Details

analyze476.0ms (4.2%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample43.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	41×	body	2048	valid
8.0ms	158×	body	128	valid
5.0ms	17×	body	4096	valid
4.0ms	19×	body	1024	valid
2.0ms	13×	body	512	valid
1.0ms	18×	body	128	invalid
1.0ms	8×	body	256	valid
1.0ms	15×	body	128	nan

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify363.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (267.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	24

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

36.6b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.1%)

Local error

Found 8 expressions with local error:

1.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.2b	(.f64 (.f64 3 a) c)
0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_3851`
14×	`*-un-lft-identity_binary64_3829`
9×	`add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865`
8×	`add-log-exp_binary64_3868` `add-cube-cbrt_binary64_3864`
6×	`times-frac_binary64_3835` `sqrt-prod_binary64_3845` `difference-of-squares_binary64_3798` `associate-/l*_binary64_3774`
5×	`pow1_binary64_3890`
4×	`cancel-sign-sub-inv_binary64_3795` `flip--_binary64_3804` `flip3--_binary64_3833`
3×	`distribute-lft-out--_binary64_3781`
2×	`div-exp_binary64_3880` `associate-/l/_binary64_3776` `cbrt-undiv_binary64_3863` `sqrt-div_binary64_3846` `sub-neg_binary64_3822` `diff-log_binary64_3921`
1×	`div-inv_binary64_3826` `rem-sqrt-square_binary64_3842` `prod-exp_binary64_3878` `clear-num_binary64_3828` `div-sub_binary64_3834` `pow1/2_binary64_3909` `associate-/r*_binary64_3773` `frac-2neg_binary64_3840` `cbrt-unprod_binary64_3862` `sqrt-pow1_binary64_3847`

Counts

4 → 74

Calls

8 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
0.0ms	(.f64 (.f64 3 a) c)

series619.0ms (5.5%)

Counts

4 → 62

Calls

4 calls:

197.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
162.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
136.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

Compiler

Compiled 1887 to 1609 computations (14.7% saved)

simplify71.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5572	2649

prune226.0ms (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	125	11	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	11	137

Error

6.5b

Counts

137 → 11

Compiler

Compiled 2830 to 1638 computations (42.1% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.2b	(.f64 (.f64 3 a) c)
0.1b	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) 3) a)
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) 3)
0.2b	(.f64 (.f64 3 a) c)
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_3851`
10×	`pow1_binary64_3890`
9×	`add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865` `*-un-lft-identity_binary64_3829`
8×	`add-log-exp_binary64_3868`
7×	`add-cube-cbrt_binary64_3864`
4×	`cancel-sign-sub-inv_binary64_3795` `sqrt-prod_binary64_3845`
3×	`pow-prod-down_binary64_3900` `flip--_binary64_3804` `prod-exp_binary64_3878` `flip3--_binary64_3833` `associate-r_binary64_3769` `cbrt-unprod_binary64_3862`
2×	`difference-of-squares_binary64_3798` `sqrt-div_binary64_3846` `sub-neg_binary64_3822` `diff-log_binary64_3921`
1×	`rem-sqrt-square_binary64_3842` `pow1/2_binary64_3909` `distribute-lft-out--_binary64_3781` `-commutative_binary64_3760` `sqrt-pow1_binary64_3847` `associate-l*_binary64_3770`

Counts

4 → 62

Calls

8 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(.f64 (.f64 3 a) c)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
0.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) 3)

series463.0ms (4.1%)

Counts

4 → 54

Calls

4 calls:

147.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
141.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
53.0ms	(.f64 (.f64 3 a) c)

Compiler

Compiled 1604 to 1355 computations (15.5% saved)

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4951	1704
1	4951	1704

prune113.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	117	10	127

Error

6.5b

Counts

127 → 10

Compiler

Compiled 2296 to 1343 computations (41.5% saved)

localize18.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
0.2b	(.f64 (.f64 3 a) c)
0.2b	(.f64 a (.f64 c -3))
0.1b	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) 3)
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.5b	(/.f64 (/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) 3) a)
10.6b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite70.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

