Details

analyze489.0ms (6.6%)

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%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample39.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	105×	body	256	valid
9.0ms	286×	pre	128	true
8.0ms	151×	body	128	valid
1.0ms	30×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify315.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (309.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (0.1%)

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

44.8b

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	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
38.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite40.0ms (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:

17.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series273.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
67.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
35.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify87.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune100.0ms (1.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	5	87

Error

0.2b

Counts

87 → 5

Compiler

Compiled 2079 to 1234 computations (40.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite48.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
22×	`times-frac_binary64_425`
19×	`*-un-lft-identity_binary64_419`
17×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
12×	`add-sqr-sqrt_binary64_441`
11×	`add-cube-cbrt_binary64_454` `associate-/l*_binary64_364`
6×	`add-log-exp_binary64_458` `associate-/r/_binary64_365`
5×	`associate-/r*_binary64_363` `pow1_binary64_480`
4×	`div-inv_binary64_416` `distribute-lft-out_binary64_370`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `sqrt-prod_binary64_435`
2×	`sqrt-div_binary64_436` `clear-num_binary64_418` `flip3--_binary64_423` `frac-2neg_binary64_430` `flip--_binary64_394`
1×	`sub-neg_binary64_412` `pow1/2_binary64_499` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385` `rem-sqrt-square_binary64_432` `associate-/l/_binary64_366`

Counts

4 → 102

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series460.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

207.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
160.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
35.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4975	3059
1	4975	3059

prune162.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	108	6	114
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	113	6	119

Error

Counts

119 → 6

Compiler

Compiled 3341 to 2054 computations (38.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

rewrite29.0ms (0.4%)

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-/r*_binary64_363`
3×	`sqrt-prod_binary64_435` `associate-/l*_binary64_364`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip3--_binary64_423` `associate-/r/_binary64_365` `flip-+_binary64_393` `flip--_binary64_394`
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 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series337.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

180.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
36.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify78.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4905	1972
1	4905	1972

prune110.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	84	6	90

Error

Counts

90 → 6

Compiler

Compiled 2344 to 1453 computations (38% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)))
0.4b	(pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)
0.4b	(.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))) 3))) (+.f64 (.f64 b b) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))))
38.7b	(-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite126.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`sqrt-div_binary64_436`
44×	`*-un-lft-identity_binary64_419`
28×	`associate-*r/_binary64_361` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
26×	`flip3--_binary64_423` `flip--_binary64_394`
18×	`times-frac_binary64_425` `unpow-prod-down_binary64_498` `cube-prod_binary64_447`
16×	`add-sqr-sqrt_binary64_441` `frac-sub_binary64_428`
15×	`distribute-lft-out_binary64_370` `associate-l_binary64_360`
14×	`add-cube-cbrt_binary64_454`
10×	`frac-times_binary64_429` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
9×	`associate-/r*_binary64_363`
8×	`pow1_binary64_480`
7×	`associate-*l/_binary64_362`
6×	`add-log-exp_binary64_458` `sqrt-prod_binary64_435` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
4×	`flip3-+_binary64_422` `associate-/r/_binary64_365` `flip-+_binary64_393` `sub-div_binary64_426`
3×	`associate-r_binary64_359` `sum-cubes_binary64_420` `pow-pow_binary64_491` `pow-unpow_binary64_496`
2×	`div-inv_binary64_416` `cube-div_binary64_448`
1×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `distribute-rgt-out--_binary64_373` `sub-neg_binary64_412` `distribute-rgt-in_binary64_369` `pow1/2_binary64_499` `unpow3_binary64_485` `cube-mult_binary64_449` `rem-cube-cbrt_binary64_442` `unswap-sqr_binary64_387` `sqrt-pow2_binary64_438` `pow-exp_binary64_487` `sqr-pow_binary64_391` `pow-to-exp_binary64_488` `distribute-lft-in_binary64_368` `-commutative_binary64_350` `frac-2neg_binary64_430` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385` `associate-/l_binary64_364`

Counts

4 → 147

Calls

4 calls:

41.0ms	(.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))) 3))) (+.f64 (.f64 b b) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))))
22.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)))
16.0ms	(-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)

series1.3s (17.4%)

Counts

4 → 12

Calls

4 calls:

716.0ms	(.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))) 3))) (+.f64 (.f64 b b) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))))
429.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)))
98.0ms	(-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
45.0ms	(pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)

simplify138.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5061	8413

prune626.0ms (8.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	159	6	165

Error

Counts

165 → 6

Compiler

Compiled 12009 to 6978 computations (41.9% saved)

regimes377.0ms (5.1%)

Accuracy

Total 0.2b remaining (98.9%)

Threshold costs 0.2b (98.9%)

Compiler

Compiled 4812 to 3662 computations (23.9% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample2.1s (28.9%)

Algorithm

1×

intervals

Results

295.0ms	2989×	body	256	valid
277.0ms	8933×	pre	128	true
259.0ms	5011×	body	128	valid
46.0ms	933×	body	128	nan

Compiler

Compiled 1239 to 944 computations (23.8% saved)

Details

analyze489.0ms (6.6%)

sample39.0ms (0.5%)

simplify315.0ms (4.3%)

prune4.0ms (0.1%)

localize11.0ms (0.1%)

rewrite40.0ms (0.5%)

series273.0ms (3.7%)

simplify87.0ms (1.2%)

prune100.0ms (1.3%)

localize14.0ms (0.2%)

rewrite48.0ms (0.6%)

series460.0ms (6.2%)

simplify64.0ms (0.9%)

prune162.0ms (2.2%)

localize12.0ms (0.2%)

rewrite29.0ms (0.4%)

series337.0ms (4.6%)

simplify78.0ms (1.1%)

prune110.0ms (1.5%)

localize27.0ms (0.4%)

rewrite126.0ms (1.7%)

series1.3s (17.4%)

simplify138.0ms (1.9%)

prune626.0ms (8.5%)

regimes377.0ms (5.1%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.1s (28.9%)

Profiling