Details

sample251.0ms

Algorithm

intervals

Results

181.0ms	148×	body	1280	valid
44.0ms	65×	body	640	valid
6.0ms	14×	body	320	valid
3.0ms	21×	body	80	valid
2.0ms	8×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	15
1	48	15
2	79	15
3	94	15
4	94	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: 14.4b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.1b	(cos (- lambda1 lambda2))
4.4b	(sin (- lambda1 lambda2))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`pow1` `add-exp-log` `cos-sum` `sin-sum` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

13.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
14.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

series218.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
102.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
25.0ms	(cos (- lambda1 lambda2))
31.0ms	(sin (- lambda1 lambda2))

simplify44.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	416	1032
1	1286	797
2	5002	771

prune394.0ms

Filtered

98 candidates to 63 candidates (64.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	82	16	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	16	99

Merged error: 5.3b

Counts

99 → 16

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (cos lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.1b	(cos (- lambda1 lambda2))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 85

Calls

4 calls:

8.0ms	(* (sin phi1) (cos phi2))
7.0ms	(* (cos lambda1) (sin lambda2))
14.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
9.0ms	(cos (- lambda1 lambda2))

series197.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (sin phi1) (cos phi2))
44.0ms	(* (cos lambda1) (sin lambda2))
87.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
26.0ms	(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	421	787
1	1541	630
2	5001	629

prune499.0ms

Filtered

97 candidates to 65 candidates (67.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	92	5	97
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	98	15	113

Merged error: 0.1b

Counts

113 → 15

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-*r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`

Counts

4 → 91

Calls

4 calls:

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

series292.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin phi1) (cos phi2))
41.0ms	(* (cos lambda1) (sin lambda2))
45.0ms	(* (sin lambda1) (sin lambda2))
163.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify67.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	489	817
1	2434	715
2	5002	715

prune519.0ms

Filtered

103 candidates to 73 candidates (70.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	7	7	14
Picked	1	0	1
Done	0	0	0
Total	104	14	118

Merged error: 0.0b

Counts

118 → 14

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin lambda2))))))

rewrite25.0ms

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`
4×	`expm1-log1p-u` `*-commutative` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-mult`

Counts

4 → 89

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
4.0ms	(* (cos lambda1) (sin lambda2))
5.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin lambda2))))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin phi1) (cos phi2))
41.0ms	(* (cos lambda1) (sin lambda2))
46.0ms	(* (sin lambda1) (sin lambda2))
197.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin lambda2))))))

simplify62.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	463	826
1	2254	705
2	5002	705

prune450.0ms

Filtered

101 candidates to 72 candidates (71.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	102	13	115

Merged error: 0.0b

Counts

115 → 13

regimes472.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	29
1	37	29

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.9s	4549×	body	1280	valid
1.4s	1989×	body	640	valid
287.0ms	575×	body	320	valid
92.0ms	677×	body	80	valid
59.0ms	210×	body	160	valid