Details

analyze261.0ms

Algorithm

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

sample47.0ms

Algorithm

intervals

Results

16.0ms	117×	body	320	valid
9.0ms	98×	body	160	valid
8.0ms	285×	pre	80	true
2.0ms	14×	body	640	valid
1.0ms	29×	body	80	nan
1.0ms	27×	body	80	valid

simplify315.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (306.0ms)

Iter	Nodes	Cost
0	1835	24
1	1835	24

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 52.2b

Counts

2 → 1

localize11.0ms

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))
26.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 70

Calls

4 calls:

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

series257.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
105.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
62.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

simplify88.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4988	1963
1	4988	1963

prune81.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	4	83

Merged error: 0.1b

Counts

83 → 4

localize14.0ms

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))
0.2b	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64` `pow1_binary64`
4×	`distribute-lft-out_binary64` `div-inv_binary64`
3×	`flip3-+_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 101

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
17.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
154.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
215.0ms	(/.f64 (.f64 (.f64 a c) -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

simplify83.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5141	3025

prune116.0ms

Filtered

78 candidates to 113 candidates (-44.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	110	7	117

Merged error: 0b

Counts

117 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.2b	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (/.f64 2 (*.f64 c -4))))
0.3b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (/.f64 2 (*.f64 c -4)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-exp-log_binary64`
27×	`add-cbrt-cube_binary64`
16×	`prod-exp_binary64` `div-exp_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64`
8×	`cbrt-unprod_binary64` `cbrt-undiv_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `times-frac_binary64`
5×	`associate-/r/_binary64`
4×	`flip3-+_binary64` `1-exp_binary64` `associate-l_binary64` `rec-exp_binary64` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `flip3--_binary64` `associate-*r/_binary64` `div-inv_binary64` `flip--_binary64` `pow-flip_binary64` `sqrt-div_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 99

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
15.0ms	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (/.f64 2 (*.f64 c -4))))
13.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (/.f64 2 (*.f64 c -4)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
33.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
128.0ms	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (/.f64 2 (*.f64 c -4))))
82.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (/.f64 2 (*.f64 c -4)))

simplify60.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5042	2593

prune103.0ms

Filtered

75 candidates to 111 candidates (-48.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	113	5	118

Merged error: 0b

Counts

118 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.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 (.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))))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

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

series350.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
64.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
34.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
186.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))

simplify111.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4897	1965
1	4897	1965

prune78.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	83	5	88

Merged error: 0b

Counts

88 → 5

regimes43.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	24
1	64	24

end0.0ms

sample1.4s

Algorithm

intervals

Results

498.0ms	3590×	body	320	valid
287.0ms	3054×	body	160	valid
255.0ms	8829×	pre	80	true
90.0ms	503×	body	640	valid
41.0ms	853×	body	80	valid
38.0ms	829×	body	80	nan

Details

analyze261.0ms

sample47.0ms

simplify315.0ms

prune4.0ms

localize11.0ms

rewrite33.0ms

series257.0ms

simplify88.0ms

prune81.0ms

localize14.0ms

rewrite41.0ms

series461.0ms

simplify83.0ms

prune116.0ms

localize13.0ms

rewrite40.0ms

series301.0ms

simplify60.0ms

prune103.0ms

localize12.0ms

rewrite25.0ms

series350.0ms

simplify111.0ms

prune78.0ms

regimes43.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.4s

Profiling