Details

analyze455.0ms (3.6%)

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
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)

sample41.0ms (0.3%)

Algorithm

1×

intervals

Results

11.0ms	173×	body	128	valid
6.0ms	24×	body	2048	valid
5.0ms	25×	body	1024	valid
4.0ms	15×	body	4096	valid
1.0ms	10×	body	512	valid
1.0ms	9×	body	256	valid
1.0ms	17×	body	128	invalid
1.0ms	17×	body	128	nan

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify402.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (307.0ms)

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

33.6b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
2.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite160.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

33.3b

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:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
7.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 2100 to 1220 computations (41.9% saved)

series727.0ms (5.7%)

Error

7.7b

Counts

4 → 69

Calls

4 calls:

216.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
161.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
145.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
139.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 3046 to 2313 computations (24.1% saved)

simplify85.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5055	2790

prune161.0ms (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	129	14	143
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	130	14	144

Error

7.6b

Counts

144 → 14

Compiler

Compiled 3018 to 1624 computations (46.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite942.0ms (7.4%)

Algorithm

1×	rewrite-expression-head

Error

7.6b

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)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(-.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)

series727.0ms (5.7%)

Error

7.6b

Counts

4 → 69

Calls

4 calls:

222.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
155.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
151.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
140.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3308 to 2575 computations (22.2% saved)

simplify188.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4955	17097
1	4955	17097

prune845.0ms (6.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	423	2	425
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	426	13	439

Error

7.6b

Counts

439 → 13

Compiler

Compiled 13711 to 7607 computations (44.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
2.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite138.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

7.6b

Rules

28×	`add-sqr-sqrt_binary64_441`
18×	`*-un-lft-identity_binary64_419`
14×	`add-cube-cbrt_binary64_454`
13×	`associate-r_binary64_359`
10×	`times-frac_binary64_425`
9×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
8×	`add-log-exp_binary64_458`
7×	`pow1_binary64_480`
6×	`associate-l_binary64_360`
5×	`flip3--_binary64_423` `flip--_binary64_394` `sqrt-prod_binary64_435`
4×	`difference-of-squares_binary64_388` `cancel-sign-sub-inv_binary64_385`
2×	`sqrt-div_binary64_436` `diff-log_binary64_511` `sub-neg_binary64_412` `distribute-lft-out--_binary64_371` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-times_binary64_429` `unswap-sqr_binary64_387` `associate-*l/_binary64_362`
1×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `pow-prod-down_binary64_490` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-r/_binary64_361` `div-inv_binary64_416` `-commutative_binary64_350`

Counts

4 → 83

Calls

4 calls:

15.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

Compiler

Compiled 2366 to 1383 computations (41.5% saved)

series705.0ms (5.5%)

Error

7.6b

Counts

4 → 69

Calls

4 calls:

209.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
155.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
154.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
138.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 3046 to 2313 computations (24.1% saved)

simplify77.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4993	3036
1	4993	3036

prune149.0ms (1.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	149	3	152
Fresh	3	8	11
Picked	0	1	1
Done	0	1	1
Total	152	13	165

Error

7.6b

Counts

165 → 13

Compiler

Compiled 3200 to 1716 computations (46.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (sqrt.f64 1/2) a)
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite143.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

7.6b

Rules

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

Counts

4 → 83

Calls

4 calls:

8.0ms	(-.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))))
4.0ms	(/.f64 (sqrt.f64 1/2) a)

Compiler

Compiled 2435 to 1472 computations (39.5% saved)

series743.0ms (5.8%)

Error

7.6b

Counts

4 → 55

Calls

4 calls:

333.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
167.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
157.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
32.0ms	(/.f64 (sqrt.f64 1/2) a)

Compiler

Compiled 3035 to 2438 computations (19.7% saved)

simplify64.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4924	2095
1	4924	2095

prune165.0ms (1.3%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	4	6	10
Picked	0	1	1
Done	0	2	2
Total	139	12	151

Error

7.4b

Counts

151 → 12

Compiler

Compiled 3239 to 1982 computations (38.8% saved)

regimes1.8s (14.4%)

Accuracy

Total 4.4b remaining (44.3%)

Threshold costs 0b (0%)

Compiler

Compiled 12908 to 9846 computations (23.7% saved)

bsearch60.0ms (0.5%)

Steps

Iters	Range		Point
6	4.506395671377052e-64	4.207723813353611e-63	1.7464220447169885e-63
8	-2.975373334087326e+126	-4.944510384907234e+123	-2.0362182003131042e+126

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	93	52
1	93	52

end0.0ms (0%)

sample3.9s (30.6%)

Algorithm

1×

intervals

Results

273.0ms	1118×	body	2048	valid
260.0ms	5199×	body	128	valid
138.0ms	729×	body	1024	valid
133.0ms	429×	body	4096	valid
51.0ms	347×	body	512	valid
36.0ms	654×	body	128	nan
22.0ms	396×	body	128	invalid
17.0ms	178×	body	256	valid

Compiler

Compiled 3312 to 2519 computations (23.9% saved)

Details

analyze455.0ms (3.6%)

sample41.0ms (0.3%)

simplify402.0ms (3.1%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite160.0ms (1.2%)

series727.0ms (5.7%)

simplify85.0ms (0.7%)

prune161.0ms (1.3%)

localize12.0ms (0.1%)

rewrite942.0ms (7.4%)

series727.0ms (5.7%)

simplify188.0ms (1.5%)

prune845.0ms (6.6%)

localize11.0ms (0.1%)

rewrite138.0ms (1.1%)

series705.0ms (5.5%)

simplify77.0ms (0.6%)

prune149.0ms (1.2%)

localize15.0ms (0.1%)

rewrite143.0ms (1.1%)

series743.0ms (5.8%)

simplify64.0ms (0.5%)

prune165.0ms (1.3%)

regimes1.8s (14.4%)

bsearch60.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.9s (30.6%)

Profiling