Details

analyze957.0ms (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
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
18.7%	81.2%	0.1%	7
25%	73.4%	1.7%	8
28.1%	68.7%	3.2%	9
31.2%	62.8%	6%	10
32.8%	60.1%	7.1%	11
34.3%	56.7%	9%	12
35.1%	55.2%	9.7%	13
35.9%	53.4%	10.7%	14

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample54.0ms (0.8%)

Algorithm

1×

intervals

Results

19.0ms	69×	body	1024	valid
9.0ms	42×	body	512	valid
9.0ms	127×	body	128	valid
3.0ms	18×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify110.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	140	14
1	140	14

prune7.0ms (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

Error

0.1b

Counts

2 → 2

Compiler

Compiled 30 to 27 computations (10% saved)

localize10.0ms (0.1%)

Local error

Found 6 expressions with local error:

0.2b	(/.f64 x (tan.f64 B))
0.1b	(/.f64 1 (sin.f64 B))
0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(/.f64 x (tan.f64 B))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
14×	`cancel-sign-sub-inv_binary64`
9×	`add-exp-log_binary64`
7×	`add-cbrt-cube_binary64`
6×	`associate-/r_binary64` `difference-of-squares_binary64` `associate-/l_binary64`
5×	`add-log-exp_binary64`
4×	`pow1_binary64` `div-inv_binary64`
3×	`distribute-lft-out--_binary64` `div-exp_binary64`
2×	`cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `tan-quot_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `inv-pow_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64`

Counts

3 → 94

Calls

6 calls:

17.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
6.0ms	(/.f64 x (tan.f64 B))
4.0ms	(/.f64 1 (sin.f64 B))
0.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
0.0ms	(/.f64 1 (sin.f64 B))

series516.0ms (7.3%)

Counts

3 → 25

Calls

3 calls:

286.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
199.0ms	(/.f64 x (tan.f64 B))
30.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 502 to 397 computations (20.9% saved)

simplify80.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4914	1698
1	4914	1698

prune143.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	109	10	119
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Error

0.0b

Counts

121 → 10

Compiler

Compiled 1827 to 781 computations (57.3% saved)

localize9.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
0.1b	(/.f64 1 (sin.f64 B))
0.1b	(/.f64 x (sin.f64 B))
0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
0.1b	(/.f64 x (sin.f64 B))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
15×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
7×	`pow1_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-/l_binary64`
4×	`div-exp_binary64`
3×	`associate-r_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `associate-*l/_binary64`
2×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `cancel-sign-sub-inv_binary64` `inv-pow_binary64` `rec-exp_binary64` `sub-div_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 104

Calls

8 calls:

10.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
7.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
4.0ms	(/.f64 1 (sin.f64 B))
3.0ms	(/.f64 x (sin.f64 B))
0.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))

series489.0ms (6.9%)

Counts

4 → 32

Calls

4 calls:

238.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
133.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
84.0ms	(/.f64 x (sin.f64 B))
34.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 699 to 540 computations (22.7% saved)

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5203	1912

prune125.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	139	7	146

Error

0.0b

Counts

146 → 7

Compiler

Compiled 2423 to 870 computations (64.1% saved)

localize9.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
0.2b	(*.f64 x (cos.f64 B))
0.1b	(/.f64 1 (sin.f64 B))
0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(*.f64 x (cos.f64 B))
0.2b	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64` `times-frac_binary64`
15×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
8×	`div-inv_binary64`
7×	`pow1_binary64` `cancel-sign-sub-inv_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64`
4×	`associate-/l*_binary64` `div-exp_binary64`
3×	`associate-r_binary64` `distribute-rgt-out--_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `difference-of-squares_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `unswap-sqr_binary64` `inv-pow_binary64` `rec-exp_binary64` `sub-div_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 98

Calls

8 calls:

12.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
5.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
5.0ms	(*.f64 x (cos.f64 B))
4.0ms	(/.f64 1 (sin.f64 B))
0.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))

series482.0ms (6.8%)

Counts

4 → 32

Calls

4 calls:

240.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
141.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
68.0ms	(*.f64 x (cos.f64 B))
32.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 697 to 538 computations (22.8% saved)

simplify80.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4961	1820
1	4961	1820

prune105.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	130	7	137

Error

0.0b

Counts

137 → 7

Compiler

Compiled 2182 to 843 computations (61.4% saved)

localize10.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B))
0.1b	(/.f64 (sin.f64 B) x)
0.1b	(/.f64 1 (sin.f64 B))
0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B)))
0.1b	(/.f64 1 (sin.f64 B))
0.1b	(/.f64 (sin.f64 B) x)
0.2b	(*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B))
0.3b	(/.f64 1 (/.f64 (sin.f64 B) x))

rewrite52.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`times-frac_binary64`
112×	`add-sqr-sqrt_binary64`
100×	`*-un-lft-identity_binary64`
98×	`add-cube-cbrt_binary64`
44×	`associate-l_binary64`
40×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
19×	`associate-/r*_binary64`
17×	`div-exp_binary64`
11×	`div-inv_binary64`
9×	`associate-/l*_binary64`
8×	`pow1_binary64` `cbrt-undiv_binary64`
7×	`prod-exp_binary64`
5×	`1-exp_binary64` `unswap-sqr_binary64` `rec-exp_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-unprod_binary64` `associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`associate-/r/_binary64` `inv-pow_binary64` `pow-flip_binary64`
1×	`pow-prod-down_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 206

