Details

analyze746.0ms (5.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
74.9%	25%	0.1%	10
74.9%	25%	0.1%	11
74.9%	25%	0.1%	12
74.9%	25%	0.1%	13
74.9%	25%	0.1%	14

Compiler

Compiled 51 to 41 computations (19.6% saved)

sample173.0ms (1.3%)

Algorithm

1×

intervals

Results

105.0ms	103×	body	1024	valid
27.0ms	38×	body	512	valid
21.0ms	94×	body	128	valid
8.0ms	21×	body	256	valid

Compiler

Compiled 101 to 83 computations (17.8% saved)

simplify52.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4924	77
1	4924	77

prune9.0ms (0.1%)

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: 0.4b

Counts

2 → 2

Compiler

Compiled 146 to 116 computations (20.5% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
1.0b	(-.f64 3 (sqrt.f64 5))
1.8b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite56.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64` `associate-r_binary64` `associate-r/_binary64` `associate-l*_binary64`
5×	`difference-of-squares_binary64` `sqrt-prod_binary64`
4×	`sub-neg_binary64` `associate-/r/_binary64` `times-frac_binary64`
3×	`flip3-+_binary64` `flip3--_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `diff-cos_binary64` `-commutative_binary64`

Counts

4 → 84

Calls

4 calls:

17.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
15.0ms	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
5.0ms	(-.f64 3 (sqrt.f64 5))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

series3.0s (22.4%)

Counts

4 → 10

Calls

4 calls:

2.8s	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
120.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
79.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
0.0ms	(-.f64 3 (sqrt.f64 5))

simplify83.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4933	3925
1	4933	3925

prune434.0ms (3.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	81	13	94
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	83	13	96

Merged error: 0.1b

Counts

96 → 13

Compiler

Compiled 7000 to 4776 computations (31.8% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))
0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
1.0b	(-.f64 3 (sqrt.f64 5))
1.8b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite59.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64`
43×	`associate-l_binary64`
35×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
17×	`difference-of-squares_binary64` `sqrt-prod_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64` `pow1_binary64`
6×	`difference-of-sqr-1_binary64`
4×	`sub-neg_binary64` `unswap-sqr_binary64`
3×	`flip3--_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `flip--_binary64`
2×	`pow-prod-down_binary64` `diff-log_binary64` `associate-r/_binary64` `-commutative_binary64`
1×	`cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-inv_binary64` `div-exp_binary64` `diff-cos_binary64` `associate-*l/_binary64`

Counts

4 → 113

Calls

4 calls:

16.0ms	(*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))
13.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
7.0ms	(-.f64 3 (sqrt.f64 5))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

series291.0ms (2.2%)

Counts

4 → 10

Calls

4 calls:

128.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
82.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
81.0ms	(*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))
0.0ms	(-.f64 3 (sqrt.f64 5))

simplify83.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4874	2135
1	4874	2135

prune462.0ms (3.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	5	7	12
Picked	0	1	1
Done	0	0	0
Total	125	11	136

Merged error: 0.0b

Counts

136 → 11

Compiler

Compiled 7897 to 5485 computations (30.5% saved)

localize41.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
1.0b	(-.f64 3 (sqrt.f64 5))
1.0b	(-.f64 (sqrt.f64 (sqrt.f64 5)) 1)
1.8b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
15×	`sqrt-prod_binary64`
11×	`difference-of-squares_binary64`
10×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`sub-neg_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`diff-log_binary64` `difference-of-sqr-1_binary64`
2×	`associate-*r/_binary64` `unswap-sqr_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `prod-exp_binary64` `times-frac_binary64` `diff-cos_binary64` `*-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

14.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
8.0ms	(-.f64 (sqrt.f64 (sqrt.f64 5)) 1)
6.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
5.0ms	(-.f64 3 (sqrt.f64 5))

series197.0ms (1.5%)

Counts

4 → 8

Calls

4 calls:

111.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
85.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
0.0ms	(-.f64 (sqrt.f64 (sqrt.f64 5)) 1)
0.0ms	(-.f64 3 (sqrt.f64 5))

simplify74.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4993	1510
1	4993	1510

prune349.0ms (2.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	87	11	98

Merged error: 0.0b

Counts

98 → 11

Compiler

Compiled 6469 to 4699 computations (27.4% saved)

localize36.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (cos.f64 x) (-.f64 (.f64 1/2 (sqrt.f64 5)) 1/2))
0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
1.0b	(-.f64 3 (sqrt.f64 5))
1.8b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
9×	`associate-r_binary64` `add-cube-cbrt_binary64` `associate-l_binary64`
8×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`sub-neg_binary64`
5×	`difference-of-squares_binary64` `sqrt-prod_binary64`
4×	`flip3--_binary64` `associate-*r/_binary64` `flip--_binary64`
3×	`unswap-sqr_binary64` `distribute-lft-out--_binary64`
2×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`times-frac_binary64` `diff-cos_binary64`

Counts

4 → 79

Calls

4 calls:

14.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
9.0ms	(.f64 (cos.f64 x) (-.f64 (.f64 1/2 (sqrt.f64 5)) 1/2))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
5.0ms	(-.f64 3 (sqrt.f64 5))

series286.0ms (2.1%)

Counts

4 → 10

Calls

4 calls:

125.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
83.0ms	(.f64 (cos.f64 x) (-.f64 (.f64 1/2 (sqrt.f64 5)) 1/2))
78.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
0.0ms	(-.f64 3 (sqrt.f64 5))

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4943	1533
1	4943	1533

prune251.0ms (1.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	89	11	100

Merged error: 0.0b

Counts

100 → 11

Compiler

Compiled 4995 to 3355 computations (32.8% saved)

regimes129.0ms (1%)

Compiler: Compiled 1776 to 1374 computations (22.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	101	84
1	101	84

end0.0ms (0%)

sample6.3s (47.2%)

Algorithm

1×

intervals

Results

3.6s	3467×	body	1024	valid
919.0ms	1390×	body	512	valid
485.0ms	2508×	body	128	valid
264.0ms	613×	body	256	valid
45.0ms	22×	body	2048	valid

Compiler

Compiled 989 to 768 computations (22.3% saved)

Details

analyze746.0ms (5.6%)

sample173.0ms (1.3%)

simplify52.0ms (0.4%)

prune9.0ms (0.1%)

localize33.0ms (0.2%)

rewrite56.0ms (0.4%)

series3.0s (22.4%)

simplify83.0ms (0.6%)

prune434.0ms (3.3%)

localize33.0ms (0.2%)

rewrite59.0ms (0.4%)

series291.0ms (2.2%)

simplify83.0ms (0.6%)

prune462.0ms (3.5%)

localize41.0ms (0.3%)

rewrite45.0ms (0.3%)

series197.0ms (1.5%)

simplify74.0ms (0.6%)

prune349.0ms (2.6%)

localize36.0ms (0.3%)

rewrite45.0ms (0.3%)

series286.0ms (2.1%)

simplify75.0ms (0.6%)

prune251.0ms (1.9%)

regimes129.0ms (1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.3s (47.2%)

Profiling