Details

analyze1.9s (16.1%)

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)

sample169.0ms (1.4%)

Algorithm

1×

intervals

Results

108.0ms	140×	body	1024	valid
24.0ms	55×	body	512	valid
13.0ms	26×	body	256	valid
7.0ms	4×	body	2048	valid
4.0ms	31×	body	128	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify185.0ms (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: 1.1b

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)))))
0.6b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
6.0b	(sin.f64 (-.f64 lambda1 lambda2))
6.0b	(cos.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	(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)))))

series351.0ms (3%)

Counts

4 → 12

Calls

4 calls:

215.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
75.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
32.0ms	(sin.f64 (-.f64 lambda1 lambda2))
29.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4992	1058
1	4992	1058

prune352.0ms (3%)

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: 0.9b

Counts

57 → 14

Compiler

Compiled 6761 to 3676 computations (45.6% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
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)))))
0.6b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
6.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite30.0ms (0.3%)

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`
5×	`cancel-sign-sub-inv_binary64_389`
4×	`cos-sum_binary64_557`
3×	`distribute-rgt-in_binary64_373` `sub-neg_binary64_416` `distribute-lft-in_binary64_372` `associate-l_binary64_364` `cos-diff_binary64_560` `associate-r_binary64_363`
2×	`associate-+r+_binary64_355` `associate-*r/_binary64_365`
1×	`pow-prod-down_binary64_494` `flip-+_binary64_397` `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 → 56

Calls

4 calls:

10.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
8.0ms	(+.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)))))

series601.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

274.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
219.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
81.0ms	(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)))))
28.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify74.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4933	1723
1	4933	1723

prune178.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	70	12	82

Merged error: 0.1b

Counts

82 → 12

Compiler

Compiled 4288 to 1430 computations (66.7% saved)

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite29.0ms (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`
3×	`distribute-rgt-in_binary64_373` `distribute-lft-in_binary64_372`
2×	`pow-prod-down_binary64_494` `sub-neg_binary64_416` `associate-+r+_binary64_355` `cancel-sign-sub-inv_binary64_389` `prod-exp_binary64_472` `associate-r/_binary64_365` `-commutative_binary64_354` `unswap-sqr_binary64_391` `cbrt-unprod_binary64_456`
1×	`flip-+_binary64_397` `sin-mult_binary64_578` `+-commutative_binary64_353` `flip3--_binary64_427` `flip3-+_binary64_426` `flip--_binary64_398` `sum-log_binary64_514`

Counts

4 → 63

Calls

4 calls:

10.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
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)) (*.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))))))

series874.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

438.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
257.0ms	(.f64 (cos.f64 phi2) (-.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))))))
70.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4963	2107
1	4963	2107

prune103.0ms (0.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	75	12	87

Merged error: 0.1b

Counts

87 → 12

Compiler

Compiled 3442 to 540 computations (84.3% saved)

localize36.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 phi2))
0.3b	(cbrt.f64 (cos.f64 phi2))
0.6b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
6.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445`
6×	`add-log-exp_binary64_462` `cbrt-prod_binary64_454`
4×	`cos-sum_binary64_557` `pow1_binary64_484` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
3×	`cancel-sign-sub-inv_binary64_389` `cos-diff_binary64_560`
2×	`associate-+r+_binary64_355` `pow1/3_binary64_505`
1×	`distribute-rgt-in_binary64_373` `sub-neg_binary64_416` `distribute-lft-in_binary64_372` `flip-+_binary64_397` `+-commutative_binary64_353` `flip3-+_binary64_426` `sum-log_binary64_514`

Counts

4 → 47

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))))
2.0ms	(cbrt.f64 (cos.f64 phi2))
1.0ms	(cbrt.f64 (cos.f64 phi2))

series689.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

327.0ms	(cbrt.f64 (cos.f64 phi2))
218.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
117.0ms	(cbrt.f64 (cos.f64 phi2))
26.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify82.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4917	780
1	4917	780

prune137.0ms (1.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	56	3	59
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	58	13	71

Merged error: 0.1b

Counts

71 → 13

Compiler

Compiled 3682 to 1033 computations (71.9% saved)

regimes212.0ms (1.8%)

Compiler: Compiled 2650 to 1534 computations (42.1% 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%)

sample5.5s (46.6%)

Algorithm

1×

intervals

Results

3.5s	4450×	body	1024	valid
790.0ms	1790×	body	512	valid
213.0ms	727×	body	256	valid
209.0ms	114×	body	2048	valid
122.0ms	919×	body	128	valid

Compiler

Compiled 494 to 287 computations (41.9% saved)

Details

analyze1.9s (16.1%)

sample169.0ms (1.4%)

simplify185.0ms (1.6%)

prune3.0ms (0%)

localize24.0ms (0.2%)

rewrite20.0ms (0.2%)

series351.0ms (3%)

simplify87.0ms (0.7%)

prune352.0ms (3%)

localize29.0ms (0.2%)

rewrite30.0ms (0.3%)

series601.0ms (5.1%)

simplify74.0ms (0.6%)

prune178.0ms (1.5%)

localize33.0ms (0.3%)

rewrite29.0ms (0.2%)

series874.0ms (7.4%)

simplify68.0ms (0.6%)

prune103.0ms (0.9%)

localize36.0ms (0.3%)

rewrite20.0ms (0.2%)

series689.0ms (5.8%)

simplify82.0ms (0.7%)

prune137.0ms (1.2%)

regimes212.0ms (1.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.5s (46.6%)

Profiling