Details

sample956.0ms

Algorithm

intervals

Results

748.0ms	108×	body	1280	valid
117.0ms	57×	body	640	valid
23.0ms	17×	body	320	valid
20.0ms	65×	body	80	valid
7.0ms	9×	body	160	valid

simplify31.0ms

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize75.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

36.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
19.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))
5.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta))))))))

series645.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
234.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))))
9.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))
291.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta))))))))

simplify915.0ms

Counts

69 → 69

Iterations

Iter	Nodes
done	5001
2	1214
1	328
0	149

prune759.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-log-exp`
3×	`associate-l/` `-commutative`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `cos-mult` `flip-+` `flip--` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

41.0ms	(* (* (cos theta) (cos phi1)) (sin delta))
42.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
113.0ms	(* (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (cos delta) (sin phi1))) (sin phi1))
11.0ms	(- (cos delta) (* (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (cos delta) (sin phi1))) (sin phi1)))

series825.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (* (cos theta) (cos phi1)) (sin delta))
104.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
276.0ms	(* (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (cos delta) (sin phi1))) (sin phi1))
312.0ms	(- (cos delta) (* (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (cos delta) (sin phi1))) (sin phi1)))

simplify1.3s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	2371
1	421
0	161

prune749.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin delta) (* (cos phi1) (sin theta)))
0.2b	(* (+ (log (pow (pow (exp (sin delta)) (cos phi1)) (cos theta))) (* (cos delta) (sin phi1))) (sin phi1))
0.4b	(- (cos delta) (* (+ (log (pow (pow (exp (sin delta)) (cos phi1)) (cos theta))) (* (cos delta) (sin phi1))) (sin phi1)))
3.4b	(log (pow (pow (exp (sin delta)) (cos phi1)) (cos theta)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log`
12×	`add-sqr-sqrt`
11×	`pow1` `log-prod` `add-cbrt-cube`
10×	`unpow-prod-down` `*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l` `add-log-exp`
5×	`rem-log-exp`
4×	`associate-r` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod`
2×	`pow-to-exp` `associate-l/` `-commutative` `sqr-pow`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `log-pow` `flip-+` `flip--` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

20.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
30.0ms	(* (+ (log (pow (pow (exp (sin delta)) (cos phi1)) (cos theta))) (* (cos delta) (sin phi1))) (sin phi1))
12.0ms	(- (cos delta) (* (+ (log (pow (pow (exp (sin delta)) (cos phi1)) (cos theta))) (* (cos delta) (sin phi1))) (sin phi1)))
12.0ms	(log (pow (pow (exp (sin delta)) (cos phi1)) (cos theta)))

series1.0s

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (sin delta) (* (cos phi1) (sin theta)))
362.0ms	(* (+ (log (pow (pow (exp (sin delta)) (cos phi1)) (cos theta))) (* (cos delta) (sin phi1))) (sin phi1))
321.0ms	(- (cos delta) (* (+ (log (pow (pow (exp (sin delta)) (cos phi1)) (cos theta))) (* (cos delta) (sin phi1))) (sin phi1)))
219.0ms	(log (pow (pow (exp (sin delta)) (cos phi1)) (cos theta)))

simplify1.3s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	2144
1	450
0	186

prune877.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta))))
0.3b	(* (cos delta) (cos delta))
0.3b	(- (* (cos delta) (cos delta)) (* (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta))) (* (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta))) (pow (sin phi1) 2))))
0.3b	(/ (- (* (cos delta) (cos delta)) (* (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta))) (* (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta))) (pow (sin phi1) 2)))) (+ (* (sin phi1) (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta)))) (cos delta)))

rewrite605.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
18×	`*-un-lft-identity` `add-cube-cbrt`
17×	`cos-mult`
16×	`associate-*l/` `frac-sub`
14×	`flip3-+` `flip-+`
13×	`pow1`
10×	`add-cbrt-cube` `add-exp-log` `associate-/l/`
9×	`times-frac`
8×	`frac-times`
6×	`associate-r` `associate-l` `associate-*r/` `add-log-exp`
3×	`associate-/r` `swap-sqr` `associate-/l`
2×	`sqr-cos` `flip3--` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `pow-plus` `diff-log` `div-sub` `div-exp` `associate--l+` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 110

Calls

4 calls:

104.0ms	(* (sin phi1) (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta))))
16.0ms	(* (cos delta) (cos delta))
217.0ms	(- (* (cos delta) (cos delta)) (* (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta))) (* (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta))) (pow (sin phi1) 2))))
261.0ms	(/ (- (* (cos delta) (cos delta)) (* (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta))) (* (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta))) (pow (sin phi1) 2)))) (+ (* (sin phi1) (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta)))) (cos delta)))

series2.7s

Counts

4 → 12

Calls

4 calls:

260.0ms	(* (sin phi1) (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta))))
24.0ms	(* (cos delta) (cos delta))
983.0ms	(- (* (cos delta) (cos delta)) (* (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta))) (* (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta))) (pow (sin phi1) 2))))
1.5s	(/ (- (* (cos delta) (cos delta)) (* (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta))) (* (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta))) (pow (sin phi1) 2)))) (+ (* (sin phi1) (+ (* (cos theta) (* (cos phi1) (sin delta))) (* (sin phi1) (cos delta)))) (cos delta)))

simplify507.0ms

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
1	965
0	295

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes803.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	29
1	29
0	22

end0.0ms

sample21.2s

Algorithm

intervals

Results

12.3s	3053×	body	1280	valid
6.1s	1912×	body	640	valid
1.0s	700×	body	320	valid
820.0ms	2014×	body	80	valid
245.0ms	321×	body	160	valid