Details

sample655.0ms

Algorithm

intervals

Results

391.0ms	107×	body	1280	valid
103.0ms	60×	body	640	valid
29.0ms	25×	body	320	valid
18.0ms	58×	body	80	valid
11.0ms	6×	body	160	valid

simplify66.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	33
1	35	33
2	56	33
3	60	33
done	60	33

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize98.0ms

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)))))))

rewrite75.0ms

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

Counts

4 → 58

Calls

4 calls:

25.0ms	(* (sin theta) (sin delta))
28.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
4.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
15.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series636.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (sin theta) (sin delta))
231.0ms	(* (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))))
303.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify862.0ms

Counts

70 → 70

Iterations

Useful iterations: done (856.0ms)

Iter	Nodes	Cost
0	139	1435
1	301	1369
2	1072	1231
done	5001	1229

prune573.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize119.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b	(- (* (cos delta) (cos delta)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))

rewrite71.0ms

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` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l` `sin-mult`
2×	`asin-acos` `associate-*l/` `cos-mult`
1×	`pow2` `sub-neg` `sqr-cos` `flip3--` `pow-plus` `diff-log` `pow-prod-down` `prod-exp` `associate--l+` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub` `flip--` `cbrt-unprod` `sqr-sin` `sub-div` `unswap-sqr`

Counts

4 → 58

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))))
21.0ms	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
43.0ms	(- (* (cos delta) (cos delta)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))

series1.0s

Counts

4 → 12

Calls

4 calls:

15.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
16.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
227.0ms	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
748.0ms	(- (* (cos delta) (cos delta)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))

simplify1.3s

Counts

70 → 70

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	146	2808
1	414	2451
2	1989	2065
done	5000	1694

prune917.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize97.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

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))))
48.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
13.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series1.6s

Counts

4 → 12

Calls

4 calls:

24.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
17.0ms	(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))
395.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify1.4s

Counts

73 → 73

Iterations

Useful iterations: 2 (427.0ms)

Iter	Nodes	Cost
0	169	2354
1	494	2188
2	2306	2022
done	5000	2022

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize95.0ms

Local error

Found 4 expressions with local error:

0.4b	(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
0.5b	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
4.5b	(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

4.0ms	(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
36.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
24.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
34.0ms	(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

9.0ms	(acos (+ (* (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))
390.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
46.0ms	(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

simplify1.9s

Counts

81 → 81

Iterations

Useful iterations: 2 (506.0ms)

Iter	Nodes	Cost
0	201	2693
1	571	2474
2	2549	2330
done	5001	2330

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes593.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify14.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	67	144
1	96	144
done	96	144

end0.0ms

sample19.1s

Algorithm

intervals

Results

12.5s	3241×	body	1280	valid
4.0s	1770×	body	640	valid
903.0ms	1993×	body	80	valid
786.0ms	695×	body	320	valid
191.0ms	301×	body	160	valid