Details

analyze206.0ms (7.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample23.0ms (0.8%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify183.0ms (6.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	165	17
1	165	17

prune4.0ms (0.2%)

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: 0.0b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize18.0ms (0.6%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))

rewrite33.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
30×	`sqrt-prod_binary64`
26×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
13×	`distribute-lft-out_binary64`
9×	`distribute-lft-out--_binary64`
6×	`associate-/l*_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `pow1_binary64` `associate-/r/_binary64`
3×	`add-log-exp_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64`

Counts

3 → 100

Calls

3 calls:

12.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
9.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

series106.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

48.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
35.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
22.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify71.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5072	2078

prune158.0ms (5.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	2	110

Merged error: 0b

Counts

110 → 2

Compiler

Compiled 2434 to 2001 computations (17.8% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(atan.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))))
0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))
0.0b	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3)

rewrite62.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

187×	`*-un-lft-identity_binary64`
125×	`add-sqr-sqrt_binary64`
120×	`times-frac_binary64`
66×	`cbrt-prod_binary64`
62×	`add-cube-cbrt_binary64`
60×	`unpow-prod-down_binary64` `cube-prod_binary64`
42×	`difference-of-squares_binary64`
31×	`distribute-lft-out_binary64`
21×	`distribute-lft-out--_binary64`
10×	`associate-/r/_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/l*_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `flip-+_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64`
3×	`pow-unpow_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `rem-cbrt-cube_binary64` `flip3--_binary64` `pow1/3_binary64` `pow-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`

Counts

4 → 214

Calls

4 calls:

14.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))
12.0ms	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3)
10.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
1.0ms	(atan.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))))

series103.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3)
29.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))
27.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
17.0ms	(atan.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))))

simplify70.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5417	4491

prune285.0ms (10.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	226	2	228

Merged error: 0b

Counts

228 → 2

Compiler

Compiled 4595 to 3783 computations (17.7% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(atan.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3)))
0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0b	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3))
0.0b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3)

rewrite73.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

191×	`*-un-lft-identity_binary64`
129×	`add-sqr-sqrt_binary64`
120×	`times-frac_binary64` `sqrt-prod_binary64`
72×	`cbrt-prod_binary64`
66×	`add-cube-cbrt_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
42×	`difference-of-squares_binary64`
31×	`distribute-lft-out_binary64`
21×	`distribute-lft-out--_binary64`
10×	`associate-/r/_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64` `associate-/l*_binary64`
5×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64`
3×	`pow-unpow_binary64` `pow-pow_binary64`
2×	`associate-/l/_binary64` `sqr-pow_binary64` `cube-div_binary64` `unpow3_binary64` `sqrt-div_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `pow1/2_binary64` `rem-cbrt-cube_binary64` `flip3--_binary64` `sqrt-pow2_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 227

Calls

4 calls:

16.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3))
14.0ms	(pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3)
9.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
1.0ms	(atan.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3)))

series156.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3)
47.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3))
28.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
17.0ms	(atan.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) 3)))

simplify114.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5189	5495

prune347.0ms (12.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	239	2	241

Merged error: 0b

Counts

241 → 2

Compiler

Compiled 5055 to 4173 computations (17.4% saved)

regimes25.0ms (0.9%)

Compiler: Compiled 116 to 106 computations (8.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	22
1	25	22

end0.0ms (0%)

sample650.0ms (24%)

Algorithm

1×

intervals

Results

441.0ms

8000×

body

128

valid

Compiler

Compiled 54 to 51 computations (5.6% saved)

Details

analyze206.0ms (7.6%)

sample23.0ms (0.8%)

simplify183.0ms (6.8%)

prune4.0ms (0.2%)

localize18.0ms (0.6%)

rewrite33.0ms (1.2%)

series106.0ms (3.9%)

simplify71.0ms (2.6%)

prune158.0ms (5.8%)

localize12.0ms (0.5%)

rewrite62.0ms (2.3%)

series103.0ms (3.8%)

simplify70.0ms (2.6%)

prune285.0ms (10.5%)

localize10.0ms (0.4%)

rewrite73.0ms (2.7%)

series156.0ms (5.7%)

simplify114.0ms (4.2%)

prune347.0ms (12.8%)

regimes25.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample650.0ms (24%)

Profiling