Details

sample1.1s

Algorithm

intervals

Results

545.0ms	63×	body	640	valid
414.0ms	114×	body	1280	valid
38.0ms	32×	body	320	valid
12.0ms	40×	body	80	valid
6.0ms	7×	body	160	valid

simplify62.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	64
3	64
2	59
1	36
0	22

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin delta) (* (cos phi1) (sin theta)))
0.3b	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
0.4b	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`*-commutative`
1×	`asin-acos` `sub-neg` `flip3--` `diff-log` `flip--` `sin-mult` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

35.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
19.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
1.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
6.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series611.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
228.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
13.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
277.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify2.7s

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
3	3391
2	995
1	370
0	166

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (sin delta)) (sin theta))
0.3b	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
0.4b	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`*-commutative`
1×	`asin-acos` `sub-neg` `flip3--` `diff-log` `flip--` `sin-mult` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

31.0ms	(* (* (cos phi1) (sin delta)) (sin theta))
10.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
1.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
6.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

series596.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (* (cos phi1) (sin delta)) (sin theta))
248.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
8.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
245.0ms	(- (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))

simplify3.0s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
3	4152
2	1115
1	381
0	167

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize93.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (sin delta)) (sin theta))
0.3b	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
0.4b	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
0.6b	(- (cos delta) (expm1 (log1p (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg`
2×	`*-commutative`
1×	`asin-acos` `sub-neg` `flip3--` `diff-log` `flip--` `sin-mult` `distribute-lft-out--` `expm1-udef` `associate--r-` `difference-of-squares` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

50.0ms	(* (* (cos phi1) (sin delta)) (sin theta))
11.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
1.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
7.0ms	(- (cos delta) (expm1 (log1p (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))

series682.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (* (cos phi1) (sin delta)) (sin theta))
219.0ms	(* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))
8.0ms	(asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))
339.0ms	(- (cos delta) (expm1 (log1p (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))

simplify3.3s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
3	4334
2	1116
1	420
0	190

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize299.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (pow (cos delta) 3) (pow (expm1 (log1p (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) 3))
0.4b	(pow (cos delta) 3)
0.4b	(* (expm1 (log1p (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))
0.5b	(pow (expm1 (log1p (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) 3)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

144×	`prod-diff`
115×	`add-sqr-sqrt`
99×	`*-un-lft-identity`
93×	`unpow-prod-down` `cube-prod`
89×	`add-cube-cbrt`
35×	`sqr-pow`
27×	`cube-mult` `unpow3`
16×	`difference-of-squares`
13×	`pow1`
12×	`fma-neg`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow-unpow` `add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`pow-to-exp` `pow-pow` `pow-exp` `rem-cube-cbrt`
1×	`pow2` `difference-cubes` `sub-neg` `pow-plus` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `unswap-sqr`

Counts

4 → 269

Calls

4 calls:

40.0ms	(- (pow (cos delta) 3) (pow (expm1 (log1p (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) 3))
3.0ms	(pow (cos delta) 3)
6.0ms	(* (expm1 (log1p (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))
2.0ms	(pow (expm1 (log1p (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) 3)

series2.1s

Counts

4 → 12

Calls

4 calls:

1.2s	(- (pow (cos delta) 3) (pow (expm1 (log1p (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) 3))
34.0ms	(pow (cos delta) 3)
367.0ms	(* (expm1 (log1p (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (expm1 (log1p (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))))
524.0ms	(pow (expm1 (log1p (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) 3)

simplify3.4s

Counts

281 → 281

Iterations

Iter	Nodes
done	5001
2	3204
1	977
0	354

prune3.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes1.4s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify17.0ms

Iterations

Iter	Nodes
done	44
1	44
0	34

end0.0ms

sample19.1s

Algorithm

intervals

Results

11.9s	3049×	body	1280	valid
4.0s	1975×	body	640	valid
1.3s	724×	body	320	valid
710.0ms	1956×	body	80	valid
606.0ms	296×	body	160	valid