Details

analyze2.3s (0.4%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

Compiler

Compiled 28 to 24 computations (14.3% saved)

sample163.0ms (0%)

Algorithm

1×

intervals

Results

64.0ms	64×	body	1024	valid
37.0ms	135×	body	128	valid
24.0ms	35×	body	512	valid
8.0ms	22×	body	256	valid
4.0ms	16×	body	128	invalid
1.0ms	4×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify355.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (183.0ms)

Iter	Nodes	Cost
0	4666	32
1	4666	32

prune15.0ms (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: 13.6b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize27.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.2b	(/.f64 x (tan.f64 B))
7.2b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
17.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite54.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
30×	`times-frac_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64`
6×	`associate-/r_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

21.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
15.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
3.0ms	(/.f64 x (tan.f64 B))
3.0ms	(/.f64 F (sin.f64 B))

series545.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
175.0ms	(/.f64 x (tan.f64 B))
114.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
57.0ms	(/.f64 F (sin.f64 B))

simplify120.0ms (0%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4933	2525
1	4933	2525

prune881.0ms (0.1%)

Pruning

71 alts after pruning (70 fresh and 1 done)

	Pruned	Kept	Total
New	58	69	127
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	58	71	129

Merged error: 0.0b

Counts

129 → 71

Compiler

Compiled 5658 to 3173 computations (43.9% saved)

localize36.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (tan.f64 B))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.3b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
17.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite58.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`times-frac_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64`
6×	`associate-/r*_binary64` `prod-exp_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

16.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
15.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
14.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
4.0ms	(/.f64 x (tan.f64 B))

series475.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

177.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
152.0ms	(/.f64 x (tan.f64 B))
83.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
62.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))

simplify90.0ms (0%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4978	2141
1	4978	2141

prune804.0ms (0.1%)

Pruning

102 alts after pruning (100 fresh and 2 done)

	Pruned	Kept	Total
New	53	52	105
Fresh	21	48	69
Picked	0	1	1
Done	0	1	1
Total	74	102	176

Merged error: 0.0b

Counts

176 → 102

Compiler

Compiled 5960 to 3756 computations (37% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
0.4b	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
17.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite54.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`associate-r_binary64` `unpow-prod-down_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
10×	`associate-/l*_binary64`
9×	`sqr-pow_binary64`
7×	`pow1_binary64` `div-exp_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `-commutative_binary64`

Counts

4 → 138

Calls

4 calls:

15.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
13.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
3.0ms	(/.f64 x (tan.f64 B))

series604.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
171.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
146.0ms	(/.f64 x (tan.f64 B))
89.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify102.0ms (0%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4950	3927
1	4950	3927

prune1.9s (0.3%)

Pruning

139 alts after pruning (136 fresh and 3 done)

	Pruned	Kept	Total
New	89	61	150
Fresh	24	75	99
Picked	0	1	1
Done	0	2	2
Total	113	139	252

Merged error: 0.0b

Counts

252 → 139

Compiler

Compiled 9201 to 5740 computations (37.6% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sin.f64 B))
0.2b	(.f64 F (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (/.f64 1 (sin.f64 B))))
0.4b	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (/.f64 1 (sin.f64 B)))
17.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite86.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-exp-log_binary64`
42×	`add-sqr-sqrt_binary64`
37×	`prod-exp_binary64`
27×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64` `times-frac_binary64`
20×	`add-cbrt-cube_binary64`
14×	`associate-r_binary64` `div-exp_binary64`
10×	`associate-l_binary64`
9×	`pow-to-exp_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `pow-exp_binary64`
8×	`pow1_binary64`
7×	`cbrt-unprod_binary64` `1-exp_binary64` `rec-exp_binary64`
5×	`sqr-pow_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64`
3×	`pow-unpow_binary64` `associate-/r_binary64` `cbrt-undiv_binary64` `associate-/l_binary64`
2×	`un-div-inv_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `pow-pow_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 132

Calls

4 calls:

25.0ms	(.f64 F (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (/.f64 1 (sin.f64 B))))
22.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (/.f64 1 (sin.f64 B)))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
7.0ms	(/.f64 1 (sin.f64 B))

series435.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(.f64 F (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (/.f64 1 (sin.f64 B))))
123.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (/.f64 1 (sin.f64 B)))
82.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
20.0ms	(/.f64 1 (sin.f64 B))

simplify144.0ms (0%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4929	3186
1	4929	3186

prune1.9s (0.3%)

Pruning

155 alts after pruning (151 fresh and 4 done)

	Pruned	Kept	Total
New	113	31	144
Fresh	15	120	135
Picked	0	1	1
Done	0	3	3
Total	128	155	283

Merged error: 0.0b

Counts

283 → 155

Compiler

Compiled 4022 to 2178 computations (45.8% saved)

regimes6.4s (1.1%)

Compiler: Compiled 42180 to 31924 computations (24.3% saved)

bsearch9.7min (97.1%)

Steps

Iters	Range		Point
9	0.0777033824339786	116610.08153294328	11387.487443649043
7	-2.8075269978759715e+20	-1.8313794772233408e+18	-1.8643187409816033e+18

Compiler

Compiled 1 to 3 computations (-200% saved)

Details

analyze2.3s (0.4%)

sample163.0ms (0%)

simplify355.0ms (0.1%)

prune15.0ms (0%)

localize27.0ms (0%)

rewrite54.0ms (0%)

series545.0ms (0.1%)

simplify120.0ms (0%)

prune881.0ms (0.1%)

localize36.0ms (0%)

rewrite58.0ms (0%)

series475.0ms (0.1%)

simplify90.0ms (0%)

prune804.0ms (0.1%)

localize17.0ms (0%)

rewrite54.0ms (0%)

series604.0ms (0.1%)

simplify102.0ms (0%)

prune1.9s (0.3%)

localize20.0ms (0%)

rewrite86.0ms (0%)

series435.0ms (0.1%)

simplify144.0ms (0%)

prune1.9s (0.3%)

regimes6.4s (1.1%)

bsearch9.7min (97.1%)

Profiling