Details

analyze453.0ms (5.4%)

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)

sample37.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	175×	body	128	valid
9.0ms	38×	body	2048	valid
5.0ms	24×	body	1024	valid
2.0ms	11×	body	512	valid
1.0ms	4×	body	4096	valid
1.0ms	18×	body	128	nan
1.0ms	14×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify233.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	927	24
1	927	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: 34.0b

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 (.f64 4 a) c))) b) (.f64 a 2))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_441`
14×	`*-un-lft-identity_binary64_419`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454`
6×	`times-frac_binary64_425` `difference-of-squares_binary64_388` `sqrt-prod_binary64_435` `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` `sub-neg_binary64_412` `diff-log_binary64_511` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `pow1/2_binary64_499` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `associate-/r*_binary64_363` `rem-sqrt-square_binary64_432` `div-sub_binary64_424`

Counts

4 → 74

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series547.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

224.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
137.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5031	1979

prune120.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	7	87

Merged error: 5.7b

Counts

87 → 7

Compiler

Compiled 2119 to 1264 computations (40.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (.f64 a 2))
1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.1b	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (.f64 a 2)) (/.f64 b (*.f64 a 2)))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_419`
14×	`add-sqr-sqrt_binary64_441`
11×	`times-frac_binary64_425` `add-cube-cbrt_binary64_454`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `sqrt-prod_binary64_435`
8×	`add-log-exp_binary64_458` `cancel-sign-sub-inv_binary64_385`
6×	`associate-/l*_binary64_364`
5×	`pow1_binary64_480`
4×	`sqrt-div_binary64_436` `div-inv_binary64_416` `flip3--_binary64_423` `flip--_binary64_394`
2×	`sub-neg_binary64_412` `distribute-lft-out--_binary64_371` `diff-log_binary64_511` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `distribute-rgt-out--_binary64_373` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `associate-/r*_binary64_363` `rem-sqrt-square_binary64_432` `sub-div_binary64_426` `frac-sub_binary64_428`

Counts

4 → 80

Calls

4 calls:

16.0ms	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (.f64 a 2)) (/.f64 b (*.f64 a 2)))
9.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (.f64 a 2))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series624.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

265.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (.f64 a 2))
171.0ms	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (.f64 a 2)) (/.f64 b (*.f64 a 2)))
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
68.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify61.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5035	2187

prune113.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	91	8	99

Merged error: 5.7b

Counts

99 → 8

Compiler

Compiled 2604 to 1610 computations (38.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite121.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

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×	`1-exp_binary64_463` `flip3--_binary64_423` `rec-exp_binary64_469` `flip--_binary64_394` `associate-/l*_binary64_364`
2×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `diff-log_binary64_511`
1×	`clear-num_binary64_418` `inv-pow_binary64_504` `pow1/2_binary64_499` `frac-2neg_binary64_430` `pow-flip_binary64_493` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`

Counts

4 → 356

Calls

4 calls:

27.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
12.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series647.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

315.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
137.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
130.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify196.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4947	16295
1	4947	16295

prune716.0ms (8.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	367	1	368
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	367	9	376

Merged error: 5.6b

Counts

376 → 9

Compiler

Compiled 12756 to 7700 computations (39.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
10.7b	(-.f64 (.f64 (/.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) a) (/.f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) 2)) (/.f64 b (.f64 a 2)))
24.4b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.4b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64_419` `add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `cancel-sign-sub-inv_binary64_385`
6×	`cbrt-prod_binary64_450`
4×	`cbrt-div_binary64_451` `flip3--_binary64_423` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `flip--_binary64_394` `pow1_binary64_480`
3×	`times-frac_binary64_425` `frac-sub_binary64_428`
2×	`pow1/3_binary64_501` `sub-neg_binary64_412` `frac-times_binary64_429` `diff-log_binary64_511`
1×	`associate-l/_binary64_362` `div-inv_binary64_416` `associate-r/_binary64_361` `sub-div_binary64_426`

Counts

4 → 60

Calls

4 calls:

19.0ms	(-.f64 (.f64 (/.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) a) (/.f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) 2)) (/.f64 b (.f64 a 2)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series838.0ms (10%)

Counts

4 → 12

Calls

4 calls:

420.0ms	(-.f64 (.f64 (/.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) a) (/.f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) 2)) (/.f64 b (.f64 a 2)))
188.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
166.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify86.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4959	2148
1	4959	2148

prune118.0ms (1.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	72	9	81

Merged error: 5.6b

Counts

81 → 9

Compiler

Compiled 2939 to 1827 computations (37.8% saved)

regimes1.1s (13.1%)

Compiler: Compiled 4068 to 3120 computations (23.3% saved)

bsearch61.0ms (0.7%)

Steps

Iters	Range		Point
8	3.000591128364517e-86	3.8061952448547226e-83	2.6283193000196084e-84
8	-4.420005681040467e+157	-5.368815422905672e+153	-6.135258149216111e+153

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	101	58
1	101	58

end0.0ms (0%)

sample2.0s (24.2%)

Algorithm

1×

intervals

Results

281.0ms	5180×	body	128	valid
280.0ms	1126×	body	2048	valid
145.0ms	730×	body	1024	valid
143.0ms	446×	body	4096	valid
50.0ms	351×	body	512	valid
33.0ms	681×	body	128	nan
21.0ms	400×	body	128	invalid
16.0ms	167×	body	256	valid

Compiler

Compiled 1051 to 801 computations (23.8% saved)

Details

analyze453.0ms (5.4%)

sample37.0ms (0.4%)

simplify233.0ms (2.8%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite43.0ms (0.5%)

series547.0ms (6.6%)

simplify69.0ms (0.8%)

prune120.0ms (1.4%)

localize13.0ms (0.1%)

rewrite43.0ms (0.5%)

series624.0ms (7.5%)

simplify61.0ms (0.7%)

prune113.0ms (1.4%)

localize13.0ms (0.2%)

rewrite121.0ms (1.5%)

series647.0ms (7.7%)

simplify196.0ms (2.3%)

prune716.0ms (8.6%)

localize18.0ms (0.2%)

rewrite41.0ms (0.5%)

series838.0ms (10%)

simplify86.0ms (1%)

prune118.0ms (1.4%)

regimes1.1s (13.1%)

bsearch61.0ms (0.7%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.0s (24.2%)

Profiling