Details

sample297.0ms

Algorithm

intervals

Results

209.0ms	142×	body	1280	valid
55.0ms	64×	body	640	valid
9.0ms	19×	body	320	valid
4.0ms	25×	body	80	valid
2.0ms	6×	body	160	valid

simplify9.0ms

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

prune4.0ms

Filtered

1 candidates to 0 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: 13.2b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

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:

7.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

series191.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
25.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

simplify105.0ms

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

prune339.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	56	16	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	16	73

Merged error: 6.3b

Counts

73 → 16

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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` `add-log-exp`
5×	`cos-diff`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`associate-*l/`
2×	`distribute-rgt-in` `sub-neg` `cos-sum` `flip3--` `distribute-lft-in` `*-commutative` `flip--` `associate--r+`
1×	`diff-log` `sin-cos-mult` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

4.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
7.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series379.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
129.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify49.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	354	777
1	1547	687
2	5001	687

prune413.0ms

Filtered

77 candidates to 54 candidates (70.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	11	4	15
Picked	1	0	1
Done	0	0	0
Total	83	10	93

Merged error: 0.0b

Counts

93 → 10

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`associate-l/` `-commutative` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 89

Calls

4 calls:

8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
8.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
49.0ms	(* (sin lambda1) (sin lambda2))
101.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
115.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify61.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	433	949
1	2002	747
2	5002	747

prune471.0ms

Filtered

101 candidates to 59 candidates (58.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	96	5	101
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	99	12	111

Merged error: 0.0b

Counts

111 → 12

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))
16.8b	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
16.8b	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
16.8b	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-div`
22×	`sin-cos-mult` `sin-mult`
20×	`frac-times`
14×	`associate-r/` `associate-l/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

11.0ms	(* (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))
7.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
7.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
7.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

series934.0ms

Counts

4 → 12

Calls

4 calls:

255.0ms	(* (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))
226.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
227.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
225.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

simplify47.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	304	1411
1	1196	1254
2	5001	1189

prune539.0ms

Filtered

94 candidates to 66 candidates (70.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	94	12	106

Merged error: 0.0b

Counts

106 → 12

regimes491.0ms

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	39	48
1	39	48

end0.0ms

sample8.7s

Algorithm

intervals

Results

6.4s	4612×	body	1280	valid
1.6s	1994×	body	640	valid
302.0ms	580×	body	320	valid
98.0ms	628×	body	80	valid
59.0ms	186×	body	160	valid

Details

sample297.0ms

simplify9.0ms

prune4.0ms

localize26.0ms

rewrite22.0ms

series191.0ms

simplify105.0ms

prune339.0ms

localize34.0ms

rewrite24.0ms

series379.0ms

simplify49.0ms

prune413.0ms

localize39.0ms

rewrite33.0ms

series395.0ms

simplify61.0ms

prune471.0ms

localize46.0ms

rewrite36.0ms

series934.0ms

simplify47.0ms

prune539.0ms

regimes491.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample8.7s

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