Details

analyze770.0ms (13.6%)

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)

sample88.0ms (1.6%)

Algorithm

1×

intervals

Results

48.0ms	109×	body	1280	valid
13.0ms	15×	body	2560	valid
12.0ms	55×	body	640	valid
3.0ms	24×	body	320	valid
2.0ms	19×	body	160	valid
1.0ms	34×	body	80	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify17.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	73	11
1	73	11

prune3.0ms (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: 33.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.6b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.6b	(tan.f64 (+.f64 x eps))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64` `tan-quot_binary64`
2×	`tan-sum_binary64` `pow1_binary64` `add-cube-cbrt_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 → 24

Calls

2 calls:

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

series47.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

27.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
20.0ms	(tan.f64 (+.f64 x eps))

simplify94.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4926	529
1	4926	529

prune32.0ms (0.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	7	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	7	31

Merged error: 13.4b

Counts

31 → 7

Compiler

Compiled 533 to 170 computations (68.1% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
9.2b	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x)))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`associate-*l/_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`tan-quot_binary64`
12×	`*-un-lft-identity_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
9×	`associate-r_binary64`
6×	`add-log-exp_binary64` `frac-sub_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `frac-add_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`associate-*r/_binary64` `frac-times_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64`

Counts

4 → 81

Calls

4 calls:

10.0ms	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x)))
8.0ms	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

series131.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x)))
28.0ms	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
25.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
23.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify102.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4983	2268
1	4983	2268

prune116.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	86	7	93
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	92	8	100

Merged error: 0.1b

Counts

100 → 8

Compiler

Compiled 3987 to 1247 computations (68.7% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))))
0.2b	(/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))
0.2b	(pow.f64 (sin.f64 x) 2)
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
33×	`add-cube-cbrt_binary64`
17×	`add-exp-log_binary64`
16×	`associate-l_binary64`
15×	`unpow-prod-down_binary64`
13×	`add-cbrt-cube_binary64`
9×	`pow1_binary64`
8×	`associate-/l*_binary64`
7×	`associate-r_binary64`
5×	`unpow2_binary64` `sqr-pow_binary64`
4×	`add-log-exp_binary64` `div-exp_binary64` `tan-quot_binary64`
3×	`pow-unpow_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `frac-times_binary64`
2×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `flip-+_binary64` `pow-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`distribute-lft-out_binary64` `pow-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 127

Calls

4 calls:

16.0ms	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))))
6.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
3.0ms	(pow.f64 (sin.f64 x) 2)

series80.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))))
24.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
9.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))
4.0ms	(pow.f64 (sin.f64 x) 2)

simplify88.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5134	2680

prune154.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	130	9	139
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	135	12	147

Merged error: 0.0b

Counts

147 → 12

Compiler

Compiled 5133 to 1927 computations (62.5% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 x) 2)
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
27.6b	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64` `tan-quot_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`cbrt-prod_binary64`
6×	`pow-unpow_binary64` `cube-div_binary64`
5×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-div_binary64` `associate-r_binary64` `associate-r/_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-l_binary64` `frac-times_binary64` `pow-exp_binary64` `associate-l/_binary64`
2×	`pow-to-exp_binary64` `pow-prod-down_binary64` `cbrt-unprod_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `cube-prod_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`rem-cbrt-cube_binary64` `unpow2_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 84

Calls

4 calls:

6.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
4.0ms	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3))
3.0ms	(pow.f64 (sin.f64 x) 2)

series93.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
26.0ms	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3))
24.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
4.0ms	(pow.f64 (sin.f64 x) 2)

simplify67.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5152	1144

prune77.0ms (1.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	96	12	108

Merged error: 0.0b

Counts

108 → 12

Compiler

Compiled 3260 to 1311 computations (59.8% saved)

regimes108.0ms (1.9%)

Compiler: Compiled 970 to 592 computations (39% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	49
1	38	49

end0.0ms (0%)

sample3.4s (60.1%)

Algorithm

1×

intervals

Results

1.2s	3258×	body	1280	valid
575.0ms	673×	body	2560	valid
384.0ms	1828×	body	640	valid
111.0ms	780×	body	320	valid
48.0ms	1102×	body	80	valid
33.0ms	359×	body	160	valid

Compiler

Compiled 531 to 331 computations (37.7% saved)

Details

analyze770.0ms (13.6%)

sample88.0ms (1.6%)

simplify17.0ms (0.3%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

rewrite12.0ms (0.2%)

series47.0ms (0.8%)

simplify94.0ms (1.7%)

prune32.0ms (0.6%)

localize21.0ms (0.4%)

rewrite32.0ms (0.6%)

series131.0ms (2.3%)

simplify102.0ms (1.8%)

prune116.0ms (2.1%)

localize27.0ms (0.5%)

rewrite35.0ms (0.6%)

series80.0ms (1.4%)

simplify88.0ms (1.6%)

prune154.0ms (2.7%)

localize27.0ms (0.5%)

rewrite21.0ms (0.4%)

series93.0ms (1.7%)

simplify67.0ms (1.2%)

prune77.0ms (1.4%)

regimes108.0ms (1.9%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample3.4s (60.1%)

Profiling