Details

analyze1.9s (16.3%)

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 (1.4%)

Algorithm

1×

intervals

Results

115.0ms	143×	body	1024	valid
26.0ms	60×	body	512	valid
7.0ms	23×	body	256	valid
4.0ms	28×	body	128	valid
3.0ms	2×	body	2048	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify180.0ms (1.5%)

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: 1.1b

Counts

2 → 1

Compiler

Compiled 40 to 28 computations (30% saved)

localize21.0ms (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)))))
0.4b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.0b	(cos.f64 (-.f64 lambda1 lambda2))
3.1b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite20.0ms (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:

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

series345.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

212.0ms	(+.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))
27.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4992	1058
1	4992	1058

prune331.0ms (2.8%)

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: 0.9b

Counts

57 → 11

Compiler

Compiled 6341 to 3282 computations (48.2% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.4b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.0b	(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 lambda1) (sin.f64 lambda2))
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 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))

series394.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
87.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
64.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
29.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify121.0ms (1%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4781	1242
1	4781	1242

prune123.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	63	10	73

Merged error: 0.1b

Counts

73 → 10

Compiler

Compiled 3148 to 908 computations (71.2% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.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))
0.4b	(+.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:

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

series697.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

447.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
111.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.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))
68.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

simplify78.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5013	1626

prune180.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	68	11	79

Merged error: 0.1b

Counts

79 → 11

Compiler

Compiled 4868 to 1458 computations (70% saved)

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.4b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
3.3b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite21.0ms (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` `pow1_binary64_484` `add-log-exp_binary64_462`
6×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
3×	`associate-l_binary64_364` `log-pow_binary64_512` `associate-r_binary64_363` `log-prod_binary64_509`
2×	`associate-+r+_binary64_355`
1×	`pow-prod-down_binary64_494` `distribute-rgt-in_binary64_373` `distribute-lft-in_binary64_372` `flip-+_binary64_397` `exp-to-pow_binary64_485` `sin-mult_binary64_578` `prod-exp_binary64_472` `+-commutative_binary64_353` `*-commutative_binary64_354` `flip3-+_binary64_426` `rem-log-exp_binary64_464` `unswap-sqr_binary64_391` `sum-log_binary64_514` `cbrt-unprod_binary64_456` `exp-prod_binary64_475`

Counts

4 → 53

Calls

4 calls:

6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
2.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))

series852.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

513.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
156.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
113.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
70.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify70.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5069	1581

prune81.0ms (0.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	65	11	76

Merged error: 0.1b

Counts

76 → 11

Compiler

Compiled 2686 to 392 computations (85.4% saved)

regimes190.0ms (1.6%)

Compiler: Compiled 2500 to 1348 computations (46.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	60
1	59	60

end0.0ms (0%)

sample5.8s (48.9%)

Algorithm

1×

intervals

Results

3.6s	4477×	body	1024	valid
782.0ms	1714×	body	512	valid
367.0ms	987×	body	128	valid
201.0ms	712×	body	256	valid
200.0ms	110×	body	2048	valid

Compiler

Compiled 471 to 258 computations (45.2% saved)

Details

analyze1.9s (16.3%)

sample168.0ms (1.4%)

simplify180.0ms (1.5%)

prune3.0ms (0%)

localize21.0ms (0.2%)

rewrite20.0ms (0.2%)

series345.0ms (2.9%)

simplify88.0ms (0.7%)

prune331.0ms (2.8%)

localize30.0ms (0.3%)

rewrite22.0ms (0.2%)

series394.0ms (3.3%)

simplify121.0ms (1%)

prune123.0ms (1%)

localize30.0ms (0.3%)

rewrite23.0ms (0.2%)

series697.0ms (5.9%)

simplify78.0ms (0.7%)

prune180.0ms (1.5%)

localize37.0ms (0.3%)

rewrite21.0ms (0.2%)

series852.0ms (7.2%)

simplify70.0ms (0.6%)

prune81.0ms (0.7%)

regimes190.0ms (1.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.8s (48.9%)

Profiling