Details

sample589.0ms

Algorithm

intervals

Results

380.0ms	99×	body	1280	valid
106.0ms	57×	body	640	valid
36.0ms	27×	body	320	valid
22.0ms	68×	body	80	valid
4.0ms	5×	body	160	valid

simplify101.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	33
1	35	33
2	56	33
3	60	33
done	60	33

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize82.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.2b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--`

Counts

4 → 58

Calls

4 calls:

26.0ms	(* (sin theta) (sin delta))
48.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
4.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
14.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series625.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sin theta) (sin delta))
230.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
13.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
313.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify845.0ms

Counts

70 → 70

Iterations

Useful iterations: done (842.0ms)

Iter	Nodes	Cost
0	139	1435
1	301	1369
2	1072	1231
done	5001	1229

prune624.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize80.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.5b	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.5b	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.5b	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

24.0ms	(* (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
1.0ms	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

358.0ms	(* (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
354.0ms	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
353.0ms	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
388.0ms	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify5.0s

Counts

85 → 85

Iterations

Useful iterations: done (5.0s)

Iter	Nodes	Cost
0	87	2790
1	206	2598
2	746	2358
3	4111	2003
done	5002	1986

prune796.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize102.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (cos delta) (* (* (cbrt (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 2)) (sin phi1)) (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.4b	(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 2)
0.5b	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
4.9b	(cbrt (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 2))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

11×	`cbrt-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `add-log-exp`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube`
3×	`pow-unpow`
2×	`pow1/3` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--`

Counts

4 → 57

Calls

4 calls:

10.0ms	(- (cos delta) (* (* (cbrt (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 2)) (sin phi1)) (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
46.0ms	(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 2)
3.0ms	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
34.0ms	(cbrt (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 2))

series1.2s

Counts

4 → 12

Calls

4 calls:

330.0ms	(- (cos delta) (* (* (cbrt (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 2)) (sin phi1)) (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
239.0ms	(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 2)
376.0ms	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
302.0ms	(cbrt (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 2))

simplify906.0ms

Counts

69 → 69

Iterations

Useful iterations: done (895.0ms)

Iter	Nodes	Cost
0	142	2207
1	358	2086
2	1251	1838
done	5001	1825

prune800.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize147.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.5b	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
4.8b	(pow (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 2) 2/3)
4.9b	(cbrt (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 2))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod` `unpow-prod-down`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log`
4×	`pow1` `pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `pow1/3` `sqr-pow`
2×	`pow-to-exp` `unpow2`
1×	`pow-pow`

Counts

4 → 62

Calls

4 calls:

3.0ms	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
3.0ms	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
82.0ms	(pow (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 2) 2/3)
32.0ms	(cbrt (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 2))

series1.6s

Counts

4 → 12

Calls

4 calls:

456.0ms	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
411.0ms	(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
321.0ms	(pow (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 2) 2/3)
381.0ms	(cbrt (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 2))

simplify1.2s

Counts

74 → 74

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	129	1948
1	291	1790
2	1160	1654
done	5001	1641

prune851.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes746.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	157
1	58	157
done	58	157

end0.0ms

sample20.1s

Algorithm

intervals

Results

12.4s	3088×	body	1280	valid
4.5s	1863×	body	640	valid
1.4s	726×	body	320	valid
824.0ms	2010×	body	80	valid
312.0ms	313×	body	160	valid