Details

sample278.0ms

Algorithm

intervals

Results

194.0ms	142×	body	1280	valid
46.0ms	62×	body	640	valid
9.0ms	19×	body	320	valid
3.0ms	24×	body	80	valid
3.0ms	9×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune7.0ms

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: 13.2b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0b	(sin (- lambda1 lambda2))
4.0b	(cos (- lambda1 lambda2))

rewrite21.0ms

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

Counts

4 → 60

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:

13.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
26.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify104.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	260	456
1	1016	389
2	4756	389
3	5001	389

prune388.0ms

Filtered

72 candidates to 51 candidates (29.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	58	14	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	14	73

Merged error: 6.4b

Counts

73 → 14

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (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)))
4.0b	(cos (- lambda1 lambda2))

rewrite26.0ms

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` `associate-l/` `-commutative`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 70

Calls

4 calls:

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

series63.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sin lambda1) (cos lambda2))
28.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
23.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	348	646
1	1462	557
2	5001	557

prune473.0ms

Filtered

82 candidates to 56 candidates (31.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	85	11	96

Merged error: 0.0b

Counts

96 → 11

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (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))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

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

series88.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sin lambda1) (cos lambda2))
27.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
9.0ms	(* (sin lambda1) (sin lambda2))
44.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify67.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	508	950
1	2424	828
2	5003	828

prune699.0ms

Filtered

97 candidates to 65 candidates (33.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	98	10	108

Merged error: 0.0b

Counts

108 → 10

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.3b	(/ (* (* (sin phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.5b	(pow (* (cos lambda1) (cos lambda2)) 3)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

98×	`cos-mult`
84×	`sin-mult`
50×	`associate-*r/` `frac-add` `associate-/r/`
49×	`pow1`
48×	`associate-*l/`
44×	`frac-times`
31×	`add-exp-log` `add-cbrt-cube`
27×	`frac-sub`
19×	`pow-prod-down`
15×	`sub-div`
13×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`associate-/l/`
6×	`cube-div` `pow-unpow`
4×	`pow-pow` `pow-exp` `pow-sqr` `pow-prod-up` `sin-cos-mult` `add-log-exp` `rem-cube-cbrt`
3×	`cbrt-undiv` `flip3--` `flip3-+` `times-frac` `div-exp` `associate-/r*` `flip--` `flip-+`
2×	`cube-mult` `pow-to-exp` `unpow-prod-down` `pow-plus` `unpow3` `cube-prod` `sqr-pow`
1×	`pow2` `frac-2neg` `swap-sqr` `associate-r` `associate-l` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 163

Calls

4 calls:

5.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
37.0ms	(/ (* (* (sin phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
10.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
4.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

series292.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
250.0ms	(/ (* (* (sin phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
12.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
15.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

simplify65.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1293	4502
1	5001	4261

prune2.2s

Filtered

175 candidates to 98 candidates (44.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	175	10	185

Merged error: 0.0b

Counts

185 → 10

regimes722.0ms

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	44	51
1	44	51

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.2s	4596×	body	1280	valid
1.5s	1992×	body	640	valid
280.0ms	565×	body	320	valid
100.0ms	639×	body	80	valid
64.0ms	208×	body	160	valid

Details

sample278.0ms

simplify8.0ms

prune7.0ms

localize25.0ms

rewrite21.0ms

series48.0ms

simplify104.0ms

prune388.0ms

localize34.0ms

rewrite26.0ms

series63.0ms

simplify45.0ms

prune473.0ms

localize33.0ms

rewrite29.0ms

series88.0ms

simplify67.0ms

prune699.0ms

localize46.0ms

rewrite67.0ms

series292.0ms

simplify65.0ms

prune2.2s

regimes722.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample8.6s

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