Details

analyze8.7s

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 0.195169%

Guaranteed chance to sample good point: 15.612793%

sample296.0ms

Algorithm

intervals

Results

210.0ms	146×	body	1280	valid
52.0ms	68×	body	640	valid
12.0ms	22×	body	320	valid
3.0ms	17×	body	80	valid
1.0ms	3×	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

prune5.0ms

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: 12.8b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.2b	(sin (- lambda1 lambda2))
3.2b	(cos (- lambda1 lambda2))

rewrite19.0ms

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:

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

series44.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (cos phi2))
26.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify109.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	254	435
1	1026	372
2	4856	372
3	5001	372

prune158.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	61	11	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	11	73

Merged error: 7.1b

Counts

73 → 11

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.2b	(cos (- lambda1 lambda2))

rewrite19.0ms

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

Counts

4 → 68

Calls

4 calls:

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

series48.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (cos phi1) (sin phi2))
9.0ms	(* (sin phi1) (cos phi2))
24.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify38.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	303	481
1	1257	409
2	5002	409

prune143.0ms

Filtered

55 candidates to 80 candidates (-45.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	82	9	91

Merged error: 0.1b

Counts

91 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

rewrite26.0ms

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/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`

Counts

4 → 83

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
4.0ms	(* (sin phi1) (cos phi2))
4.0ms	(* (sin lambda1) (sin lambda2))
11.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series72.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (cos phi1) (sin phi2))
9.0ms	(* (sin phi1) (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

95 → 95

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	480	785
1	2340	680
2	5001	680

prune177.0ms

Filtered

64 candidates to 95 candidates (-48.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	89	6	95
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	93	11	104

Merged error: 0.1b

Counts

104 → 11

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.1b	(* (cos phi1) (sin phi2))
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-l`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-r`
6×	`associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `add-log-exp`
3×	`unswap-sqr`
2×	`sin-mult`
1×	`flip3-+` `frac-add` `cos-mult` `sin-cos-mult` `flip-+`

Counts

4 → 81

Calls

4 calls:

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

series74.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin lambda1) (cos lambda2))
9.0ms	(* (cos phi1) (sin phi2))
10.0ms	(* (sin lambda1) (sin lambda2))
47.0ms	(* (sin phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	442	710
1	1758	605
2	5002	605

prune96.0ms

Filtered

62 candidates to 93 candidates (-50.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	92	12	104

Merged error: 0.0b

Counts

104 → 12

regimes652.0ms

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	33	25
1	33	25

end0.0ms

analyze8.9s

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 0.195169%

Guaranteed chance to sample good point: 15.612793%

sample9.5s

Algorithm

intervals

Results

7.0s	4685×	body	1280	valid
1.6s	1908×	body	640	valid
310.0ms	565×	body	320	valid
104.0ms	646×	body	80	valid
71.0ms	196×	body	160	valid

Details

analyze8.7s

sample296.0ms

simplify8.0ms

prune5.0ms

localize24.0ms

rewrite19.0ms

series44.0ms

simplify109.0ms

prune158.0ms

localize33.0ms

rewrite19.0ms

series48.0ms

simplify38.0ms

prune143.0ms

localize33.0ms

rewrite26.0ms

series72.0ms

simplify67.0ms

prune177.0ms

localize42.0ms

rewrite25.0ms

series74.0ms

simplify49.0ms

prune96.0ms

regimes652.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze8.9s

sample9.5s

Profiling