Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample90.0ms (1.5%)

Algorithm

1×

intervals

Results

37.0ms	61×	body	2048	valid
36.0ms	125×	body	1024	valid
7.0ms	44×	body	512	valid
2.0ms	14×	body	256	valid
1.0ms	12×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune7.0ms (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: 43.4b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.4b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.0b	(cos.f64 (+.f64 x eps))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cos-sum_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `associate--l-_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `diff-cos_binary64`

Counts

2 → 23

Calls

2 calls:

7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0ms	(cos.f64 (+.f64 x eps))

series106.0ms (1.7%)

Counts

2 → 6

Calls

2 calls:

78.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
28.0ms	(cos.f64 (+.f64 x eps))

simplify95.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4863	429
1	4863	429

prune33.0ms (0.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	24	5	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	5	30

Merged error: 0.5b

Counts

30 → 5

Compiler

Compiled 449 to 160 computations (64.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`associate-l_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
3×	`distribute-lft-out_binary64` `sum-log_binary64`
2×	`sin-mult_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64`

Counts

4 → 60

Calls

4 calls:

13.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
12.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(+.f64 x (+.f64 x eps))

series290.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
97.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
41.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
30.0ms	(+.f64 x (+.f64 x eps))

simplify56.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4969	1369
1	4969	1369

prune94.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	65	7	72
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	65	12	77

Merged error: 0.4b

Counts

77 → 12

Compiler

Compiled 1715 to 1129 computations (34.2% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
5.0b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
5.0b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
5.0b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
3×	`cbrt-div_binary64` `pow1/3_binary64` `sin-mult_binary64` `cbrt-prod_binary64`

Counts

4 → 37

Calls

4 calls:

9.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
9.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
9.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series820.0ms (13.5%)

Counts

4 → 12

Calls

4 calls:

272.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
255.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
255.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
38.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4855	1133
1	4855	1133

prune126.0ms (2.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	49	12	61

Merged error: 0.4b

Counts

61 → 12

Compiler

Compiled 2774 to 1778 computations (35.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
3.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64`

Counts

4 → 40

Calls

4 calls:

8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))

series473.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
146.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
143.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
36.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5015	692

prune89.0ms (1.5%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	51	13	64

Merged error: 0.4b

Counts

64 → 13

Compiler

Compiled 1705 to 1255 computations (26.4% saved)

regimes105.0ms (1.7%)

Compiler: Compiled 700 to 554 computations (20.9% saved)

bsearch61.0ms (1%)

Steps

Iters	Range		Point
8	1.0986571555932432e-10	1.0464067636595074e-06	1.0218016712578999e-06
7	-3.9092861706778204e-08	-3.3430077415887593e-10	-3.8292398350027e-08

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	60
1	80	60

end0.0ms (0%)

sample3.3s (54.2%)

Algorithm

1×

intervals

Results

1.3s	2016×	body	2048	valid
1.1s	3848×	body	1024	valid
247.0ms	1355×	body	512	valid
62.0ms	548×	body	256	valid
14.0ms	232×	body	128	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 394 to 310 computations (21.3% saved)

Details

analyze2.0ms (0%)

sample90.0ms (1.5%)

simplify10.0ms (0.2%)

prune7.0ms (0.1%)

localize8.0ms (0.1%)

rewrite13.0ms (0.2%)

series106.0ms (1.7%)

simplify95.0ms (1.6%)

prune33.0ms (0.5%)

localize12.0ms (0.2%)

rewrite44.0ms (0.7%)

series290.0ms (4.8%)

simplify56.0ms (0.9%)

prune94.0ms (1.5%)

localize20.0ms (0.3%)

rewrite41.0ms (0.7%)

series820.0ms (13.5%)

simplify68.0ms (1.1%)

prune126.0ms (2.1%)

localize16.0ms (0.3%)

rewrite19.0ms (0.3%)

series473.0ms (7.8%)

simplify76.0ms (1.3%)

prune89.0ms (1.5%)

regimes105.0ms (1.7%)

bsearch61.0ms (1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.3s (54.2%)

Profiling