274×	`times-frac_binary64_3835`
138×	`*-un-lft-identity_binary64_3829`
111×	`add-sqr-sqrt_binary64_3851`
110×	`add-cube-cbrt_binary64_3864`
35×	`associate-/l*_binary64_3774`
33×	`add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865`
26×	`associate-/r/_binary64_3775`
18×	`div-inv_binary64_3826`
15×	`div-exp_binary64_3880` `cbrt-undiv_binary64_3863`
14×	`distribute-lft-out_binary64_3780`
13×	`flip3-+_binary64_3832` `flip-+_binary64_3803`
7×	`associate-/r*_binary64_3773`
6×	`add-log-exp_binary64_3868` `prod-exp_binary64_3878` `cbrt-unprod_binary64_3862`
5×	`pow1_binary64_3890`
3×	`sqrt-prod_binary64_3845`
2×	`flip--_binary64_3804` `flip3--_binary64_3833` `clear-num_binary64_3828` `sqrt-div_binary64_3846` `frac-2neg_binary64_3840`
1×	`cancel-sign-sub-inv_binary64_3795` `rem-sqrt-square_binary64_3842` `associate-/l/_binary64_3776` `pow1/2_binary64_3909` `sqrt-pow1_binary64_3847` `sub-neg_binary64_3822` `diff-log_binary64_3921`

Counts

4 → 214

Calls

8 calls:

20.0ms	(/.f64 (/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) 3) a)
11.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) 3)

series815.0ms (7.3%)

Counts

4 → 64

Calls

4 calls:

284.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
224.0ms	(/.f64 (/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) 3) a)
157.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
150.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

Compiler

Compiled 2527 to 1996 computations (21% saved)

simplify129.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5531	10954

prune501.0ms (4.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	277	1	278
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	278	10	288

Error

6.5b

Counts

288 → 10

Compiler

Compiled 9458 to 5543 computations (41.4% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.2b	(.f64 1/3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) a))
0.2b	(.f64 (.f64 3 a) c)
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) a)
0.2b	(.f64 1/3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) a))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
25.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_3851`
25×	`*-un-lft-identity_binary64_3829`
22×	`associate-r_binary64_3769`
19×	`times-frac_binary64_3835`
17×	`add-cube-cbrt_binary64_3864`
9×	`add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865`
8×	`add-log-exp_binary64_3868` `difference-of-squares_binary64_3798`
7×	`sqrt-prod_binary64_3845` `pow1_binary64_3890`
4×	`cancel-sign-sub-inv_binary64_3795` `distribute-lft-out--_binary64_3781`
3×	`flip--_binary64_3804` `flip3--_binary64_3833` `associate-l_binary64_3770`
2×	`unswap-sqr_binary64_3797` `prod-exp_binary64_3878` `sqrt-div_binary64_3846` `cbrt-unprod_binary64_3862` `sub-neg_binary64_3822` `diff-log_binary64_3921`
1×	`pow-prod-down_binary64_3900` `div-inv_binary64_3826` `div-exp_binary64_3880` `rem-sqrt-square_binary64_3842` `pow1/2_binary64_3909` `cbrt-undiv_binary64_3863` `associate-r/_binary64_3771` `-commutative_binary64_3760` `sqrt-pow1_binary64_3847`

Counts

4 → 85

Calls

8 calls:

14.0ms	(.f64 1/3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
0.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) a)

series622.0ms (5.5%)

Counts

4 → 62

Calls

4 calls:

203.0ms	(.f64 1/3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) a))
163.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
136.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

Compiler

Compiled 1887 to 1609 computations (14.7% saved)

simplify70.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5053	2857

prune142.0ms (1.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	147	10	157

Error

6.5b

Counts

157 → 10

Compiler

Compiled 3023 to 1679 computations (44.5% saved)

simplify22.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	440	1371
1	440	1371

regimes1.3s (12%)

Compiler: Compiled 4070 to 3292 computations (19.1% saved)

bsearch68.0ms (0.6%)

Steps

Iters	Range		Point
8	4.3922612475487306e-42	2.4158215440760546e-38	1.2901844560369386e-39
10	-1.2695926624795638e+160	-3.091154619274828e+145	-5.45892145913632e+153

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes473.0ms (4.2%)

Compiler: Compiled 792 to 824 computations (-4% saved)

bsearch42.0ms (0.4%)

Steps

Iters	Range		Point
8	4.3922612475487306e-42	2.4158215440760546e-38	4.7425045090226674e-42
2	-1.2315499324190027e+138	-1.1049780562537373e+138	-1.152442509815712e+138

