Details

analyze3.7s (18.1%)

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
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)

sample321.0ms (1.6%)

Algorithm

1×

intervals

Results

244.0ms	172×	body	1024	valid
36.0ms	47×	body	512	valid
12.0ms	4×	body	2048	valid
5.0ms	12×	body	256	valid
5.0ms	21×	body	128	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify242.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	367	39
1	367	39

prune4.0ms (0%)

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: 14.1b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))
3.7b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cbrt-cube_binary64_1819` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `pow1_binary64_1844`
9×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
6×	`cancel-sign-sub-inv_binary64_1749` `associate-r_binary64_1723`
4×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `associate-l_binary64_1724` `pow-prod-down_binary64_1854` `cos-sum_binary64_1917` `sin-sum_binary64_1916` `add-log-exp_binary64_1822`
3×	`cos-diff_binary64_1920`
2×	`sin-cos-mult_binary64_1939` `*-commutative_binary64_1714` `sub-neg_binary64_1776`
1×	`distribute-lft-in_binary64_1732` `associate-*l/_binary64_1726` `sin-diff_binary64_1919` `distribute-rgt-in_binary64_1733` `unswap-sqr_binary64_1751`

Counts

4 → 64

Calls

4 calls:

8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series437.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

288.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
86.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
35.0ms	(sin.f64 (-.f64 lambda1 lambda2))
28.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify135.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	4876	1051
1	4876	1051

prune139.0ms (0.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	63	13	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	13	77

Merged error: 6.0b

Counts

77 → 13

Compiler

Compiled 2551 to 572 computations (77.6% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite40.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1805`
13×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `pow1_binary64_1844`
10×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
9×	`associate-r_binary64_1723`
7×	`associate-l_binary64_1724`
5×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-prod-down_binary64_1854`
4×	`cos-sum_binary64_1917` `add-log-exp_binary64_1822`
3×	`cancel-sign-sub-inv_binary64_1749` `*-commutative_binary64_1714` `cos-diff_binary64_1920`
2×	`sin-cos-mult_binary64_1939` `unswap-sqr_binary64_1751`
1×	`distribute-lft-in_binary64_1732` `associate-*l/_binary64_1726` `distribute-rgt-in_binary64_1733` `sub-neg_binary64_1776`

Counts

4 → 70

Calls

4 calls:

12.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
8.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
5.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series488.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

290.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
83.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
77.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
37.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify111.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5171	1103

prune148.0ms (0.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	85	10	95

Merged error: 0.1b

Counts

95 → 10

Compiler

Compiled 3227 to 577 computations (82.1% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite53.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_1805`
15×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `pow1_binary64_1844`
12×	`associate-r_binary64_1723`
11×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
10×	`associate-l_binary64_1724`
6×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-prod-down_binary64_1854`
5×	`sin-cos-mult_binary64_1939`
4×	`*-commutative_binary64_1714` `add-log-exp_binary64_1822`
3×	`associate-*r/_binary64_1725` `sin-mult_binary64_1938` `frac-times_binary64_1793` `unswap-sqr_binary64_1751`
2×	`cos-mult_binary64_1937` `frac-add_binary64_1791` `flip-+_binary64_1757` `flip3-+_binary64_1786`
1×	`distribute-lft-in_binary64_1732` `associate-*l/_binary64_1726` `distribute-rgt-in_binary64_1733`

Counts

4 → 83

Calls

4 calls:

12.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
9.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))

series777.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

455.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
130.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
99.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
92.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

simplify94.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5009	1744

prune197.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	90	5	95
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	93	12	105

Merged error: 0.0b

Counts

105 → 12

Compiler

Compiled 4614 to 768 computations (83.4% saved)

localize41.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
2.4b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite64.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1805` `pow1_binary64_1844`
13×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
10×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
9×	`associate-r_binary64_1723`
7×	`associate-l_binary64_1724`
5×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-prod-down_binary64_1854` `add-log-exp_binary64_1822`
4×	`sin-cos-mult_binary64_1939`
3×	`log-prod_binary64_1869` `log-pow_binary64_1872` `*-commutative_binary64_1714`
2×	`associate-*r/_binary64_1725` `flip-+_binary64_1757` `frac-times_binary64_1793` `flip3-+_binary64_1786` `unswap-sqr_binary64_1751`
1×	`distribute-lft-in_binary64_1732` `exp-to-pow_binary64_1845` `associate-*l/_binary64_1726` `sin-mult_binary64_1938` `distribute-rgt-in_binary64_1733` `exp-prod_binary64_1835` `rem-log-exp_binary64_1824`

Counts

4 → 77

Calls

4 calls:

15.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
11.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
10.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
2.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

series956.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

600.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
174.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
106.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
76.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify73.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5058	1606

prune206.0ms (1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	89	12	101

Merged error: 0.0b

Counts

101 → 12

Compiler

Compiled 4000 to 495 computations (87.6% saved)

regimes725.0ms (3.6%)

Compiler: Compiled 6126 to 4142 computations (32.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	128	67
1	128	67

end0.0ms (0%)

sample11.3s (55.5%)

Algorithm

1×

intervals

Results

7.5s	5292×	body	1024	valid
1.1s	1330×	body	512	valid
647.0ms	181×	body	2048	valid
210.0ms	394×	body	256	valid
182.0ms	803×	body	128	valid

Compiler

Compiled 1010 to 680 computations (32.7% saved)

Details

analyze3.7s (18.1%)

sample321.0ms (1.6%)

simplify242.0ms (1.2%)

prune4.0ms (0%)

localize25.0ms (0.1%)

rewrite30.0ms (0.1%)

series437.0ms (2.1%)

simplify135.0ms (0.7%)

prune139.0ms (0.7%)

localize34.0ms (0.2%)

rewrite40.0ms (0.2%)

series488.0ms (2.4%)

simplify111.0ms (0.5%)

prune148.0ms (0.7%)

localize37.0ms (0.2%)

rewrite53.0ms (0.3%)

series777.0ms (3.8%)

simplify94.0ms (0.5%)

prune197.0ms (1%)

localize41.0ms (0.2%)

rewrite64.0ms (0.3%)

series956.0ms (4.7%)

simplify73.0ms (0.4%)

prune206.0ms (1%)

regimes725.0ms (3.6%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample11.3s (55.5%)

Profiling