Details

sample282.0ms

Algorithm

intervals

Results

173.0ms	100×	body	1280	valid
53.0ms	56×	body	640	valid
21.0ms	34×	body	320	valid
13.0ms	60×	body	80	valid
3.0ms	6×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	22
1	56	22
2	59	22
3	59	22

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

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:

4.0ms	(* (sin theta) (sin delta))
4.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series385.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin theta) (sin delta))
155.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
180.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify96.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	289	930
1	894	837
2	3513	835
3	5002	835

prune405.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (cos delta) (* (sin phi1) (sin (* (* (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
0.6b	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.6b	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.6b	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 45

Calls

4 calls:

2.0ms	(- (cos delta) (* (sin phi1) (sin (* (* (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
0.0ms	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.0ms	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
1.0ms	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(- (cos delta) (* (sin phi1) (sin (* (* (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
63.0ms	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
63.0ms	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
61.0ms	(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

simplify156.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 4 (146.0ms)

Iter	Nodes	Cost
0	166	1483
1	413	1333
2	1396	1327
3	4599	1327
4	5003	1324

prune442.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin phi1) 2)
0.3b	(* (sin theta) (sin delta))
0.3b	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
0.5b	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-exp-log`
15×	`add-cbrt-cube`
13×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt` `add-log-exp`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-l`
4×	`associate-r`
3×	`unpow-prod-down` `pow-unpow`
2×	`diff-log` `*-commutative`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `sin-mult` `associate--r+` `distribute-lft-out--` `unpow2` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

1.0ms	(pow (sin phi1) 2)
4.0ms	(* (sin theta) (sin delta))
19.0ms	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
9.0ms	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

series339.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin phi1) 2)
49.0ms	(* (sin theta) (sin delta))
92.0ms	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
179.0ms	(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	400	786
1	1562	674
2	5001	673

prune419.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
0.3b	(- (pow (cos delta) 3) (pow (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))) 3))
0.3b	(pow (cos delta) 3)
0.5b	(pow (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))) 3)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
18×	`unpow-prod-down` `cube-prod`
16×	`difference-of-squares`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`add-cube-cbrt`
10×	`sqr-pow`
6×	`pow-unpow` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`distribute-lft-out--`
3×	`associate-l`
2×	`cube-div` `cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `sub-neg` `flip3--` `flip3-+` `diff-log` `associate-r` `*-commutative` `flip--` `flip-+`

Counts

4 → 103

Calls

4 calls:

19.0ms	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
25.0ms	(- (pow (cos delta) 3) (pow (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))) 3))
2.0ms	(pow (cos delta) 3)
9.0ms	(pow (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))) 3)

series1.1s

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))
738.0ms	(- (pow (cos delta) 3) (pow (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))) 3))
28.0ms	(pow (cos delta) 3)
234.0ms	(pow (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))) 3)

simplify128.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	666	1906
1	3555	1778
2	5001	1764

prune536.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes445.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	57
1	43	57

end0.0ms

sample8.6s

Algorithm

intervals

Results

5.5s	3193×	body	1280	valid
1.7s	1786×	body	640	valid
477.0ms	736×	body	320	valid
457.0ms	1960×	body	80	valid
142.0ms	325×	body	160	valid