Details

sample420.0ms

Algorithm

intervals

Results

272.0ms	114×	body	1280	valid
72.0ms	50×	body	640	valid
18.0ms	18×	body	320	valid
15.0ms	60×	body	80	valid
7.0ms	14×	body	160	valid

simplify73.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--` `sin-mult`

Counts

4 → 57

Calls

4 calls:

14.0ms	(* (cos phi1) (sin delta))
14.0ms	(* (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)))))))

series489.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (cos phi1) (sin delta))
177.0ms	(* (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))))
250.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify2.6s

Counts

69 → 69

Iterations

Useful iterations: 3 (698.0ms)

Iter	Nodes	Cost
0	138	1438
1	294	1371
2	754	1238
3	1829	1232
done	5000	1232

prune621.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize74.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
0.4b	(pow (cos delta) 3)
0.5b	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `difference-of-squares` `sqr-pow`
6×	`unpow-prod-down` `pow-unpow` `cube-prod` `add-log-exp`
3×	`pow-pow` `pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `unpow3`
1×	`difference-cubes` `cube-div` `sub-neg` `asin-acos` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `sin-mult` `distribute-lft-out--`

Counts

4 → 76

Calls

4 calls:

4.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
32.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
4.0ms	(pow (cos delta) 3)
11.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series1.6s

Counts

4 → 12

Calls

4 calls:

16.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.2s	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
47.0ms	(pow (cos delta) 3)
405.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify1.5s

Counts

88 → 88

Iterations

Useful iterations: 2 (379.0ms)

Iter	Nodes	Cost
0	188	2316
1	490	2102
2	1891	1964
done	5000	1964

prune917.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize104.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos delta) 3)
0.4b	(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
2.8b	(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`pow-unpow` `add-log-exp`
4×	`unpow-prod-down` `cube-prod`
3×	`pow-pow` `pow-exp` `rem-cube-cbrt`
2×	`acos-asin` `cube-mult` `pow-to-exp` `unpow3` `difference-of-squares` `sqr-pow`
1×	`cube-div` `sub-neg` `flip3--` `times-frac` `diff-log` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `sin-mult` `distribute-lft-out--` `associate--r-`

Counts

4 → 70

Calls

4 calls:

3.0ms	(pow (cos delta) 3)
2.0ms	(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
11.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
35.0ms	(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

series540.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(pow (cos delta) 3)
16.0ms	(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
427.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
50.0ms	(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

simplify4.0s

Counts

82 → 82

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	141	1604
1	323	1467
2	887	1347
3	4732	1337
done	5001	1337

prune866.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cbrt-prod` `pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 39

Calls

4 calls:

14.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (* (cbrt (* (cos phi1) (sin delta))) (cbrt (* (cos phi1) (sin delta)))) (cbrt (* (cos phi1) (sin delta)))) (cos theta)))))))
11.0ms	(cbrt (* (cos phi1) (sin delta)))
10.0ms	(cbrt (* (cos phi1) (sin delta)))
16.0ms	(cbrt (* (cos phi1) (sin delta)))

series620.0ms

Counts

4 → 12

Calls

4 calls:

279.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (* (cbrt (* (cos phi1) (sin delta))) (cbrt (* (cos phi1) (sin delta)))) (cbrt (* (cos phi1) (sin delta)))) (cos theta)))))))
125.0ms	(cbrt (* (cos phi1) (sin delta)))
101.0ms	(cbrt (* (cos phi1) (sin delta)))
114.0ms	(cbrt (* (cos phi1) (sin delta)))

simplify4.1s

Counts

51 → 51

Iterations

Useful iterations: 4 (1.9s)

Iter	Nodes	Cost
0	83	1143
1	195	1091
2	478	777
3	1338	711
4	4635	708
done	5000	708

prune424.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes524.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	37	90
1	49	90
done	49	90

end0.0ms

sample10.6s

Algorithm

intervals

Results

6.4s	3138×	body	1280	valid
2.6s	1860×	body	640	valid
499.0ms	651×	body	320	valid
418.0ms	2048×	body	80	valid
149.0ms	303×	body	160	valid