Details

analyze2.8s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

sample299.0ms

Algorithm

intervals

Results

218.0ms	147×	body	1280	valid
47.0ms	61×	body	640	valid
10.0ms	20×	body	320	valid
4.0ms	24×	body	80	valid
1.0ms	4×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	384	24
1	384	24

prune23.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 14.3b

Counts

2 → 2

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(sin (- lambda1 lambda2))
2.7b	(cos (- lambda1 lambda2))

rewrite22.0ms

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` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `sin-sum` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

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

series48.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
25.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify55.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4879	620
1	4879	620

prune185.0ms

Filtered

50 candidates to 70 candidates (-40.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	57	13	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	58	14	72

Merged error: 6.3b

Counts

72 → 14

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.7b	(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`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `cos-sum` `distribute-lft-in` `associate-*l/` `sin-cos-mult`

Counts

4 → 66

Calls

4 calls:

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

series50.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (cos lambda1) (sin lambda2))
9.0ms	(* (cos phi1) (sin phi2))
25.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify73.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4789	639
1	4789	639

prune164.0ms

Filtered

53 candidates to 78 candidates (-47.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	81	11	92

Merged error: 0.1b

Counts

92 → 11

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`associate-l`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
5×	`associate-*r/`
4×	`*-commutative` `add-log-exp`
3×	`sin-cos-mult`
1×	`unswap-sqr`

Counts

4 → 81

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
9.0ms	(* (cos lambda1) (* (cos lambda2) (* (sin phi1) (cos phi2))))
9.0ms	(* (sin lambda1) (* (sin lambda2) (* (sin phi1) (cos phi2))))
7.0ms	(* (sin lambda2) (* (sin phi1) (cos phi2)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos phi1) (sin phi2))
33.0ms	(* (cos lambda1) (* (cos lambda2) (* (sin phi1) (cos phi2))))
27.0ms	(* (sin lambda1) (* (sin lambda2) (* (sin phi1) (cos phi2))))
18.0ms	(* (sin lambda2) (* (sin phi1) (cos phi2)))

simplify63.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5313	900

prune183.0ms

Filtered

59 candidates to 93 candidates (-57.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	92	12	104

Merged error: 0.0b

Counts

104 → 12

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow1` `add-exp-log` `add-cbrt-cube`
14×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`associate-l`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r`
4×	`*-commutative` `add-log-exp`
3×	`associate-*r/`
2×	`sin-mult` `unswap-sqr`
1×	`associate-*l/` `sin-cos-mult`

Counts

4 → 81

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
9.0ms	(* (cos lambda1) (* (cos lambda2) (* (sin phi1) (cos phi2))))
9.0ms	(* (sin lambda1) (* (* (sin lambda2) (sin phi1)) (cos phi2)))
5.0ms	(* (sin lambda2) (sin phi1))

series79.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos phi1) (sin phi2))
30.0ms	(* (cos lambda1) (* (cos lambda2) (* (sin phi1) (cos phi2))))
29.0ms	(* (sin lambda1) (* (* (sin lambda2) (sin phi1)) (cos phi2)))
10.0ms	(* (sin lambda2) (sin phi1))

simplify54.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5036	852

prune95.0ms

Filtered

60 candidates to 93 candidates (-55.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	93	12	105

Merged error: 0.0b

Counts

105 → 12

regimes717.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	159	44
1	159	44

end0.0ms

sample9.2s

Algorithm

intervals

Results

6.7s	4551×	body	1280	valid
1.6s	1983×	body	640	valid
320.0ms	579×	body	320	valid
124.0ms	693×	body	80	valid
72.0ms	194×	body	160	valid

Details

analyze2.8s

sample299.0ms

simplify13.0ms

prune23.0ms

localize29.0ms

rewrite22.0ms

series48.0ms

simplify55.0ms

prune185.0ms

localize37.0ms

rewrite21.0ms

series50.0ms

simplify73.0ms

prune164.0ms

localize42.0ms

rewrite32.0ms

series88.0ms

simplify63.0ms

prune183.0ms

localize39.0ms

rewrite30.0ms

series79.0ms

simplify54.0ms

prune95.0ms

regimes717.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample9.2s

Profiling