Details

analyze664.0ms (3.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5132	96
0	3	3
1	3	3

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Symmetry

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample43.0ms (0.2%)

Algorithm

1×

intervals

Results

10.0ms	41×	body	2048	valid
8.0ms	164×	body	128	valid
6.0ms	31×	body	1024	valid
3.0ms	11×	body	4096	valid
1.0ms	25×	body	128	nan
1.0ms	6×	body	512	valid
1.0ms	13×	body	128	invalid
0.0ms	3×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify309.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (304.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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

37.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
27.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite149.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

37.5b

Rules

21×	`add-sqr-sqrt_binary64_441`
14×	`*-un-lft-identity_binary64_419`
9×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
8×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454`
6×	`sqrt-prod_binary64_435` `difference-of-squares_binary64_388` `times-frac_binary64_425` `associate-/l*_binary64_364`
5×	`pow1_binary64_480`
4×	`flip3--_binary64_423` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385`
3×	`distribute-lft-out--_binary64_371`
2×	`sqrt-div_binary64_436` `diff-log_binary64_511` `sub-neg_binary64_412` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-2neg_binary64_430` `div-sub_binary64_424` `clear-num_binary64_418` `div-inv_binary64_416` `associate-/r*_binary64_363`

Counts

4 → 74

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2100 to 1088 computations (48.2% saved)

series719.0ms (3.4%)

Error

5.3b

Counts

4 → 69

Calls

4 calls:

216.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
157.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
148.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
137.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3046 to 2313 computations (24.1% saved)

simplify71.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4973	2790
1	4973	2790

prune155.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	134	9	143
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	135	9	144

Error

5.2b

Counts

144 → 9

Compiler

Compiled 2950 to 1538 computations (47.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
27.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite1.1s (5%)

Algorithm

1×	rewrite-expression-head

Error

5.2b

Rules

693×	`times-frac_binary64_425`
439×	`add-sqr-sqrt_binary64_441`
364×	`*-un-lft-identity_binary64_419`
290×	`add-cube-cbrt_binary64_454`
74×	`difference-of-squares_binary64_388`
71×	`associate-/r*_binary64_363`
40×	`sqrt-prod_binary64_435`
37×	`distribute-lft-out--_binary64_371`
25×	`add-exp-log_binary64_457`
17×	`div-inv_binary64_416`
15×	`div-exp_binary64_470`
13×	`add-cbrt-cube_binary64_455`
8×	`add-log-exp_binary64_458`
6×	`pow1_binary64_480` `cbrt-undiv_binary64_453`
5×	`associate-/r/_binary64_365`
4×	`cancel-sign-sub-inv_binary64_385`
3×	`flip3--_binary64_423` `flip--_binary64_394` `1-exp_binary64_463` `rec-exp_binary64_469` `associate-/l*_binary64_364`
2×	`sqrt-div_binary64_436` `diff-log_binary64_511` `sub-neg_binary64_412`
1×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `inv-pow_binary64_504` `pow-flip_binary64_493` `frac-2neg_binary64_430` `clear-num_binary64_418`

Counts

4 → 356

Calls

4 calls:

24.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 14021 to 8305 computations (40.8% saved)

series736.0ms (3.5%)

Error

5.2b

Counts

4 → 69

Calls

4 calls:

220.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
172.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
158.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
132.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3308 to 2575 computations (22.2% saved)

simplify189.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4955	17097
1	4955	17097

prune748.0ms (3.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	422	3	425
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	425	9	434

Error

5.2b

Counts

434 → 9

Compiler

Compiled 13615 to 7538 computations (44.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 1 a) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
27.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite5.5s (26.4%)

Algorithm

1×	rewrite-expression-head

Error

5.2b

Rules

3251×	`times-frac_binary64_425`
1761×	`add-sqr-sqrt_binary64_441`
1506×	`*-un-lft-identity_binary64_419`
1252×	`add-cube-cbrt_binary64_454`
254×	`difference-of-squares_binary64_388`
130×	`sqrt-prod_binary64_435`
129×	`div-inv_binary64_416`
127×	`distribute-lft-out--_binary64_371`
87×	`add-exp-log_binary64_457`
71×	`associate-/r*_binary64_363`
70×	`div-exp_binary64_470`
25×	`add-cbrt-cube_binary64_455`
15×	`1-exp_binary64_463` `rec-exp_binary64_469` `cbrt-undiv_binary64_453` `associate-/r/_binary64_365`
13×	`associate-/l*_binary64_364`
8×	`add-log-exp_binary64_458`
5×	`pow1_binary64_480`
4×	`cancel-sign-sub-inv_binary64_385`
3×	`flip3--_binary64_423` `flip--_binary64_394`
2×	`sqrt-div_binary64_436` `diff-log_binary64_511` `sub-neg_binary64_412`
1×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `frac-2neg_binary64_430` `clear-num_binary64_418` `associate-/l/_binary64_366`

Counts

4 → 1097

Calls

4 calls:

44.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 50764 to 33343 computations (34.3% saved)

series742.0ms (3.5%)

Error

5.2b

Counts

4 → 69

Calls

4 calls:

215.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
165.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
158.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
141.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3570 to 2837 computations (20.5% saved)

simplify512.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1166 → 1166

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5005	64110

prune4.1s (19.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	1165	1	1166
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	1166	9	1175

Error

5.2b

Counts

1175 → 9

Compiler

Compiled 44499 to 26773 computations (39.8% saved)

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

5.2b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 5.2b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	2	2
Total	9	9

Error

5.2b

Counts

9 → 9

Compiler

Compiled 0 to 0 computations (0% saved)

regimes1.9s (9%)

Accuracy

Total 5.2b remaining (48.3%)

Threshold costs 0b (0%)

Compiler

Compiled 9604 to 7458 computations (22.3% saved)

bsearch64.0ms (0.3%)

Steps

Iters	Range		Point
8	8.324905310804601e-172	2.3367490958240273e-168	2.2891625273632207e-168
7	-6.624062797328146e+155	-6.331415709625061e+153	-1.2407130559301658e+154

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	98	54
1	98	54

Removed

()

end0.0ms (0%)

sample3.3s (15.6%)

Algorithm

1×

intervals

Results

285.0ms	1117×	body	2048	valid
272.0ms	5140×	body	128	valid
157.0ms	804×	body	1024	valid
132.0ms	407×	body	4096	valid
54.0ms	351×	body	512	valid
33.0ms	686×	body	128	nan
25.0ms	420×	body	128	invalid
18.0ms	181×	body	256	valid

Compiler

Compiled 2487 to 1924 computations (22.6% saved)

Details

analyze664.0ms (3.2%)

sample43.0ms (0.2%)

simplify309.0ms (1.5%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite149.0ms (0.7%)

series719.0ms (3.4%)

simplify71.0ms (0.3%)

prune155.0ms (0.7%)

localize12.0ms (0.1%)

rewrite1.1s (5%)

series736.0ms (3.5%)

simplify189.0ms (0.9%)

prune748.0ms (3.6%)

localize13.0ms (0.1%)

rewrite5.5s (26.4%)

series742.0ms (3.5%)

simplify512.0ms (2.4%)

prune4.1s (19.5%)

localize3.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune1.0ms (0%)

regimes1.9s (9%)

bsearch64.0ms (0.3%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.3s (15.6%)

Profiling