Details

analyze2.6s

Algorithm: search

sample287.0ms

Algorithm

intervals

Results

194.0ms	138×	body	1280	valid
59.0ms	60×	body	640	valid
12.0ms	23×	body	320	valid
5.0ms	31×	body	80	valid
1.0ms	4×	body	160	valid

simplify9.0ms

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

prune5.0ms

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: 14.9b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0b	(cos (- lambda1 lambda2))
3.0b	(sin (- lambda1 lambda2))

rewrite27.0ms

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:

6.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series43.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
21.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

simplify107.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	260	456
1	1016	389
2	4756	389
3	5001	389

prune158.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	60	12	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	12	73

Merged error: 8.3b

Counts

73 → 12

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0b	(cos (- lambda1 lambda2))

rewrite25.0ms

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` `associate-l/` `-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `sin-cos-mult` `flip--`

Counts

4 → 69

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series60.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos phi1) (sin phi2))
27.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
21.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify46.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	357	648
1	1484	552
2	5002	552

prune160.0ms

Filtered

55 candidates to 81 candidates (-47.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	74	7	81
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	82	11	93

Merged error: 0.1b

Counts

93 → 11

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`associate-l/` `-commutative` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 89

Calls

4 calls:

7.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms	(* (sin lambda1) (sin lambda2))
8.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
8.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
9.0ms	(* (sin lambda1) (sin lambda2))
25.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
24.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify61.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	433	949
1	2002	747
2	5002	747

prune180.0ms

Filtered

59 candidates to 101 candidates (-71.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	95	6	101
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	98	14	112

Merged error: 0.0b

Counts

112 → 14

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
7.5b	(cbrt (* (sin lambda1) (sin lambda2)))
7.5b	(cbrt (* (sin lambda1) (sin lambda2)))
7.5b	(cbrt (* (sin lambda1) (sin lambda2)))

rewrite19.0ms

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)))
5.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
3.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2))))
19.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
19.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
20.0ms	(cbrt (* (sin lambda1) (sin lambda2)))

simplify122.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (115.0ms)

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

prune97.0ms

Filtered

54 candidates to 76 candidates (-40.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	76	14	90

Merged error: 0.0b

Counts

90 → 14

regimes723.0ms

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	39	40
1	39	40

end0.0ms

analyze2.6s

Algorithm: search

sample9.2s

Algorithm

intervals

Results

6.9s	4579×	body	1280	valid
1.6s	1977×	body	640	valid
294.0ms	556×	body	320	valid
107.0ms	677×	body	80	valid
74.0ms	211×	body	160	valid

Details

analyze2.6s

sample287.0ms

simplify9.0ms

prune5.0ms

localize26.0ms

rewrite27.0ms

series43.0ms

simplify107.0ms

prune158.0ms

localize35.0ms

rewrite25.0ms

series60.0ms

simplify46.0ms

prune160.0ms

localize38.0ms

rewrite31.0ms

series86.0ms

simplify61.0ms

prune180.0ms

localize41.0ms

rewrite19.0ms

series89.0ms

simplify122.0ms

prune97.0ms

regimes723.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze2.6s

sample9.2s

Profiling