts

4 → 12

Calls

4 calls:

870.0ms	(/ 2 (/ (* (/ (* (sin k) t) (/ l t)) (* (fma (/ k t) (/ k t) 2) (tan k))) (/ l t)))
125.0ms	(/ (* (sin k) t) (/ l t))
334.0ms	(/ (* (/ (* (sin k) t) (/ l t)) (* (fma (/ k t) (/ k t) 2) (tan k))) (/ l t))
301.0ms	(* (/ (* (sin k) t) (/ l t)) (* (fma (/ k t) (/ k t) 2) (tan k)))

simplify1.6s

Counts

339 → 339

Iterations

Iter	Nodes
done	2001
2	2001
1	1654
0	523

prune5.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.5b

localize71.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 2 (/ (* t (sin k)) (/ l t)))
1.0b	(/ (* t (sin k)) (/ l t))
11.4b	(/ (* (fma (/ k t) (/ k t) 2) (tan k)) (/ l t))
13.0b	(/ (/ 2 (/ (* t (sin k)) (/ l t))) (/ (* (fma (/ k t) (/ k t) 2) (tan k)) (/ l t)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

4866×	`times-frac`
1380×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
269×	`div-inv`
219×	`add-cbrt-cube` `add-exp-log`
144×	`cbrt-undiv` `div-exp` `associate-/r/`
64×	`associate-/l*`
62×	`associate-/r*`
28×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-/l/`
1×	`tan-quot` `associate-*r/`

Counts

4 → 1412

Calls

4 calls:

10.0ms	(/ 2 (/ (* t (sin k)) (/ l t)))
22.0ms	(/ (* t (sin k)) (/ l t))
29.0ms	(/ (* (fma (/ k t) (/ k t) 2) (tan k)) (/ l t))
49.0ms	(/ (/ 2 (/ (* t (sin k)) (/ l t))) (/ (* (fma (/ k t) (/ k t) 2) (tan k)) (/ l t)))

series1.0s

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ 2 (/ (* t (sin k)) (/ l t)))
83.0ms	(/ (* t (sin k)) (/ l t))
213.0ms	(/ (* (fma (/ k t) (/ k t) 2) (tan k)) (/ l t))
630.0ms	(/ (/ 2 (/ (* t (sin k)) (/ l t))) (/ (* (fma (/ k t) (/ k t) 2) (tan k)) (/ l t)))

simplify2.5s

Counts

1424 → 1424

Iterations

Iter	Nodes
done	2537
0	2537

prune25.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.5b

regimes583.0ms

Accuracy

57.6% (2.6b remaining)

Error of 9.1b against oracle of 6.6b and baseline of 12.6b

bsearch734.0ms

Steps

Iters	Range		Point
9	5.6676831206187345e-114	1.7939671322110348e-104	1.1003810475973448e-104
8	-2.7456529084332178e-33	-7.931866077960998e-37	-8.448835479690807e-37

simplify8.0ms

Iterations

Iter	Nodes
done	44
1	44
0	35

end0.0ms

sample15.1s

Algorithm

intervals

Results

6.6s	2142×	body	1280	valid
3.5s	1657×	body	640	valid
2.5s	5953×	body	80	valid
1.3s	892×	body	320	valid
811.0ms	423×	body	160	valid