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes652.0ms (5.8%)

Compiler: Compiled 712 to 759 computations (-6.6% saved)

bsearch62.0ms (0.6%)

Steps

Iters	Range		Point
8	4.3922612475487306e-42	2.4158215440760546e-38	4.3034790776983455e-41
8	-1.8594808919683444e+141	-1.2315499324190027e+138	-8.887918546354078e+139

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes450.0ms (4%)

Compiler: Compiled 648 to 707 computations (-9.1% saved)

bsearch79.0ms (0.7%)

Steps

Iters	Range		Point
10	1.504646891257893e-60	4.3922612475487306e-42	2.7246677044628124e-51
10	-2.8384235997398763e-134	-1.494813238907461e-149	-3.216026123156104e-136

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes274.0ms (2.4%)

Compiler: Compiled 292 to 371 computations (-27.1% saved)

bsearch31.0ms (0.3%)

Steps

Iters	Range		Point
8	7.297406334415802e-212	1.1179131203524545e-208	7.39592424827649e-212

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes218.0ms (1.9%)

Compiler: Compiled 113 to 192 computations (-69.9% saved)

bsearch32.0ms (0.3%)

Steps

Iters	Range		Point
8	7.297406334415802e-212	1.1179131203524545e-208	4.641734365265361e-210

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes107.0ms (1%)

Compiler: Compiled 45 to 90 computations (-100% saved)

bsearch31.0ms (0.3%)

Steps

Iters	Range		Point
8	7.297406334415802e-212	1.1179131203524545e-208	4.5984243801846445e-211

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes33.0ms (0.3%)

Compiler: Compiled 30 to 72 computations (-140% saved)

bsearch36.0ms (0.3%)

Steps

Iters	Range		Point
10	-3.4039374770558263e-299	9.048194046201865e-304	4.1858178371903e-310

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes23.0ms (0.2%)

Accuracy

Total 4.7b remaining (46%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch11.0ms (0.1%)

Compiler: Compiled 195 to 162 computations (16.9% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	130	284
1	130	284

end0.0ms (0%)

sample2.3s (20.5%)

Algorithm

1×

intervals

Results

296.0ms	1154×	body	2048	valid
275.0ms	5161×	body	128	valid
150.0ms	728×	body	1024	valid
124.0ms	396×	body	4096	valid
55.0ms	371×	body	512	valid
32.0ms	637×	body	128	nan
22.0ms	374×	body	128	invalid
19.0ms	190×	body	256	valid

Compiler

Compiled 1100 to 895 computations (18.6% saved)

Pareto

0.6257154064555538

Details

analyze476.0ms (4.2%)

sample43.0ms (0.4%)

simplify363.0ms (3.2%)

prune5.0ms (0%)

localize10.0ms (0.1%)

rewrite34.0ms (0.3%)

series619.0ms (5.5%)

simplify71.0ms (0.6%)

prune226.0ms (2%)

localize11.0ms (0.1%)

rewrite28.0ms (0.3%)

series463.0ms (4.1%)

simplify52.0ms (0.5%)

prune113.0ms (1%)

localize18.0ms (0.2%)

rewrite70.0ms (0.6%)

series815.0ms (7.3%)

simplify129.0ms (1.1%)

prune501.0ms (4.5%)

localize14.0ms (0.1%)

rewrite39.0ms (0.3%)

series622.0ms (5.5%)

simplify70.0ms (0.6%)

prune142.0ms (1.3%)

simplify22.0ms (0.2%)

regimes1.3s (12%)

bsearch68.0ms (0.6%)

regimes473.0ms (4.2%)

bsearch42.0ms (0.4%)

regimes652.0ms (5.8%)

bsearch62.0ms (0.6%)

regimes450.0ms (4%)

bsearch79.0ms (0.7%)

regimes274.0ms (2.4%)

bsearch31.0ms (0.3%)

regimes218.0ms (1.9%)

bsearch32.0ms (0.3%)

regimes107.0ms (1%)

bsearch31.0ms (0.3%)

regimes33.0ms (0.3%)

bsearch36.0ms (0.3%)

regimes23.0ms (0.2%)

bsearch11.0ms (0.1%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.3s (20.5%)

Profiling