Details

analyze1.9s (18.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
9.4%	90.4%	0.2%	9
9.4%	90.4%	0.2%	10
10.9%	88.9%	0.2%	11
10.9%	88.9%	0.2%	12
10.9%	88.9%	0.2%	13
10.9%	88.9%	0.2%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample165.0ms (1.6%)

Algorithm

1×

intervals

Results

113.0ms	146×	body	1024	valid
25.0ms	59×	body	512	valid
7.0ms	4×	body	2048	valid
4.0ms	15×	body	256	valid
4.0ms	32×	body	128	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify189.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	211	32
1	211	32

prune3.0ms (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: 0.8b

Counts

2 → 1

Compiler

Compiled 40 to 28 computations (30% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.7b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.7b	(sin.f64 (-.f64 lambda1 lambda2))
3.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64_450`
4×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `add-exp-log_binary64_449` `*-un-lft-identity_binary64_414` `add-cbrt-cube_binary64_447` `add-sqr-sqrt_binary64_435`
3×	`cos-diff_binary64_548`
2×	`associate-+r+_binary64_348` `sub-neg_binary64_407`
1×	`distribute-lft-in_binary64_365` `flip3-+_binary64_417` `distribute-rgt-in_binary64_366` `sin-diff_binary64_547` `+-commutative_binary64_346` `cos-sum_binary64_545` `flip-+_binary64_388` `sin-sum_binary64_544` `sum-log_binary64_502`

Counts

4 → 38

Calls

4 calls:

5.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))

series359.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
70.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
39.0ms	(sin.f64 (-.f64 lambda1 lambda2))
29.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify108.0ms (1%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4805	950
1	4805	950

prune86.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	39	11	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	11	51

Merged error: 0.6b

Counts

51 → 11

Compiler

Compiled 1642 to 441 computations (73.1% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.2b	(-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
0.7b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_450`
4×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `add-exp-log_binary64_449` `*-un-lft-identity_binary64_414` `add-cbrt-cube_binary64_447` `add-sqr-sqrt_binary64_435`
3×	`cos-diff_binary64_548`
2×	`associate-+r+_binary64_348` `sub-neg_binary64_407`
1×	`distribute-lft-in_binary64_365` `flip3--_binary64_418` `flip3-+_binary64_417` `distribute-rgt-in_binary64_366` `diff-log_binary64_503` `+-commutative_binary64_346` `cos-sum_binary64_545` `flip-+_binary64_388` `flip--_binary64_389` `sum-log_binary64_502`

Counts

4 → 40

Calls

4 calls:

5.0ms	(-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
4.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))

series480.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

222.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
145.0ms	(-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
84.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
29.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4889	1326
1	4889	1326

prune75.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	52	11	63

Merged error: 0.1b

Counts

63 → 11

Compiler

Compiled 2170 to 465 computations (78.6% saved)

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b	(-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.7b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_450` `add-sqr-sqrt_binary64_435`
6×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `add-exp-log_binary64_449` `*-un-lft-identity_binary64_414` `add-cbrt-cube_binary64_447`
3×	`associate-l_binary64_357` `associate-r_binary64_356`
2×	`associate-+r+_binary64_348`
1×	`distribute-lft-in_binary64_365` `flip3--_binary64_418` `flip3-+_binary64_417` `distribute-rgt-in_binary64_366` `diff-log_binary64_503` `*-commutative_binary64_347` `+-commutative_binary64_346` `prod-exp_binary64_460` `pow-prod-down_binary64_482` `sub-neg_binary64_407` `flip-+_binary64_388` `flip--_binary64_389` `unswap-sqr_binary64_382` `cbrt-unprod_binary64_444` `sum-log_binary64_502` `sin-mult_binary64_566`

Counts

4 → 50

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
5.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series754.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

433.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
147.0ms	(-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
103.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
70.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4993	1764
1	4993	1764

prune89.0ms (0.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	62	11	73

Merged error: 0.1b

Counts

73 → 11

Compiler

Compiled 2923 to 511 computations (82.5% saved)

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.7b	(sin.f64 (-.f64 lambda1 lambda2))
3.8b	(cos.f64 (-.f64 lambda1 lambda2))
3.8b	(cos.f64 (-.f64 lambda1 lambda2))
3.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `add-exp-log_binary64_449` `*-un-lft-identity_binary64_414` `sub-neg_binary64_407` `add-cbrt-cube_binary64_447` `add-log-exp_binary64_450` `add-sqr-sqrt_binary64_435`
3×	`cos-sum_binary64_545` `cos-diff_binary64_548`
1×	`sin-diff_binary64_547` `sin-sum_binary64_544`

Counts

4 → 36

Calls

4 calls:

5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

series111.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(sin.f64 (-.f64 lambda1 lambda2))
27.0ms	(cos.f64 (-.f64 lambda1 lambda2))
26.0ms	(cos.f64 (-.f64 lambda1 lambda2))
25.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify130.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	4922	504
1	4922	504

prune78.0ms (0.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	48	11	59

Merged error: 0.1b

Counts

59 → 11

Compiler

Compiled 2556 to 569 computations (77.7% saved)

regimes179.0ms (1.7%)

Compiler: Compiled 2338 to 1306 computations (44.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	56
1	57	56

end0.0ms (0%)

sample5.3s (51.4%)

Algorithm

1×

intervals

Results

3.4s	4495×	body	1024	valid
739.0ms	1720×	body	512	valid
195.0ms	110×	body	2048	valid
192.0ms	690×	body	256	valid
133.0ms	985×	body	128	valid

Compiler

Compiled 442 to 249 computations (43.7% saved)

Details

analyze1.9s (18.1%)

sample165.0ms (1.6%)

simplify189.0ms (1.8%)

prune3.0ms (0%)

localize20.0ms (0.2%)

rewrite18.0ms (0.2%)

series359.0ms (3.5%)

simplify108.0ms (1%)

prune86.0ms (0.8%)

localize30.0ms (0.3%)

rewrite19.0ms (0.2%)

series480.0ms (4.7%)

simplify67.0ms (0.7%)

prune75.0ms (0.7%)

localize33.0ms (0.3%)

rewrite22.0ms (0.2%)

series754.0ms (7.3%)

simplify62.0ms (0.6%)

prune89.0ms (0.9%)

localize33.0ms (0.3%)

rewrite23.0ms (0.2%)

series111.0ms (1.1%)

simplify130.0ms (1.3%)

prune78.0ms (0.8%)

regimes179.0ms (1.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.3s (51.4%)

Profiling