Calls

8 calls:

15.0ms	(*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B))
8.0ms	(/.f64 1 (/.f64 (sin.f64 B) x))
4.0ms	(/.f64 (sin.f64 B) x)
4.0ms	(/.f64 1 (sin.f64 B))
0.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B)))

series329.0ms (4.7%)

Counts

4 → 27

Calls

4 calls:

124.0ms	(*.f64 (/.f64 1 (/.f64 (sin.f64 B) x)) (cos.f64 B))
93.0ms	(/.f64 1 (/.f64 (sin.f64 B) x))
80.0ms	(/.f64 (sin.f64 B) x)
31.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 678 to 529 computations (22% saved)

simplify114.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5081	3175

prune210.0ms (3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	233	0	233
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	233	7	240

Error

0.0b

Counts

240 → 7

Compiler

Compiled 4577 to 1786 computations (61% saved)

simplify19.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	613	1013
1	613	1013

regimes141.0ms (2%)

Compiler: Compiled 1244 to 896 computations (28% saved)

bsearch0.0ms (0%)

regimes51.0ms (0.7%)

Compiler: Compiled 262 to 246 computations (6.1% saved)

bsearch0.0ms (0%)

regimes44.0ms (0.6%)

Compiler: Compiled 214 to 210 computations (1.9% saved)

bsearch0.0ms (0%)

regimes63.0ms (0.9%)

Compiler: Compiled 108 to 116 computations (-7.4% saved)

bsearch88.0ms (1.3%)

Steps

Iters	Range		Point
10	1.1344802496316657e-05	445251.9708680129	1.3878256789184826
10	-1.1193793398428997	-1.8310662052187292e-10	-1.1034874914804986

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes53.0ms (0.7%)

Compiler: Compiled 44 to 60 computations (-36.4% saved)

bsearch57.0ms (0.8%)

Steps

Iters	Range		Point
9	8.515010878601158e-37	1.0937208631827059e-30	1.0781172739611247e-30
6	-1.8310662052187292e-10	-2.0154168983258813e-11	-1.802072515051807e-10

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes44.0ms (0.6%)

Compiler: Compiled 28 to 46 computations (-64.3% saved)

bsearch45.0ms (0.6%)

Steps

Iters	Range		Point
7	1.1577378362623305e-11	1.6024558530434965e-09	1.5765190973992149e-09
10	-0.06136238431202851	-7.257292908202583e-13	-0.0003805296447401917

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes19.0ms (0.3%)

Compiler: Compiled 20 to 36 computations (-80% saved)

bsearch0.0ms (0%)

regimes15.0ms (0.2%)

Accuracy

Total 0.2b remaining (95.9%)

Threshold costs 0.2b (95.9%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 120 to 90 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	126	157
1	126	157

end0.0ms (0%)

sample2.3s (32.8%)

Algorithm

1×

intervals

Results

629.0ms	2280×	body	1024	valid
313.0ms	4020×	body	128	valid
225.0ms	1117×	body	512	valid
85.0ms	577×	body	256	valid
16.0ms	189×	body	128	invalid
3.0ms	6×	body	2048	valid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 736 to 543 computations (26.2% saved)

Pareto

0.6750029024486133

Details

analyze957.0ms (13.6%)

sample54.0ms (0.8%)

simplify110.0ms (1.6%)

prune7.0ms (0.1%)

localize10.0ms (0.1%)

rewrite42.0ms (0.6%)

series516.0ms (7.3%)

simplify80.0ms (1.1%)

prune143.0ms (2%)

localize9.0ms (0.1%)

rewrite33.0ms (0.5%)

series489.0ms (6.9%)

simplify75.0ms (1.1%)

prune125.0ms (1.8%)

localize9.0ms (0.1%)

rewrite33.0ms (0.5%)

series482.0ms (6.8%)

simplify80.0ms (1.1%)

prune105.0ms (1.5%)

localize10.0ms (0.1%)

rewrite52.0ms (0.7%)

series329.0ms (4.7%)

simplify114.0ms (1.6%)

prune210.0ms (3%)

simplify19.0ms (0.3%)

regimes141.0ms (2%)

bsearch0.0ms (0%)

regimes51.0ms (0.7%)

bsearch0.0ms (0%)

regimes44.0ms (0.6%)

bsearch0.0ms (0%)

regimes63.0ms (0.9%)

bsearch88.0ms (1.3%)

regimes53.0ms (0.7%)

bsearch57.0ms (0.8%)

regimes44.0ms (0.6%)

bsearch45.0ms (0.6%)

regimes19.0ms (0.3%)

bsearch0.0ms (0%)

regimes15.0ms (0.2%)

bsearch7.0ms (0.1%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.3s (32.8%)

Profiling