Details

analyze2.8s (16.2%)

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
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample283.0ms (1.7%)

Algorithm

1×

intervals

Results

201.0ms	143×	body	1280	valid
50.0ms	60×	body	640	valid
12.0ms	22×	body	320	valid
4.0ms	23×	body	80	valid
3.0ms	8×	body	160	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify46.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	368	39
1	368	39

prune9.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 14.0b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.9b	(sin.f64 (-.f64 lambda1 lambda2))
3.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64`
5×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `cos-diff_binary64` `add-sqr-sqrt_binary64`
4×	`insert-posit16`
3×	`pow-prod-down_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
2×	`associate--r+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
1×	`sin-diff_binary64` `flip3--_binary64` `diff-log_binary64` `sin-sum_binary64` `associate-l_binary64` `sin-cos-mult_binary64` `cos-sum_binary64` `flip--_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

9.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
6.0ms	(-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series597.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

320.0ms	(-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))
207.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
38.0ms	(sin.f64 (-.f64 lambda1 lambda2))
32.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify132.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	5523	1320

prune116.0ms (0.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	52	16	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	16	69

Merged error: 6.6b

Counts

69 → 16

Compiler

Compiled 2565 to 607 computations (76.3% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))
0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite28.0ms (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`
5×	`cos-diff_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `insert-posit16`
2×	`sub-neg_binary64` `associate--r+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `diff-log_binary64` `unswap-sqr_binary64` `sin-cos-mult_binary64` `cos-sum_binary64` `flip--_binary64` `associate-*l/_binary64`

Counts

4 → 65

Calls

4 calls:

9.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
6.0ms	(-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))
6.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series645.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

324.0ms	(-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))
204.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
79.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
38.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify146.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	5745	1428

prune122.0ms (0.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	8	7	15
Picked	1	0	1
Done	0	0	0
Total	80	13	93

Merged error: 0.1b

Counts

93 → 13

Compiler

Compiled 3315 to 624 computations (81.2% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.3b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`associate-l_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `sin-cos-mult_binary64` `insert-posit16` `*-commutative_binary64`
3×	`associate-*r/_binary64` `unswap-sqr_binary64` `sin-mult_binary64` `frac-times_binary64`
2×	`flip3-+_binary64` `cos-mult_binary64` `frac-add_binary64` `flip-+_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-*l/_binary64`

Counts

4 → 86

Calls

4 calls:

14.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
6.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
6.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

series572.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

358.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
73.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
71.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
70.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

simplify144.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4969	1790
1	4969	1790

prune164.0ms (1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	98	13	111

Merged error: 0.0b

Counts

111 → 13

Compiler

Compiled 4859 to 802 computations (83.5% saved)

localize42.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
0.4b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))

rewrite59.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`pow1_binary64`
40×	`cos-mult_binary64`
38×	`sin-mult_binary64`
37×	`associate-*r/_binary64`
33×	`frac-times_binary64`
25×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`pow-prod-down_binary64` `associate-*l/_binary64`
18×	`frac-sub_binary64`
17×	`sin-cos-mult_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
11×	`associate-r_binary64`
10×	`sub-div_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-l_binary64`
4×	`add-log-exp_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `insert-posit16` `*-commutative_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `flip--_binary64`
1×	`swap-sqr_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `pow2_binary64`

Counts

4 → 133

Calls

4 calls:

27.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
11.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

series871.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

615.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
114.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
72.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
70.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify97.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5969	4157

prune264.0ms (1.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	145	13	158

Merged error: 0.0b

Counts

158 → 13

Compiler

Compiled 9845 to 1399 computations (85.8% saved)

regimes235.0ms (1.4%)

Compiler: Compiled 3075 to 1738 computations (43.5% saved)

bsearch0.0ms (0%)

simplify26.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	474	103
1	474	103

end0.0ms (0%)

sample9.5s (55.8%)

Algorithm

1×

intervals

Results

6.6s	4601×	body	1280	valid
1.6s	1951×	body	640	valid
321.0ms	589×	body	320	valid
104.0ms	646×	body	80	valid
71.0ms	213×	body	160	valid

Compiler

Compiled 656 to 366 computations (44.2% saved)

Details

analyze2.8s (16.2%)

sample283.0ms (1.7%)

simplify46.0ms (0.3%)

prune9.0ms (0.1%)

localize26.0ms (0.2%)

rewrite26.0ms (0.2%)

series597.0ms (3.5%)

simplify132.0ms (0.8%)

prune116.0ms (0.7%)

localize35.0ms (0.2%)

rewrite28.0ms (0.2%)

series645.0ms (3.8%)

simplify146.0ms (0.9%)

prune122.0ms (0.7%)

localize36.0ms (0.2%)

rewrite35.0ms (0.2%)

series572.0ms (3.4%)

simplify144.0ms (0.8%)

prune164.0ms (1%)

localize42.0ms (0.2%)

rewrite59.0ms (0.3%)

series871.0ms (5.1%)

simplify97.0ms (0.6%)

prune264.0ms (1.6%)

regimes235.0ms (1.4%)

bsearch0.0ms (0%)

simplify26.0ms (0.2%)

end0.0ms (0%)

sample9.5s (55.8%)

Profiling