Details

sample268.0ms

Algorithm

intervals

Results

173.0ms	105×	body	1280	valid
46.0ms	53×	body	640	valid
13.0ms	24×	body	320	valid
10.0ms	64×	body	80	valid
4.0ms	10×	body	160	valid

simplify26.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	33
1	35	33
2	55	33
3	58	33
done	58	33

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

3.0ms	(sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
13.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series507.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
165.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
9.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
198.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify3.7s

Counts

60 → 60

Iterations

Useful iterations: 3 (413.0ms)

Iter	Nodes	Cost
0	112	1516
1	232	1446
2	547	1278
3	1451	1276
4	4423	1276
done	5001	1276

prune335.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (log (exp (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))))
0.4b	(- (cos delta) (* (sin phi1) (log (exp (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
3.6b	(log (exp (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `log-prod`
13×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-exp-log` `distribute-rgt-in` `exp-prod` `distribute-lft-in` `add-cbrt-cube` `associate--r+` `add-log-exp`
3×	`associate-l`
2×	`asin-acos`
1×	`sub-neg` `log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `sin-diff` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

20.0ms	(* (sin phi1) (log (exp (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
9.0ms	(- (cos delta) (* (sin phi1) (log (exp (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
8.0ms	(log (exp (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series502.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (sin phi1) (log (exp (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
9.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
197.0ms	(- (cos delta) (* (sin phi1) (log (exp (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
132.0ms	(log (exp (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.8s

Counts

82 → 82

Iterations

Useful iterations: 3 (450.0ms)

Iter	Nodes	Cost
0	147	2264
1	279	2063
2	647	1798
3	1632	1792
done	5001	1792

prune450.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(- (cos delta) (* (sin phi1) (log (exp (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
3.6b	(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
3.6b	(log (exp (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

30×	`log-prod`
13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`associate--r+`
9×	`sin-sum` `exp-sum`
8×	`log-pow`
6×	`pow1` `distribute-rgt-in` `exp-prod` `distribute-lft-in` `add-log-exp`
4×	`add-exp-log` `add-cbrt-cube`
3×	`log-div` `asin-acos` `exp-diff`
2×	`rem-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `sin-diff` `flip--`

Counts

4 → 67

Calls

4 calls:

2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
13.0ms	(- (cos delta) (* (sin phi1) (log (exp (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
6.0ms	(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
20.0ms	(log (exp (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series347.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
193.0ms	(- (cos delta) (* (sin phi1) (log (exp (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
9.0ms	(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
137.0ms	(log (exp (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify3.0s

Counts

79 → 79

Iterations

Useful iterations: 3 (307.0ms)

Iter	Nodes	Cost
0	181	2447
1	324	2173
2	622	1835
3	1567	1802
4	4931	1802
done	5001	1802

prune554.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`asin-acos` `swap-sqr` `associate-r` `associate-l`
1×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `sqr-sin` `sin-mult` `unswap-sqr`

Counts

4 → 51

Calls

4 calls:

2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
18.0ms	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series184.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
11.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
8.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
157.0ms	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify1.3s

Counts

63 → 63

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	71	1804
1	129	1608
2	249	1322
3	521	1140
4	1184	1122
done	5000	1099

prune402.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes319.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	37
1	34	37
done	34	37

end0.0ms

sample8.2s

Algorithm

intervals

Results

5.0s	3125×	body	1280	valid
1.8s	1728×	body	640	valid
476.0ms	782×	body	320	valid
336.0ms	2032×	body	80	valid
130.0ms	333×	body	160	valid