Details

analyze2.7s (19.6%)

Algorithm

1×

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

sample292.0ms (2.1%)

Algorithm

1×

intervals

Results

215.0ms	152×	body	1280	valid
47.0ms	61×	body	640	valid
10.0ms	18×	body	320	valid
3.0ms	9×	body	160	valid
2.0ms	16×	body	80	valid

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	384	24
1	384	24

prune12.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 12.0b

Counts

2 → 1

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos (- lambda1 lambda2)))
2.8b	(cos (- lambda1 lambda2))
2.9b	(sin (- lambda1 lambda2))

rewrite21.0ms (0.2%)

Algorithm

1×	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`
4×	`add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `sin-sum` `sin-diff` `sin-cos-mult`

Counts

4 → 57

Calls

4 calls:

8.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
5.0ms	(* (cos phi1) (sin phi2))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

series28.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
8.0ms	(* (cos phi1) (sin phi2))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4938	517
1	4938	517

prune181.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	57	12	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	12	70

Merged error: 6.3b

Counts

70 → 12

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos (- lambda1 lambda2)))
2.8b	(cos (- lambda1 lambda2))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

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

series52.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
12.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
8.0ms	(* (cos phi1) (sin phi2))
4.0ms	(cos (- lambda1 lambda2))

simplify38.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4970	800
1	4970	800

prune190.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	80	12	92

Merged error: 0.0b

Counts

92 → 12

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

10.0ms	(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
8.0ms	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
5.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(* (cos phi1) (sin phi2))

series90.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
29.0ms	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
9.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (cos phi1) (sin phi2))

simplify34.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5081	1210

prune210.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	92	5	97
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	98	11	109

Merged error: 0.0b

Counts

109 → 11

localize38.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
0.6b	(cbrt (sin lambda1))
0.6b	(cbrt (sin lambda1))
0.6b	(cbrt (sin lambda1))

rewrite14.0ms (0.1%)

Algorithm

1×	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:

7.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
2.0ms	(cbrt (sin lambda1))
1.0ms	(cbrt (sin lambda1))
1.0ms	(cbrt (sin lambda1))

series71.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
17.0ms	(cbrt (sin lambda1))
17.0ms	(cbrt (sin lambda1))
17.0ms	(cbrt (sin lambda1))

simplify51.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4991	490
1	4991	490

prune123.0ms (0.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

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

Merged error: 0.0b

Counts

96 → 11

regimes629.0ms (4.6%)

Accuracy

Total 0.1b remaining (60.7%)

Threshold costs 0.1b (60.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	157	47
1	157	47

end0.0ms (0%)

sample8.8s (63.8%)

Algorithm

1×

intervals

Results

6.5s	4590×	body	1280	valid
1.5s	1939×	body	640	valid
294.0ms	577×	body	320	valid
108.0ms	692×	body	80	valid
65.0ms	202×	body	160	valid

Details

analyze2.7s (19.6%)

sample292.0ms (2.1%)

simplify14.0ms (0.1%)

prune12.0ms (0.1%)

localize26.0ms (0.2%)

rewrite21.0ms (0.2%)

series28.0ms (0.2%)

simplify50.0ms (0.4%)

prune181.0ms (1.3%)

localize35.0ms (0.3%)

rewrite24.0ms (0.2%)

series52.0ms (0.4%)

simplify38.0ms (0.3%)

prune190.0ms (1.4%)

localize35.0ms (0.3%)

rewrite30.0ms (0.2%)

series90.0ms (0.7%)

simplify34.0ms (0.2%)

prune210.0ms (1.5%)

localize38.0ms (0.3%)

rewrite14.0ms (0.1%)

series71.0ms (0.5%)

simplify51.0ms (0.4%)

prune123.0ms (0.9%)

regimes629.0ms (4.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample8.8s (63.8%)

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