Details

analyze1.9s

Algorithm

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

sample218.0ms

Algorithm

intervals

Results

92.0ms	84×	body	2560	valid
67.0ms	114×	body	1280	valid
13.0ms	34×	body	640	valid
9.0ms	19×	body	1280	overflowed
8.0ms	17×	body	320	valid
7.0ms	306×	pre	80	true
3.0ms	11×	body	640	overflowed
3.0ms	5×	body	2560	overflowed
1.0ms	5×	body	320	overflowed
1.0ms	7×	body	80	valid
1.0ms	7×	body	80	overflowed
0.0ms	3×	body	160	overflowed

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	5221	24

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 62.2b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
2.7b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
3.9b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
6.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64`
9×	`flip3--_binary64` `flip--_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`sub-neg_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
4×	`frac-times_binary64`
3×	`diff-log_binary64`
2×	`associate-r/_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 81

Calls

4 calls:

11.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
6.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series71.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
13.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
13.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
21.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify68.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5017	1225

prune62.0ms

Filtered

70 candidates to 93 candidates (-32.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	3	94

Merged error: 52.3b

Counts

94 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

4.3b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
6.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
7.7b	(.f64 eps (.f64 1/2 (*.f64 a a)))
14.9b	(*.f64 (pow.f64 eps 3) (pow.f64 a 3))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
37×	`add-exp-log_binary64`
27×	`add-cbrt-cube_binary64`
19×	`prod-exp_binary64`
16×	`unswap-sqr_binary64`
15×	`associate-l_binary64`
14×	`*-un-lft-identity_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
13×	`pow1_binary64` `associate-r_binary64`
11×	`cbrt-unprod_binary64` `add-cube-cbrt_binary64`
10×	`sqr-pow_binary64`
8×	`associate-/r/_binary64`
7×	`pow-prod-down_binary64`
6×	`pow-to-exp_binary64` `add-log-exp_binary64` `pow-exp_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`cbrt-undiv_binary64` `associate-*r/_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `difference-of-squares_binary64` `unpow3_binary64` `associate-l/_binary64` `-commutative_binary64` `cube-mult_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `div-inv_binary64`

Counts

4 → 126

Calls

4 calls:

21.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
8.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
10.0ms	(*.f64 (pow.f64 eps 3) (pow.f64 a 3))

series355.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
14.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
11.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
12.0ms	(*.f64 (pow.f64 eps 3) (pow.f64 a 3))

simplify66.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5094	2599

prune139.0ms

Filtered

87 candidates to 138 candidates (-58.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	139	2	141

Merged error: 0.0b

Counts

141 → 2

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (/.f64 1 b) (/.f64 1 a))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
7×	`distribute-lft-out_binary64`
6×	`times-frac_binary64`
4×	`div-inv_binary64`
3×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
1×	`flip3-+_binary64` `pow1_binary64` `frac-add_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

1 → 19

Calls

1 calls:

13.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

simplify80.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4881	196
1	4881	196

prune12.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	22	2	24

Merged error: 0.0b

Counts

24 → 2

regimes119.0ms

Accuracy

92.8% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 3.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	86
1	50	86

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.9s	2592×	body	2560	valid
2.1s	3453×	body	1280	valid
389.0ms	1049×	body	640	valid
303.0ms	662×	body	1280	overflowed
220.0ms	9657×	pre	80	true
115.0ms	364×	body	640	overflowed
110.0ms	157×	body	2560	overflowed
89.0ms	347×	body	320	valid
39.0ms	175×	body	320	overflowed
35.0ms	445×	body	80	valid
20.0ms	114×	body	160	valid
17.0ms	211×	body	80	overflowed
13.0ms	87×	body	160	overflowed
1.0ms	1×	body	2560	invalid

Details

analyze1.9s

sample218.0ms

simplify17.0ms

prune6.0ms

localize16.0ms

rewrite29.0ms

series71.0ms

simplify68.0ms

prune62.0ms

localize27.0ms

rewrite48.0ms

series355.0ms

simplify66.0ms

prune139.0ms

localize5.0ms

rewrite14.0ms

series3.0ms

simplify80.0ms

prune12.0ms

regimes119.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.7s

Profiling