Details

analyze1.9s (15.7%)

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)

sample192.0ms (1.6%)

Algorithm

1×

intervals

Results

113.0ms	116×	body	1280	valid
46.0ms	84×	body	640	valid
15.0ms	28×	body	320	valid
2.0ms	19×	body	80	valid
2.0ms	9×	body	160	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	212	32
1	212	32

prune4.0ms (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)

localize26.0ms (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))))
3.1b	(sin.f64 (-.f64 lambda1 lambda2))
3.2b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `insert-posit16`
3×	`cos-diff_binary64`
2×	`sub-neg_binary64` `associate-+r+_binary64`
1×	`flip3-+_binary64` `sin-diff_binary64` `sin-sum_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `cos-sum_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 42

Calls

4 calls:

6.0ms	(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)))))

series339.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

206.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
72.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
33.0ms	(sin.f64 (-.f64 lambda1 lambda2))
28.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify214.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (188.0ms)

Iter	Nodes	Cost
0	4811	1015
1	4811	1015

prune91.0ms (0.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	42	12	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	12	55

Merged error: 0.8b

Counts

55 → 12

Compiler

Compiled 1763 to 470 computations (73.3% saved)

localize32.0ms (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	(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)))))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.2b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`insert-posit16`
3×	`sub-neg_binary64` `associate-r_binary64` `associate-l_binary64` `cos-diff_binary64`
2×	`associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `cos-sum_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 55

Calls

4 calls:

9.0ms	(.f64 (cos.f64 phi2) (-.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) (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)))))

series598.0ms (5%)

Counts

4 → 12

Calls

4 calls:

265.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
212.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 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)))))
33.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify134.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4980	1707
1	4980	1707

prune95.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	68	11	79

Merged error: 0.1b

Counts

79 → 11

Compiler

Compiled 2650 to 498 computations (81.2% saved)

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2))) (.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.5b	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `insert-posit16`
2×	`sin-mult_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-*l/_binary64` `sum-log_binary64`

Counts

4 → 60

Calls

4 calls:

8.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
6.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2))) (.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))))

series559.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

227.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))
141.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))
116.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2))) (.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))))
75.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4994	1601
1	4994	1601

prune105.0ms (0.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 0.1b

Counts

83 → 10

Compiler

Compiled 3366 to 533 computations (84.2% saved)

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(exp.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2))))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.5b	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))
0.7b	(log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-prod_binary64`
4×	`log-prod_binary64` `log-pow_binary64` `insert-posit16`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`rem-exp-log_binary64` `exp-sum_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-mult_binary64` `+-commutative_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 63

Calls

4 calls:

9.0ms	(log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))))
7.0ms	(exp.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2))))
6.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

series871.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

338.0ms	(exp.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2))))
231.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))
225.0ms	(log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))))
77.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify108.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5030	1416

prune94.0ms (0.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	74	11	85

Merged error: 0.1b

Counts

85 → 11

Compiler

Compiled 3329 to 401 computations (88% saved)

regimes189.0ms (1.6%)

Compiler: Compiled 2386 to 1294 computations (45.8% saved)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	61	65
1	61	65

end0.0ms (0%)

sample6.2s (51.5%)

Algorithm

1×

intervals

Results

3.5s	3549×	body	1280	valid
1.3s	2366×	body	640	valid
588.0ms	952×	body	320	valid
102.0ms	426×	body	160	valid
88.0ms	707×	body	80	valid

Compiler

Compiled 455 to 250 computations (45.1% saved)

Details

analyze1.9s (15.7%)

sample192.0ms (1.6%)

simplify44.0ms (0.4%)

prune4.0ms (0%)

localize26.0ms (0.2%)

rewrite18.0ms (0.2%)

series339.0ms (2.8%)

simplify214.0ms (1.8%)

prune91.0ms (0.8%)

localize32.0ms (0.3%)

rewrite22.0ms (0.2%)

series598.0ms (5%)

simplify134.0ms (1.1%)

prune95.0ms (0.8%)

localize33.0ms (0.3%)

rewrite23.0ms (0.2%)

series559.0ms (4.6%)

simplify96.0ms (0.8%)

prune105.0ms (0.9%)

localize35.0ms (0.3%)

rewrite30.0ms (0.2%)

series871.0ms (7.2%)

simplify108.0ms (0.9%)

prune94.0ms (0.8%)

regimes189.0ms (1.6%)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample6.2s (51.5%)

Profiling