Details

analyze2.6s

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

sample278.0ms

Algorithm

intervals

Results

196.0ms	146×	body	1280	valid
54.0ms	66×	body	640	valid
7.0ms	15×	body	320	valid
3.0ms	21×	body	80	valid
3.0ms	8×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	384	24
1	384	24

prune21.0ms

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: 9.9b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

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

series45.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
12.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

simplify59.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4919	693
1	4919	693

prune138.0ms

Filtered

54 candidates to 74 candidates (-37.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	66	8	74
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	68	8	76

Merged error: 5.6b

Counts

76 → 8

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
0.2b	(* (sin phi1) (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-l*`
7×	`cos-diff` `associate-r`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`*-commutative` `sin-cos-mult`
2×	`unswap-sqr`
1×	`sub-neg` `cos-sum` `associate-*r/`

Counts

4 → 72

Calls

4 calls:

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

series47.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sin lambda1) (cos lambda2))
23.0ms	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
12.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify67.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4865	764
1	4865	764

prune127.0ms

Filtered

62 candidates to 84 candidates (-35.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	86	6	92

Merged error: 0.1b

Counts

92 → 6

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

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-+`
1×	`sin-cos-mult`

Counts

4 → 86

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(* (sin lambda1) (cos lambda2))
10.0ms	(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
9.0ms	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series91.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin lambda1) (sin lambda2))
8.0ms	(* (sin lambda1) (cos lambda2))
44.0ms	(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
30.0ms	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify35.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5026	1219

prune161.0ms

Filtered

69 candidates to 98 candidates (-42.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	93	5	98
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Merged error: 0.0b

Counts

104 → 8

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (cos lambda2)) (cbrt (cos lambda2)))
0.3b	(cbrt (cos lambda2))
0.3b	(cbrt (cos lambda2))
0.3b	(cbrt (cos lambda2))

rewrite12.0ms

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:

6.0ms	(* (cbrt (cos lambda2)) (cbrt (cos lambda2)))
1.0ms	(cbrt (cos lambda2))
1.0ms	(cbrt (cos lambda2))
1.0ms	(cbrt (cos lambda2))

series82.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (cbrt (cos lambda2)) (cbrt (cos lambda2)))
21.0ms	(cbrt (cos lambda2))
17.0ms	(cbrt (cos lambda2))
18.0ms	(cbrt (cos lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5009	459

prune81.0ms

Filtered

50 candidates to 85 candidates (-70.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Merged error: 0.0b

Counts

93 → 9

regimes550.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	139	47
1	139	47

end0.0ms

sample8.8s

Algorithm

intervals

Results

6.5s	4672×	body	1280	valid
1.5s	1968×	body	640	valid
273.0ms	535×	body	320	valid
94.0ms	624×	body	80	valid
66.0ms	201×	body	160	valid

Details

analyze2.6s

sample278.0ms

simplify12.0ms

prune21.0ms

localize25.0ms

rewrite20.0ms

series45.0ms

simplify59.0ms

prune138.0ms

localize36.0ms

rewrite21.0ms

series47.0ms

simplify67.0ms

prune127.0ms

localize34.0ms

rewrite31.0ms

series91.0ms

simplify35.0ms

prune161.0ms

localize39.0ms

rewrite12.0ms

series82.0ms

simplify45.0ms

prune81.0ms

regimes550.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample8.8s

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