Details

analyze1.7s

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

sample208.0ms

Algorithm

intervals

Results

89.0ms	88×	body	2560	valid
66.0ms	115×	body	1280	valid
11.0ms	32×	body	640	valid
9.0ms	301×	pre	80	true
7.0ms	16×	body	1280	overflowed
5.0ms	8×	body	2560	overflowed
3.0ms	9×	body	640	overflowed
1.0ms	6×	body	320	valid
1.0ms	5×	body	320	overflowed
1.0ms	12×	body	80	valid
1.0ms	4×	body	160	overflowed
1.0ms	3×	body	160	valid
0.0ms	3×	body	80	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: 60.6b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
2.0b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
2.9b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
4.1b	(-.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)
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series42.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
7.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
7.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
15.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify65.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5017	1225

prune109.0ms

Filtered

70 candidates to 93 candidates (-32.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	5	94

Merged error: 51.6b

Counts

94 → 5

localize221.0ms

Local error

Found 4 expressions with local error:

2.9b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 b 3))) (.f64 b (+.f64 eps (.f64 b (.f64 1/2 (.f64 eps eps))))))))
4.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
6.8b	(.f64 b (.f64 1/2 (*.f64 eps eps)))
14.0b	(*.f64 (pow.f64 eps 3) (pow.f64 b 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 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 b 3))) (.f64 b (+.f64 eps (.f64 b (.f64 1/2 (.f64 eps eps))))))))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
8.0ms	(.f64 b (.f64 1/2 (*.f64 eps eps)))
9.0ms	(*.f64 (pow.f64 eps 3) (pow.f64 b 3))

series974.0ms

Counts

4 → 12

Calls

4 calls:

940.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 b 3))) (.f64 b (+.f64 eps (.f64 b (.f64 1/2 (.f64 eps eps))))))))
14.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
8.0ms	(.f64 b (.f64 1/2 (*.f64 eps eps)))
11.0ms	(*.f64 (pow.f64 eps 3) (pow.f64 b 3))

simplify68.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5146	2580

prune192.0ms

Filtered

87 candidates to 138 candidates (-58.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	139	4	143

Merged error: 0.1b

Counts

143 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite15.0ms

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:

14.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify79.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4881	196
1	4881	196

prune30.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	21	5	26

Merged error: 0.1b

Counts

26 → 5

localize5.0ms

Local error

Found 1 expressions with local error:

11.2b

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/l*_binary64` `times-frac_binary64`
3×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
2×	`associate-/l/_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip-+_binary64`

Counts

1 → 25

Calls

1 calls:

7.0ms

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

series9.0ms

Counts

1 → 3

Calls

1 calls:

9.0ms

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

simplify41.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5240	241

prune20.0ms

Filtered

18 candidates to 28 candidates (-55.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	28	5	33

Merged error: 0.1b

Counts

33 → 5

regimes148.0ms

Accuracy

0% (3.2b remaining)

Error of 3.3b against oracle of 0.1b and baseline of 3.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7
1	8	7

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.7s	2593×	body	2560	valid
1.9s	3368×	body	1280	valid
367.0ms	1096×	body	640	valid
282.0ms	677×	body	1280	overflowed
205.0ms	9736×	pre	80	true
106.0ms	371×	body	640	overflowed
104.0ms	158×	body	2560	overflowed
86.0ms	376×	body	320	valid
38.0ms	183×	body	320	overflowed
31.0ms	440×	body	80	valid
21.0ms	127×	body	160	valid
17.0ms	245×	body	80	overflowed
14.0ms	101×	body	160	overflowed
1.0ms	1×	body	2560	invalid

Details

analyze1.7s

sample208.0ms

simplify17.0ms

prune6.0ms

localize17.0ms

rewrite29.0ms

series42.0ms

simplify65.0ms

prune109.0ms

localize221.0ms

rewrite48.0ms

series974.0ms

simplify68.0ms

prune192.0ms

localize5.0ms

rewrite15.0ms

series3.0ms

simplify79.0ms

prune30.0ms

localize5.0ms

rewrite7.0ms

series9.0ms

simplify41.0ms

prune20.0ms

regimes148.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.2s

Profiling