Details

sample643.0ms

Algorithm

intervals

Results

345.0ms	114×	body	1280	valid
219.0ms	63×	body	640	valid
33.0ms	32×	body	320	valid
13.0ms	40×	body	80	valid
4.0ms	7×	body	160	valid

simplify26.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	62
3	62
2	56
1	35
0	22

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize93.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

18.0ms	(* (sin theta) (sin delta))
10.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series590.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sin theta) (sin delta))
246.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
16.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
262.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.6s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
2	1120
1	312
0	144

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize263.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
0.4b	(* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))
0.6b	(- (cos delta) (cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1))))))
17.5b	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1`
17×	`pow-prod-down`
16×	`add-cbrt-cube` `add-exp-log` `sin-mult`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-div`
6×	`add-sqr-sqrt` `frac-times` `-un-lft-identity` `associate-r/` `add-log-exp`
4×	`associate-*l/` `pow-sqr` `pow-prod-up` `add-cube-cbrt`
2×	`pow-plus`
1×	`cbrt-prod` `pow2` `asin-acos` `sub-neg` `flip3--` `pow1/3` `diff-log` `cube-unmult` `swap-sqr` `associate-r` `associate-l` `*-commutative` `rem-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 76

Calls

4 calls:

3.0ms	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
73.0ms	(* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))
11.0ms	(- (cos delta) (cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1))))))
153.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

series783.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
239.0ms	(* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))
282.0ms	(- (cos delta) (cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1))))))
254.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

simplify2.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	1611
1	378
0	164

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize831.0ms

Local error

Found 4 expressions with local error:

17.5b	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
17.5b	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
17.5b	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
17.5b	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

rewrite555.0ms

Algorithm

rewrite-expression-head

Rules

48×	`sin-mult`
28×	`cbrt-div`
20×	`frac-times` `associate-*r/`
12×	`associate-*l/`
4×	`cbrt-prod` `add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `pow1/3` `cube-unmult` `add-exp-log` `add-cube-cbrt` `rem-cbrt-cube` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

120.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
176.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
126.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
131.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

series989.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
242.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
265.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
221.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

simplify2.5s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
4	2103
3	774
2	286
1	128
0	63

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize719.0ms

Local error

Found 4 expressions with local error:

17.5b	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
17.5b	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
17.5b	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
17.5b	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

rewrite606.0ms

Algorithm

rewrite-expression-head

Rules

48×	`sin-mult`
28×	`cbrt-div`
20×	`frac-times` `associate-*r/`
12×	`associate-*l/`
4×	`cbrt-prod` `add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `pow1/3` `cube-unmult` `add-exp-log` `add-cube-cbrt` `rem-cbrt-cube` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

128.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
174.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
149.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
152.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

259.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
306.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
245.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))
218.0ms	(cbrt (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)) (* (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))) (sin phi1)))))

simplify2.5s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
4	2103
3	774
2	286
1	128
0	63

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes1.2s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify27.0ms

Iterations

Iter	Nodes
done	53
1	53
0	39

end0.0ms

sample20.3s

Algorithm

intervals

Results

11.8s	3049×	body	1280	valid
5.1s	1975×	body	640	valid
1.3s	724×	body	320	valid
909.0ms	1956×	body	80	valid
710.0ms	296×	body	160	valid