Details

analyze1.5s (14.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample242.0ms (2.4%)

Algorithm

1×

intervals

Results

174.0ms	62×	body	2048	valid
34.0ms	96×	body	1024	valid
8.0ms	42×	body	512	valid
8.0ms	4×	body	4096	valid
5.0ms	31×	body	256	valid
2.0ms	21×	body	128	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify171.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	1005	14
1	1005	14

prune4.0ms (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: 31.5b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
2.8b	(-.f64 x (tan.f64 x))
2.8b	(-.f64 x (sin.f64 x))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-log-exp_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`associate-/r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 84

Calls

3 calls:

17.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series143.0ms (1.4%)

Counts

3 → 9

Calls

3 calls:

59.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
50.0ms	(-.f64 x (tan.f64 x))
34.0ms	(-.f64 x (sin.f64 x))

simplify84.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	6199	1847

prune85.0ms (0.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	5	94

Merged error: 0.0b

Counts

94 → 5

Compiler

Compiled 1641 to 361 computations (78% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
0.0b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
2.8b	(-.f64 x (tan.f64 x))
2.8b	(-.f64 x (sin.f64 x))

rewrite56.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
202×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
94×	`add-cube-cbrt_binary64`
54×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
36×	`associate-/r*_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64` `flip3--_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip--_binary64`
6×	`cancel-sign-sub-inv_binary64` `div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`div-sub_binary64` `inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 232

Calls

4 calls:

13.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
8.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
4.0ms	(-.f64 x (sin.f64 x))
3.0ms	(-.f64 x (tan.f64 x))

series181.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
56.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
44.0ms	(-.f64 x (tan.f64 x))
21.0ms	(-.f64 x (sin.f64 x))

simplify99.0ms (1%)

Algorithm

1×	egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5078	6321

prune185.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	243	1	244
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	243	6	249

Merged error: 0b

Counts

249 → 6

Compiler

Compiled 5122 to 1165 computations (77.3% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 (pow.f64 x 4) 513/1400)
0.1b	(.f64 (.f64 x x) 9/10)
0.1b	(/.f64 1 (-.f64 -2 (+.f64 (.f64 (.f64 x x) 9/10) (*.f64 (pow.f64 x 4) 513/1400))))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64` `add-exp-log_binary64`
15×	`times-frac_binary64`
12×	`add-cbrt-cube_binary64`
9×	`pow1_binary64`
8×	`associate-l_binary64`
6×	`associate-r_binary64` `prod-exp_binary64`
5×	`associate-/r*_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
3×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-/l*_binary64`
2×	`sqr-pow_binary64` `associate-/r/_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `flip3--_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `flip--_binary64` `pow-flip_binary64` `pow-exp_binary64`

Counts

3 → 85

Calls

3 calls:

9.0ms	(/.f64 1 (-.f64 -2 (+.f64 (.f64 (.f64 x x) 9/10) (*.f64 (pow.f64 x 4) 513/1400))))
6.0ms	(.f64 (.f64 x x) 9/10)
5.0ms	(*.f64 (pow.f64 x 4) 513/1400)

series81.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

34.0ms	(/.f64 1 (-.f64 -2 (+.f64 (.f64 (.f64 x x) 9/10) (*.f64 (pow.f64 x 4) 513/1400))))
26.0ms	(*.f64 (pow.f64 x 4) 513/1400)
21.0ms	(.f64 (.f64 x x) 9/10)

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4860	1784
1	4860	1784

prune116.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	94	6	100

Merged error: 0b

Counts

100 → 6

Compiler

Compiled 2109 to 1597 computations (24.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.0b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
2.8b	(-.f64 x (tan.f64 x))
2.8b	(-.f64 x (sin.f64 x))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
50×	`times-frac_binary64`
32×	`log-pow_binary64`
31×	`exp-prod_binary64`
30×	`add-cube-cbrt_binary64`
24×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `cancel-sign-sub-inv_binary64`
5×	`associate-/r_binary64` `pow1_binary64` `flip3--_binary64` `associate-/l_binary64` `flip--_binary64`
4×	`associate-/r/_binary64`
3×	`log-prod_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `div-inv_binary64`
1×	`cbrt-undiv_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `log-div_binary64`

Counts

4 → 128

Calls

4 calls:

12.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
9.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series229.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
58.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
46.0ms	(-.f64 x (tan.f64 x))
20.0ms	(-.f64 x (sin.f64 x))

simplify121.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4892	2756
1	4892	2756

prune101.0ms (1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	1	2	3
Picked	0	1	1
Done	1	1	2
Total	141	5	146

Merged error: 0b

Counts

146 → 5

Compiler

Compiled 2716 to 570 computations (79% saved)

regimes107.0ms (1.1%)

Compiler: Compiled 761 to 492 computations (35.3% saved)

bsearch46.0ms (0.5%)

Steps

Iters	Range		Point
8	0.00029809493675648943	0.08642975904775185	0.029194764836342937
9	-1185.3069096958784	-3.493189002009014e-06	-0.026474350661182082

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	63
1	71	63

end0.0ms (0%)

sample6.4s (62.9%)

Algorithm

1×

intervals

Results

4.1s	2036×	body	2048	valid
1.1s	3056×	body	1024	valid
315.0ms	1457×	body	512	valid
109.0ms	106×	body	4096	valid
103.0ms	718×	body	256	valid
63.0ms	627×	body	128	valid

Compiler

Compiled 392 to 254 computations (35.2% saved)

Details

analyze1.5s (14.8%)

sample242.0ms (2.4%)

simplify171.0ms (1.7%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite34.0ms (0.3%)

series143.0ms (1.4%)

simplify84.0ms (0.8%)

prune85.0ms (0.8%)

localize10.0ms (0.1%)

rewrite56.0ms (0.5%)

series181.0ms (1.8%)

simplify99.0ms (1%)

prune185.0ms (1.8%)

localize11.0ms (0.1%)

rewrite27.0ms (0.3%)

series81.0ms (0.8%)

simplify71.0ms (0.7%)

prune116.0ms (1.1%)

localize11.0ms (0.1%)

rewrite39.0ms (0.4%)

series229.0ms (2.2%)

simplify121.0ms (1.2%)

prune101.0ms (1%)

regimes107.0ms (1.1%)

bsearch46.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.4s (62.9%)

Profiling