Details

analyze1.7s (21.1%)

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)

sample89.0ms (1.1%)

Algorithm

1×

intervals

Results

35.0ms	63×	body	1024	valid
17.0ms	129×	body	128	valid
16.0ms	42×	body	512	valid
5.0ms	22×	body	256	valid
2.0ms	17×	body	128	invalid
0.0ms	5×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify235.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (132.0ms)

Iter	Nodes	Cost
0	4852	32
1	4852	32

prune8.0ms (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: 15.0b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.2b	(/.f64 x (tan.f64 B))
9.3b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
17.5b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite50.0ms (0.6%)

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:

15.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
4.0ms	(/.f64 x (tan.f64 B))
3.0ms	(/.f64 F (sin.f64 B))

series391.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

156.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
111.0ms	(/.f64 x (tan.f64 B))
71.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
53.0ms	(/.f64 F (sin.f64 B))

simplify64.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5248	2525

prune199.0ms (2.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	114	13	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	13	129

Merged error: 0.0b

Counts

129 → 13

Compiler

Compiled 3868 to 1879 computations (51.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
0.2b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
17.5b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite41.0ms (0.5%)

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:

11.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
11.0ms	(/.f64 (.f64 F (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))

series353.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
108.0ms	(/.f64 x (tan.f64 B))
59.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
56.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))

simplify62.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4986	2141
1	4986	2141

prune137.0ms (1.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	105	13	118

Merged error: 0.0b

Counts

118 → 13

Compiler

Compiled 3146 to 1701 computations (45.9% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.4b	(/.f64 1 (/.f64 (tan.f64 B) x))
9.3b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
17.5b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite47.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac_binary64`
78×	`add-sqr-sqrt_binary64`
65×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`
16×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
13×	`associate-l_binary64`
11×	`div-exp_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64` `div-inv_binary64`
6×	`pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `inv-pow_binary64` `pow-flip_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 163

Calls

4 calls:

14.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
6.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
3.0ms	(/.f64 F (sin.f64 B))

series346.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

140.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
88.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
65.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
53.0ms	(/.f64 F (sin.f64 B))

simplify98.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4927	3417
1	4927	3417

prune233.0ms (2.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	173	2	175
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	175	13	188

Merged error: 0.0b

Counts

188 → 13

Compiler

Compiled 5509 to 2698 computations (51% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/4))
9.3b	(.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)))
18.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)
18.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)

rewrite75.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`add-exp-log_binary64`
47×	`prod-exp_binary64`
38×	`add-sqr-sqrt_binary64`
24×	`unpow-prod-down_binary64`
23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
20×	`pow-to-exp_binary64` `associate-l_binary64` `pow-exp_binary64`
18×	`add-cbrt-cube_binary64`
12×	`sqr-pow_binary64`
11×	`unswap-sqr_binary64`
10×	`times-frac_binary64` `div-exp_binary64`
8×	`pow1_binary64` `associate-r_binary64`
7×	`swap-sqr_binary64` `cbrt-unprod_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `div-inv_binary64` `pow-sqr_binary64` `pow2_binary64` `associate-*l/_binary64`

Counts

4 → 136

Calls

4 calls:

23.0ms	(.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)))
17.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/4))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)

series312.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)))
68.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)
61.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4)
38.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/4) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/4))

simplify87.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4946	3861
1	4946	3861

prune206.0ms (2.5%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	148	13	161

Merged error: 0.0b

Counts

161 → 13

Compiler

Compiled 4927 to 2614 computations (46.9% saved)

regimes115.0ms (1.4%)

Compiler: Compiled 1047 to 801 computations (23.5% saved)

bsearch129.0ms (1.6%)

Steps

Iters	Range		Point
9	286.5249022675136	135792479317.8364	44617.533291442145
7	-4.365804674810573e+139	-1.769153459762356e+138	-4.3225938167391743e+139

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	113	98
1	113	98

end0.0ms (0%)

sample3.1s (37.6%)

Algorithm

1×

intervals

Results

1.2s	2255×	body	1024	valid
507.0ms	4037×	body	128	valid
423.0ms	1156×	body	512	valid
137.0ms	544×	body	256	valid
83.0ms	642×	body	128	invalid
14.0ms	136×	body	128	nan
8.0ms	8×	body	2048	valid
1.0ms	2×	body	1024	invalid
0.0ms	1×	body	512	invalid

Compiler

Compiled 439 to 327 computations (25.5% saved)

Details

analyze1.7s (21.1%)

sample89.0ms (1.1%)

simplify235.0ms (2.9%)

prune8.0ms (0.1%)

localize18.0ms (0.2%)

rewrite50.0ms (0.6%)

series391.0ms (4.8%)

simplify64.0ms (0.8%)

prune199.0ms (2.5%)

localize19.0ms (0.2%)

rewrite41.0ms (0.5%)

series353.0ms (4.4%)

simplify62.0ms (0.8%)

prune137.0ms (1.7%)

localize18.0ms (0.2%)

rewrite47.0ms (0.6%)

series346.0ms (4.3%)

simplify98.0ms (1.2%)

prune233.0ms (2.9%)

localize17.0ms (0.2%)

rewrite75.0ms (0.9%)

series312.0ms (3.8%)

simplify87.0ms (1.1%)

prune206.0ms (2.5%)

regimes115.0ms (1.4%)

bsearch129.0ms (1.6%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.1s (37.6%)

Profiling