Details

sample647.0ms

Algorithm

intervals

Results

342.0ms	91×	body	1280	valid
136.0ms	67×	body	640	valid
88.0ms	67×	body	80	valid
35.0ms	20×	body	320	valid
10.0ms	11×	body	160	valid

simplify35.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	55
3	55
2	54
1	35
0	22

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize160.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

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`
4×	`insert-posit16`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`asin-acos` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 62

Calls

4 calls:

12.0ms	(* (sin theta) (sin delta))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
32.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
13.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series606.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (sin theta) (sin delta))
13.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
227.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
306.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify2.3s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
3	2286
2	739
1	317
0	148

prune850.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize109.0ms

Local error

Found 4 expressions with local error:

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

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
20×	`add-cbrt-cube` `add-exp-log`
18×	`add-sqr-sqrt` `pow-prod-down`
10×	`*-un-lft-identity`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `difference-of-squares` `sqr-pow`
6×	`pow-unpow` `unpow-prod-down` `cube-prod` `add-log-exp`
5×	`sin-mult`
4×	`pow-sqr` `pow-prod-up` `insert-posit16`
3×	`pow-pow` `pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `pow-plus` `unpow3`
1×	`cube-div` `pow2` `frac-times` `difference-cubes` `sub-neg` `flip3--` `diff-log` `swap-sqr` `associate-r` `associate-l` `associate-l/` `associate-r/` `*-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 109

Calls

4 calls:

38.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
79.0ms	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
4.0ms	(pow (cos delta) 3)
27.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series2.5s

Counts

4 → 12

Calls

4 calls:

1.8s	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
262.0ms	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
29.0ms	(pow (cos delta) 3)
347.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify2.9s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	2951
1	751
0	240

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize339.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (sin phi1) (sin phi1)) (* (sin phi1) (sin phi1)))
0.4b	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.5b	(pow (sin phi1) 5)
0.5b	(pow (sin phi1) 5)

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

156×	`pow1`
40×	`pow-prod-down` `pow-prod-up`
30×	`add-exp-log`
28×	`add-cbrt-cube`
26×	`pow-sqr`
20×	`pow-plus`
16×	`prod-exp` `cbrt-unprod`
14×	`pow2`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `sin-mult`
6×	`pow-unpow` `unpow-prod-down`
4×	`insert-posit16` `add-log-exp`
2×	`frac-times` `pow-to-exp` `pow-pow` `swap-sqr` `associate-r` `associate-l` `associate-l/` `pow-exp` `associate-r/` `*-commutative` `sqr-pow`
1×	`unswap-sqr`

Counts

4 → 141

Calls

4 calls:

58.0ms	(* (* (sin phi1) (sin phi1)) (* (sin phi1) (sin phi1)))
90.0ms	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
7.0ms	(pow (sin phi1) 5)
7.0ms	(pow (sin phi1) 5)

series444.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* (sin phi1) (sin phi1)) (* (sin phi1) (sin phi1)))
263.0ms	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
80.0ms	(pow (sin phi1) 5)
51.0ms	(pow (sin phi1) 5)

simplify3.0s

Counts

153 → 153

Iterations

Iter	Nodes
done	5000
3	3678
2	1319
1	485
0	169

prune2.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize396.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (- (* (* (cos delta) (cos delta)) (cos delta)) (* (* (* (* (sin delta) (sin delta)) (sin delta)) (* (* (cos theta) (* (cos theta) (cos theta))) (* (* (sin phi1) (sin phi1)) (sin phi1)))) (* (cos phi1) (* (cos phi1) (cos phi1))))) (+ (* (* (cos theta) (* (cos phi1) (* (cos delta) (cos delta)))) (* (sin delta) (pow (sin phi1) 5))) (* (* (* (* (sin phi1) (sin phi1)) (* (sin phi1) (sin phi1))) (* (sin phi1) (sin phi1))) (* (* (cos delta) (cos delta)) (cos delta)))))
0.4b	(* (* (sin phi1) (sin phi1)) (* (sin phi1) (sin phi1)))
0.5b	(pow (sin phi1) 5)
0.5b	(pow (sin phi1) 5)

rewrite18.5s

Algorithm

rewrite-expression-head

Rules

2136×	`associate-*l/`
1618×	`associate-*r/`
1335×	`cos-mult`
967×	`sin-mult`
767×	`frac-times`
676×	`frac-sub`
379×	`frac-add`
132×	`sub-div`
117×	`pow1`
36×	`pow-prod-up`
23×	`pow-prod-down`
22×	`pow-sqr`
21×	`flip3-+` `flip-+`
18×	`pow-plus` `flip3--` `add-exp-log` `flip--`
16×	`add-cbrt-cube` `add-log-exp`
13×	`pow2`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`prod-exp` `add-cube-cbrt` `cbrt-unprod`
6×	`pow-unpow` `unpow-prod-down` `diff-log`
4×	`insert-posit16`
2×	`pow-to-exp` `sum-log` `sub-neg` `pow-pow` `pow-exp` `associate--l+` `sqr-pow`
1×	`associate--l-` `swap-sqr` `associate-r` `associate-l` `*-commutative` `associate--r+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 546

Calls

4 calls:

18.2s	(- (- (* (* (cos delta) (cos delta)) (cos delta)) (* (* (* (* (sin delta) (sin delta)) (sin delta)) (* (* (cos theta) (* (cos theta) (cos theta))) (* (* (sin phi1) (sin phi1)) (sin phi1)))) (* (cos phi1) (* (cos phi1) (cos phi1))))) (+ (* (* (cos theta) (* (cos phi1) (* (cos delta) (cos delta)))) (* (sin delta) (pow (sin phi1) 5))) (* (* (* (* (sin phi1) (sin phi1)) (* (sin phi1) (sin phi1))) (* (sin phi1) (sin phi1))) (* (* (cos delta) (cos delta)) (cos delta)))))
77.0ms	(* (* (sin phi1) (sin phi1)) (* (sin phi1) (sin phi1)))
3.0ms	(pow (sin phi1) 5)
7.0ms	(pow (sin phi1) 5)

series846.0ms

Counts

4 → 12

Calls

4 calls:

646.0ms	(- (- (* (* (cos delta) (cos delta)) (cos delta)) (* (* (* (* (sin delta) (sin delta)) (sin delta)) (* (* (cos theta) (* (cos theta) (cos theta))) (* (* (sin phi1) (sin phi1)) (sin phi1)))) (* (cos phi1) (* (cos phi1) (cos phi1))))) (+ (* (* (cos theta) (* (cos phi1) (* (cos delta) (cos delta)))) (* (sin delta) (pow (sin phi1) 5))) (* (* (* (* (sin phi1) (sin phi1)) (* (sin phi1) (sin phi1))) (* (sin phi1) (sin phi1))) (* (* (cos delta) (cos delta)) (cos delta)))))
54.0ms	(* (* (sin phi1) (sin phi1)) (* (sin phi1) (sin phi1)))
66.0ms	(pow (sin phi1) 5)
80.0ms	(pow (sin phi1) 5)

simplify8.0s

Counts

558 → 558

Iterations

Iter	Nodes
done	5002
1	4218
0	1096

prune12.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes1.2s

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify63.0ms

Iterations

Iter	Nodes
done	130
1	130
0	83

end0.0ms

sample20.6s

Algorithm

intervals

Results

13.2s	3092×	body	1280	valid
4.7s	1841×	body	640	valid
994.0ms	719×	body	320	valid
933.0ms	2026×	body	80	valid
295.0ms	322×	body	160	valid