Details

analyze734.0ms (6.6%)

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
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample79.0ms (0.7%)

Algorithm

1×

intervals

Results

33.0ms	112×	body	1024	valid
25.0ms	37×	body	2048	valid
9.0ms	57×	body	512	valid
2.0ms	20×	body	256	valid
1.0ms	30×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune2.0ms (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: 38.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.9b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0b	(tan.f64 (+.f64 x eps))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `tan-quot_binary64`
3×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64`
2×	`tan-sum_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `frac-sub_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

2 → 27

Calls

2 calls:

12.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	(tan.f64 (+.f64 x eps))

series347.0ms (3.1%)

Counts

2 → 6

Calls

2 calls:

223.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
123.0ms	(tan.f64 (+.f64 x eps))

simplify89.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4837	544
1	4837	544

prune103.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	25	8	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	8	34

Merged error: 13.9b

Counts

34 → 8

Compiler

Compiled 1580 to 806 computations (49% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.1b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
2.0b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`tan-quot_binary64`
6×	`pow1_binary64`
4×	`distribute-lft-out_binary64` `cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
3×	`associate-/l/_binary64` `associate-/r_binary64` `flip3--_binary64` `associate-r_binary64` `associate-l*_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64` `difference-of-squares_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `frac-add_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 87

Calls

4 calls:

14.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
9.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

series1.9s (17.5%)

Counts

4 → 12

Calls

4 calls:

967.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
547.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
239.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
191.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify78.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5832	2593

prune680.0ms (6.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	84	15	99
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	88	19	107

Merged error: 13.8b

Counts

107 → 19

Compiler

Compiled 14033 to 7033 computations (49.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))
0.1b	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
0.3b	(*.f64 (tan.f64 eps) (sin.f64 x))
2.0b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))

rewrite49.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`cancel-sign-sub-inv_binary64`
8×	`add-log-exp_binary64`
7×	`times-frac_binary64`
6×	`pow1_binary64`
4×	`difference-of-squares_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `tan-quot_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `frac-sub_binary64` `-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

21.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))
8.0ms	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
7.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))
5.0ms	(*.f64 (tan.f64 eps) (sin.f64 x))

series1.6s (14.7%)

Counts

4 → 12

Calls

4 calls:

1.0s	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))
259.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))
214.0ms	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
134.0ms	(*.f64 (tan.f64 eps) (sin.f64 x))

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4963	2111
1	4963	2111

prune198.0ms (1.8%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	2	16	18
Picked	0	1	1
Done	0	0	0
Total	92	19	111

Merged error: 13.8b

Counts

111 → 19

Compiler

Compiled 4605 to 1844 computations (60% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))
0.2b	(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))
0.2b	(*.f64 (tan.f64 x) (sin.f64 eps))
2.0b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))) (tan.f64 x))

rewrite47.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`cancel-sign-sub-inv_binary64`
8×	`add-log-exp_binary64`
7×	`times-frac_binary64`
6×	`pow1_binary64`
4×	`difference-of-squares_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `tan-quot_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `frac-sub_binary64` `-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

21.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))) (tan.f64 x))
7.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))
6.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))
5.0ms	(*.f64 (tan.f64 x) (sin.f64 eps))

series1.6s (14%)

Counts

4 → 12

Calls

4 calls:

994.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))) (tan.f64 x))
231.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))
207.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))
121.0ms	(*.f64 (tan.f64 x) (sin.f64 eps))

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5079	2097

prune200.0ms (1.8%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	1	16	17
Picked	1	0	1
Done	0	1	1
Total	92	19	111

Merged error: 13.8b

Counts

111 → 19

Compiler

Compiled 4647 to 1853 computations (60.1% saved)

regimes134.0ms (1.2%)

Compiler: Compiled 1110 to 590 computations (46.8% saved)

bsearch86.0ms (0.8%)

Steps

Iters	Range		Point
10	1.7542111797321302e-59	3.527021878686262e-48	4.9499569793722125e-51
10	-9.51787035254729e-05	-7.696276609811415e-16	-7.776131049831412e-16

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	87
1	72	87

end0.0ms (0%)

sample2.9s (26.1%)

Algorithm

1×

intervals

Results

1.0s	3442×	body	1024	valid
865.0ms	1258×	body	2048	valid
220.0ms	1400×	body	512	valid
67.0ms	620×	body	256	valid
58.0ms	1279×	body	128	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 626 to 335 computations (46.5% saved)

Details

analyze734.0ms (6.6%)

sample79.0ms (0.7%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite17.0ms (0.2%)

series347.0ms (3.1%)

simplify89.0ms (0.8%)

prune103.0ms (0.9%)

localize11.0ms (0.1%)

rewrite40.0ms (0.4%)

series1.9s (17.5%)

simplify78.0ms (0.7%)

prune680.0ms (6.1%)

localize16.0ms (0.1%)

rewrite49.0ms (0.4%)

series1.6s (14.7%)

simplify63.0ms (0.6%)

prune198.0ms (1.8%)

localize16.0ms (0.1%)

rewrite47.0ms (0.4%)

series1.6s (14%)

simplify63.0ms (0.6%)

prune200.0ms (1.8%)

regimes134.0ms (1.2%)

bsearch86.0ms (0.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.9s (26.1%)

Profiling