Details

analyze493.0ms (4.8%)

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
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

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample43.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	166×	body	128	valid
8.0ms	30×	body	2048	valid
7.0ms	20×	body	4096	valid
5.0ms	23×	body	1024	valid
2.0ms	12×	body	512	valid
1.0ms	16×	body	128	invalid
1.0ms	16×	body	128	nan
1.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify428.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (328.0ms)

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

Merged error: 35.9b

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 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_419`
15×	`add-sqr-sqrt_binary64_441`
14×	`add-cube-cbrt_binary64_454`
12×	`times-frac_binary64_425`
8×	`add-log-exp_binary64_458`
6×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
5×	`distribute-lft-out_binary64_370` `pow1_binary64_480`
4×	`associate-/l*_binary64_364`
3×	`sqrt-prod_binary64_435` `associate-/r*_binary64_363`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip3--_binary64_423` `flip-+_binary64_393` `flip--_binary64_394` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `pow1/2_binary64_499` `div-inv_binary64_416` `sum-log_binary64_510` `frac-2neg_binary64_430` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 72

Calls

4 calls:

8.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series615.0ms (6%)

Counts

4 → 72

Calls

4 calls:

185.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
158.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
157.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2108 to 1794 computations (14.9% saved)

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4959	2989
1	4959	2989

prune182.0ms (1.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	129	15	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	130	15	145

Merged error: 16.1b

Counts

145 → 15

Compiler

Compiled 3180 to 1765 computations (44.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.3b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
3.7b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
11.2b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite57.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_425`
59×	`add-sqr-sqrt_binary64_441`
44×	`*-un-lft-identity_binary64_419`
30×	`add-cube-cbrt_binary64_454`
27×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
14×	`difference-of-squares_binary64_388`
13×	`sqrt-prod_binary64_435` `associate-/l*_binary64_364`
10×	`associate-/r/_binary64_365` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
9×	`associate-/r*_binary64_363`
7×	`flip3--_binary64_423` `distribute-lft-out--_binary64_371` `flip--_binary64_394`
6×	`add-log-exp_binary64_458` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `cancel-sign-sub-inv_binary64_385`
5×	`pow1_binary64_480`
2×	`sqrt-div_binary64_436` `clear-num_binary64_418` `frac-2neg_binary64_430`
1×	`sub-neg_binary64_412` `pow1/2_binary64_499` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `associate-/l/_binary64_366`

Counts

4 → 136

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
12.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series1.2s (11.4%)

Counts

4 → 75

Calls

4 calls:

348.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
321.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
318.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
174.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

Compiler

Compiled 3105 to 2453 computations (21% saved)

simplify91.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4976	6471
1	4976	6471

prune294.0ms (2.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	204	7	211
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	211	15	226

Merged error: 13.1b

Counts

226 → 15

Compiler

Compiled 6364 to 3377 computations (46.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_441`
28×	`*-un-lft-identity_binary64_419`
18×	`times-frac_binary64_425` `add-cube-cbrt_binary64_454`
11×	`sqrt-prod_binary64_435`
10×	`difference-of-squares_binary64_388`
8×	`add-log-exp_binary64_458`
7×	`cancel-sign-sub-inv_binary64_385`
6×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `associate-/r*_binary64_363`
5×	`distribute-lft-out--_binary64_371` `pow1_binary64_480`
4×	`flip3--_binary64_423` `flip--_binary64_394`
3×	`associate-/l*_binary64_364`
2×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `associate-/r/_binary64_365` `diff-log_binary64_511`
1×	`clear-num_binary64_418` `pow1/2_binary64_499` `div-inv_binary64_416` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 88

Calls

4 calls:

9.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series724.0ms (7.1%)

Counts

4 → 72

Calls

4 calls:

272.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
158.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
154.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
139.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2640 to 2273 computations (13.9% saved)

simplify93.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4940	3616
1	4940	3616

prune214.0ms (2.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	152	8	160
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	157	18	175

Merged error: 12.7b

Counts

175 → 18

Compiler

Compiled 4360 to 2704 computations (38% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 4 (.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) c)))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.3b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_457`
14×	`add-sqr-sqrt_binary64_441`
13×	`add-cbrt-cube_binary64_455`
11×	`*-un-lft-identity_binary64_419`
9×	`add-cube-cbrt_binary64_454`
8×	`add-log-exp_binary64_458`
7×	`sqrt-prod_binary64_435` `cancel-sign-sub-inv_binary64_385` `div-exp_binary64_470`
5×	`pow1_binary64_480`
4×	`prod-exp_binary64_468` `cbrt-undiv_binary64_453`
3×	`times-frac_binary64_425` `flip3--_binary64_423` `flip--_binary64_394` `associate-/l*_binary64_364`
2×	`sqrt-div_binary64_436` `1-exp_binary64_463` `sub-neg_binary64_412` `difference-of-squares_binary64_388` `cbrt-unprod_binary64_452` `diff-log_binary64_511`
1×	`clear-num_binary64_418` `pow1/2_binary64_499` `div-inv_binary64_416` `associate-r/_binary64_361` `distribute-lft-out--_binary64_371` `associate-/r/_binary64_365` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `associate-/r_binary64_363` `rem-sqrt-square_binary64_432`

Counts

4 → 73

Calls

4 calls:

15.0ms	(/.f64 4 (.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) c)))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series765.0ms (7.5%)

Counts

4 → 72

Calls

4 calls:

318.0ms	(/.f64 4 (.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) c)))
158.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
158.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
130.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2790 to 2423 computations (13.2% saved)

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4939	2926
1	4939	2926

prune161.0ms (1.6%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	145	18	163

Merged error: 12.7b

Counts

163 → 18

Compiler

Compiled 3527 to 2274 computations (35.5% saved)

regimes1.5s (14.9%)

Compiler: Compiled 8592 to 6426 computations (25.2% saved)

bsearch65.0ms (0.6%)

Steps

Iters	Range		Point
7	5.352215957988127e+93	1.003314743233553e+96	5.072204432072848e+95
9	3.3680153201665277e-277	9.233270115749582e-270	1.5253865352374434e-276

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	112	75
1	112	75

end0.0ms (0%)

sample3.0s (29.4%)

Algorithm

1×

intervals

Results

314.0ms	1120×	body	2048	valid
307.0ms	5260×	body	128	valid
152.0ms	698×	body	1024	valid
147.0ms	396×	body	4096	valid
56.0ms	344×	body	512	valid
38.0ms	702×	body	128	nan
22.0ms	389×	body	128	invalid
20.0ms	182×	body	256	valid

Compiler

Compiled 2248 to 1674 computations (25.5% saved)

Details

analyze493.0ms (4.8%)

sample43.0ms (0.4%)

simplify428.0ms (4.2%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite29.0ms (0.3%)

series615.0ms (6%)

simplify89.0ms (0.9%)

prune182.0ms (1.8%)

localize13.0ms (0.1%)

rewrite57.0ms (0.6%)

series1.2s (11.4%)

simplify91.0ms (0.9%)

prune294.0ms (2.9%)

localize13.0ms (0.1%)

rewrite33.0ms (0.3%)

series724.0ms (7.1%)

simplify93.0ms (0.9%)

prune214.0ms (2.1%)

localize15.0ms (0.1%)

rewrite38.0ms (0.4%)

series765.0ms (7.5%)

simplify71.0ms (0.7%)

prune161.0ms (1.6%)

regimes1.5s (14.9%)

bsearch65.0ms (0.6%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.0s (29.4%)

Profiling