Details

analyze1.9s (17.2%)

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)

sample168.0ms (1.5%)

Algorithm

1×

intervals

Results

110.0ms	146×	body	1024	valid
29.0ms	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)

simplify179.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

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))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `cancel-sign-sub-inv_binary64_389` `add-sqr-sqrt_binary64_445` `add-log-exp_binary64_462`
4×	`cos-sum_binary64_557` `pow1_binary64_484` `sin-sum_binary64_556` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
3×	`cos-diff_binary64_560`
2×	`sub-neg_binary64_416` `associate-+r+_binary64_355`
1×	`distribute-rgt-in_binary64_373` `distribute-lft-in_binary64_372` `flip-+_binary64_397` `+-commutative_binary64_353` `flip3-+_binary64_426` `sin-diff_binary64_559` `sum-log_binary64_514`

Counts

4 → 44

Calls

4 calls:

8.0ms	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
5.0ms	(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)))))

series346.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

208.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
71.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
34.0ms	(sin.f64 (-.f64 lambda1 lambda2))
33.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify86.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4992	1058
1	4992	1058

prune362.0ms (3.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	45	11	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	11	57

Merged error: 0.6b

Counts

57 → 11

Compiler

Compiled 6699 to 3471 computations (48.2% saved)

localize29.0ms (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))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_462`
5×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445`
4×	`cos-sum_binary64_557` `cancel-sign-sub-inv_binary64_389` `pow1_binary64_484` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
3×	`cos-diff_binary64_560`
2×	`sub-neg_binary64_416` `associate-+r+_binary64_355`
1×	`distribute-rgt-in_binary64_373` `distribute-lft-in_binary64_372` `flip-+_binary64_397` `diff-log_binary64_515` `+-commutative_binary64_353` `flip3--_binary64_427` `flip3-+_binary64_426` `flip--_binary64_398` `sum-log_binary64_514`

Counts

4 → 44

Calls

4 calls:

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

series492.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

233.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
142.0ms	(-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
88.0ms	(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))

simplify128.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4855	1390
1	4855	1390

prune121.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	56	11	67

Merged error: 0.1b

Counts

67 → 11

Compiler

Compiled 3068 to 892 computations (70.9% saved)

localize31.0ms (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-sqr-sqrt_binary64_445` `add-log-exp_binary64_462`
6×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `pow1_binary64_484` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
3×	`associate-l_binary64_364` `associate-r_binary64_363`
2×	`associate-+r+_binary64_355`
1×	`pow-prod-down_binary64_494` `distribute-rgt-in_binary64_373` `sub-neg_binary64_416` `distribute-lft-in_binary64_372` `flip-+_binary64_397` `diff-log_binary64_515` `sin-mult_binary64_578` `cancel-sign-sub-inv_binary64_389` `prod-exp_binary64_472` `+-commutative_binary64_353` `flip3--_binary64_427` `*-commutative_binary64_354` `flip3-+_binary64_426` `flip--_binary64_398` `unswap-sqr_binary64_391` `sum-log_binary64_514` `cbrt-unprod_binary64_456`

Counts

4 → 51

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))))))

series776.0ms (7%)

Counts

4 → 12

Calls

4 calls:

443.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
155.0ms	(-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
109.0ms	(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))))))
68.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4997	1774
1	4997	1774

prune94.0ms (0.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	63	11	74

Merged error: 0.1b

Counts

74 → 11

Compiler

Compiled 2958 to 511 computations (82.7% 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))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cos-sum_binary64_557` `cancel-sign-sub-inv_binary64_389`
8×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445`
4×	`sub-neg_binary64_416` `pow1_binary64_484` `sin-sum_binary64_556` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459` `add-log-exp_binary64_462`
3×	`cos-diff_binary64_560`
1×	`sin-diff_binary64_559`

Counts

4 → 48

Calls

4 calls:

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

series111.0ms (1%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(sin.f64 (-.f64 lambda1 lambda2))
26.0ms	(cos.f64 (-.f64 lambda1 lambda2))
25.0ms	(cos.f64 (-.f64 lambda1 lambda2))
24.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify170.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (157.0ms)

Iter	Nodes	Cost
0	4684	720
1	4684	720

prune97.0ms (0.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	60	11	71

Merged error: 0.1b

Counts

71 → 11

Compiler

Compiled 3240 to 665 computations (79.5% saved)

regimes186.0ms (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%)

sample5.6s (50.3%)

Algorithm

1×

intervals

Results

3.4s	4495×	body	1024	valid
942.0ms	1720×	body	512	valid
194.0ms	690×	body	256	valid
193.0ms	110×	body	2048	valid
129.0ms	985×	body	128	valid

Compiler

Compiled 442 to 249 computations (43.7% saved)

Details

analyze1.9s (17.2%)

sample168.0ms (1.5%)

simplify179.0ms (1.6%)

prune3.0ms (0%)

localize20.0ms (0.2%)

rewrite23.0ms (0.2%)

series346.0ms (3.1%)

simplify86.0ms (0.8%)

prune362.0ms (3.3%)

localize29.0ms (0.3%)

rewrite21.0ms (0.2%)

series492.0ms (4.4%)

simplify128.0ms (1.2%)

prune121.0ms (1.1%)

localize31.0ms (0.3%)

rewrite22.0ms (0.2%)

series776.0ms (7%)

simplify63.0ms (0.6%)

prune94.0ms (0.9%)

localize33.0ms (0.3%)

rewrite29.0ms (0.3%)

series111.0ms (1%)

simplify170.0ms (1.5%)

prune97.0ms (0.9%)

regimes186.0ms (1.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.6s (50.3%)

Profiling