Details

analyze1.8s (15.5%)

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)

sample106.0ms (0.9%)

Algorithm

1×

intervals

Results

46.0ms	79×	body	1024	valid
21.0ms	118×	body	128	valid
16.0ms	38×	body	512	valid
5.0ms	21×	body	256	valid
2.0ms	17×	body	128	invalid
0.0ms	2×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify234.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	4666	32
1	4666	32

prune15.0ms (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: 12.2b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))
4.1b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
16.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite45.0ms (0.4%)

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:

16.0ms	(.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))
4.0ms	(/.f64 F (sin.f64 B))

series608.0ms (5.3%)

Counts

4 → 27

Calls

4 calls:

233.0ms	(/.f64 x (tan.f64 B))
207.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
93.0ms	(/.f64 F (sin.f64 B))
74.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

simplify91.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4963	3047
1	4963	3047

prune226.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	132	10	142
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	134	10	144

Merged error: 0.0b

Counts

144 → 10

Compiler

Compiled 4342 to 2086 computations (52% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.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))
16.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite55.0ms (0.5%)

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:

16.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
11.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
4.0ms	(/.f64 x (tan.f64 B))

series675.0ms (5.9%)

Counts

4 → 30

Calls

4 calls:

241.0ms	(/.f64 x (tan.f64 B))
198.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
175.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
61.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify87.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4989	4727
1	4989	4727

prune243.0ms (2.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	167	11	178

Merged error: 0.0b

Counts

178 → 11

Compiler

Compiled 5618 to 2948 computations (47.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.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)))
16.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite57.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`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`
13×	`div-exp_binary64`
10×	`associate-l_binary64`
9×	`pow-to-exp_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `pow-exp_binary64`
7×	`pow1_binary64` `cbrt-unprod_binary64`
6×	`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` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `tan-quot_binary64`

Counts

4 → 129

Calls

4 calls:

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

series674.0ms (5.9%)

Counts

4 → 30

Calls

4 calls:

230.0ms	(/.f64 x (tan.f64 B))
201.0ms	(.f64 F (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (/.f64 1 (sin.f64 B))))
184.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (/.f64 1 (sin.f64 B)))
59.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5125	4018

prune223.0ms (2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	158	12	170

Merged error: 0.0b

Counts

170 → 12

Compiler

Compiled 4975 to 2702 computations (45.7% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (/.f64 1 (sin.f64 B)))
0.5b	(cbrt.f64 (/.f64 1 (sin.f64 B)))
0.5b	(*.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B))))
16.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite53.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`cbrt-prod_binary64`
92×	`add-sqr-sqrt_binary64`
70×	`times-frac_binary64`
62×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
18×	`swap-sqr_binary64`
16×	`associate-r_binary64` `associate-l_binary64` `unswap-sqr_binary64`
12×	`pow1_binary64`
8×	`pow1/3_binary64` `div-inv_binary64`
7×	`add-exp-log_binary64`
6×	`cbrt-div_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-plus_binary64` `prod-exp_binary64` `frac-times_binary64` `pow-exp_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 148

Calls

4 calls:

17.0ms	(*.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B))))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
3.0ms	(cbrt.f64 (/.f64 1 (sin.f64 B)))
3.0ms	(cbrt.f64 (/.f64 1 (sin.f64 B)))

series376.0ms (3.3%)

Counts

4 → 15

Calls

4 calls:

133.0ms	(*.f64 (cbrt.f64 (/.f64 1 (sin.f64 B))) (cbrt.f64 (/.f64 1 (sin.f64 B))))
92.0ms	(cbrt.f64 (/.f64 1 (sin.f64 B)))
87.0ms	(cbrt.f64 (/.f64 1 (sin.f64 B)))
63.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify90.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5275	3405

prune381.0ms (3.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	9	9
Picked	1	0	1
Done	0	2	2
Total	163	12	175

Merged error: 0.0b

Counts

175 → 12

Compiler

Compiled 6975 to 4197 computations (39.8% saved)

regimes714.0ms (6.3%)

Compiler: Compiled 7328 to 5472 computations (25.3% saved)

bsearch146.0ms (1.3%)

Steps

Iters	Range		Point
7	501.8143773096569	52621.51817336589	51770.872556656
9	-36585593462271784.0	-130368406.85721968	-32049635508.5477

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	127	131
1	127	131

end0.0ms (0%)

sample4.4s (38.5%)

Algorithm

1×

intervals

Results

1.3s	2322×	body	1024	valid
527.0ms	4011×	body	128	valid
426.0ms	1101×	body	512	valid
142.0ms	561×	body	256	valid
91.0ms	722×	body	128	invalid
16.0ms	128×	body	128	nan
5.0ms	5×	body	2048	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	512	invalid

Compiler

Compiled 1930 to 1420 computations (26.4% saved)

Details

analyze1.8s (15.5%)

sample106.0ms (0.9%)

simplify234.0ms (2%)

prune15.0ms (0.1%)

localize19.0ms (0.2%)

rewrite45.0ms (0.4%)

series608.0ms (5.3%)

simplify91.0ms (0.8%)

prune226.0ms (2%)

localize17.0ms (0.1%)

rewrite55.0ms (0.5%)

series675.0ms (5.9%)

simplify87.0ms (0.8%)

prune243.0ms (2.1%)

localize20.0ms (0.2%)

rewrite57.0ms (0.5%)

series674.0ms (5.9%)

simplify64.0ms (0.6%)

prune223.0ms (2%)

localize25.0ms (0.2%)

rewrite53.0ms (0.5%)

series376.0ms (3.3%)

simplify90.0ms (0.8%)

prune381.0ms (3.3%)

regimes714.0ms (6.3%)

bsearch146.0ms (1.3%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.4s (38.5%)

Profiling