Details

sample266.0ms

Algorithm

intervals

Results

189.0ms	140×	body	1280	valid
46.0ms	65×	body	640	valid
9.0ms	19×	body	320	valid
3.0ms	26×	body	80	valid
2.0ms	6×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 13.3b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(sin (- lambda1 lambda2))
3.5b	(cos (- lambda1 lambda2))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

8.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
16.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

series214.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
100.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms	(sin (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))

simplify115.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	293	556
1	1064	489
2	4839	489
3	5001	489

prune354.0ms

Filtered

85 candidates to 63 candidates (25.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	70	15	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	15	86

Merged error: 8.0b

Counts

86 → 15

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(cos (- lambda1 lambda2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
33×	`associate-l`
20×	`*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `associate-r`
10×	`unswap-sqr`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`*-commutative` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`cos-diff` `associate-*l/`
2×	`cos-sum` `sin-cos-mult`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 91

Calls

4 calls:

5.0ms	(* (sin lambda1) (cos lambda2))
23.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series309.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin lambda1) (cos lambda2))
147.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
98.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify50.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	397	830
1	1522	741
2	5001	741

prune505.0ms

Filtered

103 candidates to 72 candidates (30.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	91	12	103
Fresh	13	1	14
Picked	1	0	1
Done	0	0	0
Total	105	13	118

Merged error: 0.1b

Counts

118 → 13

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

40×	`associate-l`
39×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
19×	`associate-r`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
14×	`add-cube-cbrt`
11×	`unswap-sqr`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`*-commutative` `sin-cos-mult`
4×	`distribute-lft-out` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`frac-times` `associate-r/` `associate-l/` `sin-mult`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`flip3--` `flip--`

Counts

4 → 112

Calls

4 calls:

5.0ms	(* (sin lambda1) (cos lambda2))
20.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
25.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series428.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin lambda1) (cos lambda2))
144.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
52.0ms	(* (sin lambda1) (sin lambda2))
187.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify78.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	600	1249
1	2682	1127
2	5002	1127

prune724.0ms

Filtered

124 candidates to 82 candidates (33.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	112	12	124
Fresh	11	1	12
Picked	1	0	1
Done	0	0	0
Total	124	13	137

Merged error: 0.0b

Counts

137 → 13

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
0.3b	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

rewrite737.0ms

Algorithm

rewrite-expression-head

Rules

6346×	`add-sqr-sqrt`
2932×	`unswap-sqr`
2327×	`*-un-lft-identity`
1569×	`difference-of-squares`
1504×	`associate-r`
1413×	`associate-l`
1408×	`times-frac`
912×	`swap-sqr`
841×	`distribute-lft-out--`
270×	`*-commutative`
221×	`add-cube-cbrt`
128×	`associate-/l*`
87×	`pow1`
78×	`cos-mult` `sin-mult`
74×	`associate-*r/`
66×	`frac-times`
44×	`associate-*l/`
42×	`add-exp-log` `add-cbrt-cube`
37×	`pow-prod-down` `frac-sub`
34×	`sin-cos-mult`
33×	`associate-/l/`
22×	`prod-exp` `cbrt-unprod`
21×	`sub-div`
11×	`associate-/r*`
8×	`pow-sqr` `pow-prod-up`
5×	`flip3--` `flip--`
4×	`pow-plus` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 1926

Calls

4 calls:

219.0ms	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
158.0ms	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
19.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
16.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

series860.0ms

Counts

4 → 12

Calls

4 calls:

511.0ms	(/ (* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
228.0ms	(* (* (sin phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
55.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
66.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

simplify558.0ms

Algorithm

egg-herbie

Counts

1938 → 1938

Iterations

Useful iterations: 1 (73.0ms)

Iter	Nodes	Cost
0	3979	61894
1	5001	60571

prune3.6s

Filtered

1938 candidates to 463 candidates (76.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	1934	4	1938
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	1939	12	1951

Merged error: 0.0b

Counts

1951 → 12

regimes705.0ms

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	35	41
1	35	41

end0.0ms

sample8.5s

Algorithm

intervals

Results

6.3s	4627×	body	1280	valid
1.5s	1946×	body	640	valid
279.0ms	574×	body	320	valid
105.0ms	665×	body	80	valid
56.0ms	188×	body	160	valid