Details

analyze2.7s

Algorithm: search

sample313.0ms

Algorithm

intervals

Results

231.0ms	157×	body	1280	valid
42.0ms	53×	body	640	valid
12.0ms	21×	body	320	valid
8.0ms	18×	body	80	valid
3.0ms	7×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 14.0b

Counts

2 → 1

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0b	(cos (- lambda1 lambda2))
4.0b	(sin (- lambda1 lambda2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `sin-sum` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series40.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sin phi1) (cos phi2))
23.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

simplify110.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	254	435
1	1026	372
2	4856	372
3	5001	372

prune138.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	8	73

Merged error: 6.2b

Counts

73 → 8

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0b	(cos (- lambda1 lambda2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `*-commutative` `sin-cos-mult`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 69

Calls

4 calls:

5.0ms	(* (sin lambda1) (cos lambda2))
4.0ms	(* (sin phi1) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series46.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sin lambda1) (cos lambda2))
9.0ms	(* (sin phi1) (cos phi2))
25.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify41.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	308	486
1	1294	414
2	5002	414

prune125.0ms

Filtered

56 candidates to 81 candidates (-44.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 0.1b

Counts

89 → 6

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin lambda2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `sin-cos-mult` `cbrt-unprod`
4×	`*-commutative` `add-log-exp`
3×	`frac-times` `associate-*r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`

Counts

4 → 84

Calls

4 calls:

4.0ms	(* (sin lambda1) (cos lambda2))
4.0ms	(* (sin phi1) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
5.0ms	(* (sin lambda1) (sin lambda2))

series68.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sin lambda1) (cos lambda2))
8.0ms	(* (sin phi1) (cos phi2))
41.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
9.0ms	(* (sin lambda1) (sin lambda2))

simplify65.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	474	790
1	2287	685
2	5001	684

prune157.0ms

Filtered

64 candidates to 96 candidates (-50.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	94	8	102

Merged error: 0.1b

Counts

102 → 8

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
6.9b	(cbrt (* (sin lambda1) (sin lambda2)))
6.9b	(cbrt (* (sin lambda1) (sin lambda2)))
6.9b	(cbrt (* (sin lambda1) (sin lambda2)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

6.0ms	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
3.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
3.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
3.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
20.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
21.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
21.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

simplify121.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (114.0ms)

Iter	Nodes	Cost
0	199	632
1	731	547
2	4086	514
3	5002	504

prune96.0ms

Filtered

54 candidates to 76 candidates (-40.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	76	8	84

Merged error: 0.1b

Counts

84 → 8

regimes537.0ms

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	37	36
1	37	36

end0.0ms

analyze2.7s

Algorithm: search

sample9.6s

Algorithm

intervals

Results

7.1s	4635×	body	1280	valid
1.7s	1955×	body	640	valid
305.0ms	569×	body	320	valid
116.0ms	643×	body	80	valid
83.0ms	198×	body	160	valid

Details

analyze2.7s

sample313.0ms

simplify8.0ms

prune6.0ms

localize33.0ms

rewrite19.0ms

series40.0ms

simplify110.0ms

prune138.0ms

localize37.0ms

rewrite21.0ms

series46.0ms

simplify41.0ms

prune125.0ms

localize36.0ms

rewrite27.0ms

series68.0ms

simplify65.0ms

prune157.0ms

localize42.0ms

rewrite18.0ms

series94.0ms

simplify121.0ms

prune96.0ms

regimes537.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze2.7s

sample9.6s

Profiling