Details

analyze2.0s

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
9.4%	90.4%	0.2%	9
9.4%	90.4%	0.2%	10
10.9%	88.9%	0.2%	11
10.9%	88.9%	0.2%	12
10.9%	88.9%	0.2%	13
10.9%	88.9%	0.2%	14

sample191.0ms

Algorithm

intervals

Results

115.0ms	111×	body	1280	valid
42.0ms	75×	body	640	valid
13.0ms	33×	body	320	valid
3.0ms	14×	body	160	valid
3.0ms	23×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	20
1	18	20

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: 0.9b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.0b	(sin (- lambda1 lambda2))
3.2b	(cos (- lambda1 lambda2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
4×	`sub-neg`
3×	`cos-diff` `sin-sum` `associate-r` `associate-l`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
1×	`+-commutative` `cos-sum` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `sin-diff` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 51

Calls

4 calls:

6.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

series49.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
23.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
8.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5201	589

prune150.0ms

Filtered

51 candidates to 63 candidates (-23.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	53	10	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	10	64

Merged error: 0.6b

Counts

64 → 10

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.2b	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.2b	(cos (- lambda1 lambda2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cos-diff` `sub-neg` `associate-r` `associate-l`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `associate-*r/`
1×	`+-commutative` `cos-sum` `flip3--` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 51

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
6.0ms	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))

series68.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
30.0ms	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
25.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))

simplify64.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4977	985
1	4977	985

prune138.0ms

Filtered

48 candidates to 63 candidates (-31.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	4	63
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	61	12	73

Merged error: 0.0b

Counts

73 → 12

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
0.5b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite17.0ms

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×	`distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `sin-mult`

Counts

4 → 61

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms	(* (sin lambda1) (sin lambda2))
6.0ms	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series102.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
9.0ms	(* (sin lambda1) (sin lambda2))
29.0ms	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
51.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify36.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5211	1240

prune132.0ms

Filtered

52 candidates to 73 candidates (-40.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	74	11	85

Merged error: 0.0b

Counts

85 → 11

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.6b	(cbrt (atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.6b	(cbrt (atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.6b	(* (cbrt (atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (cbrt (atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

1.0ms	(cbrt (atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
1.0ms	(cbrt (atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
1.0ms	(cbrt (atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
5.0ms	(* (cbrt (atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (cbrt (atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(cbrt (atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
60.0ms	(cbrt (atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
59.0ms	(cbrt (atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
94.0ms	(* (cbrt (atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (cbrt (atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5071	3400

prune85.0ms

Filtered

56 candidates to 85 candidates (-51.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	85	11	96

Merged error: 0.0b

Counts

96 → 11

regimes648.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	103
1	34	103

end0.0ms

analyze2.0s

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
9.4%	90.4%	0.2%	9
9.4%	90.4%	0.2%	10
10.9%	88.9%	0.2%	11
10.9%	88.9%	0.2%	12
10.9%	88.9%	0.2%	13
10.9%	88.9%	0.2%	14

sample6.0s

Algorithm

intervals

Results

3.8s	3585×	body	1280	valid
1.4s	2382×	body	640	valid
360.0ms	938×	body	320	valid
103.0ms	404×	body	160	valid
81.0ms	690×	body	80	valid
2.0ms	1×	body	2560	valid

Details

analyze2.0s

sample191.0ms

simplify3.0ms

prune5.0ms

localize20.0ms

rewrite18.0ms

series49.0ms

simplify45.0ms

prune150.0ms

localize29.0ms

rewrite15.0ms

series68.0ms

simplify64.0ms

prune138.0ms

localize30.0ms

rewrite17.0ms

series102.0ms

simplify36.0ms

prune132.0ms

localize39.0ms

rewrite10.0ms

series273.0ms

simplify64.0ms

prune85.0ms

regimes648.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze2.0s

sample6.0s

Profiling