Details

analyze2.0s (15.1%)

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)

sample173.0ms (1.3%)

Algorithm

1×

intervals

Results

120.0ms	143×	body	1024	valid
24.0ms	56×	body	512	valid
7.0ms	27×	body	256	valid
5.0ms	3×	body	2048	valid
3.0ms	27×	body	128	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify182.0ms (1.4%)

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: 1.0b

Counts

2 → 1

Compiler

Compiled 40 to 28 computations (30% saved)

localize24.0ms (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)))))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.2b	(sin.f64 (-.f64 lambda1 lambda2))
4.4b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite21.0ms (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:

6.0ms	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
5.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.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)))))

series353.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

220.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
66.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
37.0ms	(sin.f64 (-.f64 lambda1 lambda2))
30.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4992	1058
1	4992	1058

prune403.0ms (3.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	42	14	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	14	57

Merged error: 0.8b

Counts

57 → 14

Compiler

Compiled 7481 to 3961 computations (47.1% saved)

localize31.0ms (0.2%)

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 (cos.f64 lambda2) (sin.f64 lambda1))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.4b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_445`
7×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
6×	`pow1_binary64_484` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459` `add-log-exp_binary64_462`
4×	`cos-sum_binary64_557`
3×	`associate-l_binary64_364` `cancel-sign-sub-inv_binary64_389` `cos-diff_binary64_560` `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` `prod-exp_binary64_472` `+-commutative_binary64_353` `*-commutative_binary64_354` `flip3-+_binary64_426` `unswap-sqr_binary64_391` `sum-log_binary64_514` `cbrt-unprod_binary64_456`

Counts

4 → 50

Calls

4 calls:

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

series409.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

216.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
86.0ms	(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)))))
78.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
29.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify125.0ms (1%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4763	1242
1	4763	1242

prune114.0ms (0.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	64	12	76

Merged error: 0.1b

Counts

76 → 12

Compiler

Compiled 2942 to 787 computations (73.2% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
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 (sin.f64 lambda1) (sin.f64 lambda2))
0.5b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_445`
8×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `pow1_binary64_484` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
6×	`associate-l_binary64_364` `associate-r_binary64_363` `add-log-exp_binary64_462`
2×	`pow-prod-down_binary64_494` `associate-+r+_binary64_355` `prod-exp_binary64_472` `*-commutative_binary64_354` `unswap-sqr_binary64_391` `cbrt-unprod_binary64_456`
1×	`distribute-rgt-in_binary64_373` `distribute-lft-in_binary64_372` `flip-+_binary64_397` `sin-mult_binary64_578` `+-commutative_binary64_353` `flip3-+_binary64_426` `sum-log_binary64_514`

Counts

4 → 57

Calls

4 calls:

6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
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))))))

series701.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

440.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
115.0ms	(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))))))
77.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
69.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4945	1626
1	4945	1626

prune149.0ms (1.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	69	12	81

Merged error: 0.1b

Counts

81 → 12

Compiler

Compiled 4161 to 1055 computations (74.6% saved)

localize36.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.5b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
0.6b	(cbrt.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 3))
0.6b	(pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 3)

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_445`
12×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `cbrt-prod_binary64_454`
7×	`pow1_binary64_484` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
6×	`cube-prod_binary64_451` `add-log-exp_binary64_462` `unpow-prod-down_binary64_502`
4×	`cube-div_binary64_452`
3×	`associate-l_binary64_364` `flip-+_binary64_397` `associate-r_binary64_363` `flip3-+_binary64_426` `pow-unpow_binary64_500`
2×	`associate-+r+_binary64_355` `cbrt-div_binary64_455` `unpow3_binary64_489` `cube-mult_binary64_453` `sqr-pow_binary64_395`
1×	`pow-prod-down_binary64_494` `distribute-rgt-in_binary64_373` `distribute-lft-in_binary64_372` `pow-to-exp_binary64_492` `sin-mult_binary64_578` `prod-exp_binary64_472` `+-commutative_binary64_353` `pow-exp_binary64_491` `pow1/3_binary64_505` `*-commutative_binary64_354` `rem-cbrt-cube_binary64_447` `pow-pow_binary64_495` `rem-cube-cbrt_binary64_446` `unswap-sqr_binary64_391` `sum-log_binary64_514` `cbrt-unprod_binary64_456`

Counts

4 → 80

Calls

4 calls:

6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 3)
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)))))
5.0ms	(cbrt.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 3))

series1.9s (14.6%)

Counts

4 → 12

Calls

4 calls:

998.0ms	(pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 3)
437.0ms	(cbrt.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 3))
418.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
63.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify51.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5003	2984

prune300.0ms (2.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	91	13	104

Merged error: 0.1b

Counts

104 → 13

Compiler

Compiled 8196 to 2580 computations (68.5% saved)

regimes245.0ms (1.9%)

Compiler: Compiled 3658 to 1714 computations (53.1% 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 (42.9%)

Algorithm

1×

intervals

Results

3.5s	4427×	body	1024	valid
800.0ms	1751×	body	512	valid
210.0ms	757×	body	256	valid
193.0ms	106×	body	2048	valid
129.0ms	959×	body	128	valid

Compiler

Compiled 662 to 317 computations (52.1% saved)

Details

analyze2.0s (15.1%)

sample173.0ms (1.3%)

simplify182.0ms (1.4%)

prune3.0ms (0%)

localize24.0ms (0.2%)

rewrite21.0ms (0.2%)

series353.0ms (2.7%)

simplify85.0ms (0.6%)

prune403.0ms (3.1%)

localize31.0ms (0.2%)

rewrite22.0ms (0.2%)

series409.0ms (3.1%)

simplify125.0ms (1%)

prune114.0ms (0.9%)

localize30.0ms (0.2%)

rewrite23.0ms (0.2%)

series701.0ms (5.3%)

simplify76.0ms (0.6%)

prune149.0ms (1.1%)

localize36.0ms (0.3%)

rewrite32.0ms (0.2%)

series1.9s (14.6%)

simplify51.0ms (0.4%)

prune300.0ms (2.3%)

regimes245.0ms (1.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.6s (42.9%)

Profiling