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

sample197.0ms

Algorithm

intervals

Results

84.0ms	79×	body	2560	valid
60.0ms	103×	body	1280	valid
15.0ms	43×	body	640	valid
6.0ms	308×	pre	80	true
6.0ms	15×	body	1280	overflowed
4.0ms	16×	body	640	overflowed
3.0ms	14×	body	320	valid
2.0ms	5×	body	2560	overflowed
1.0ms	6×	body	320	overflowed
1.0ms	13×	body	80	valid
1.0ms	9×	body	80	overflowed
1.0ms	4×	body	160	valid
0.0ms	1×	body	160	overflowed

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4855	24
1	4855	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: 60.5b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1.0) (-.f64 (exp.f64 (*.f64 b eps)) 1.0))
2.2b	(-.f64 (exp.f64 (*.f64 b eps)) 1.0)
3.1b	(-.f64 (exp.f64 (*.f64 a eps)) 1.0)
4.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`flip3--_binary64` `flip--_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`sub-neg_binary64` `associate-r_binary64` `associate-l_binary64` `difference-of-squares_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 → 71

Calls

4 calls:

11.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1.0) (-.f64 (exp.f64 (*.f64 b eps)) 1.0))
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1.0)
4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1.0)
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)

series48.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1.0) (-.f64 (exp.f64 (*.f64 b eps)) 1.0))
8.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1.0)
8.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1.0)
18.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4887	1142
1	4887	1142

prune99.0ms

Filtered

61 candidates to 83 candidates (-36.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	3	84

Merged error: 49.3b

Counts

84 → 3

localize24.0ms

Local error

Found 4 expressions with local error:

3.7b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1.0)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1.0) (+.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)) 1.0)
7.2b	(.f64 b (.f64 1/2 (*.f64 eps eps)))
16.5b	(*.f64 (pow.f64 eps 3) (pow.f64 b 3))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
27×	`add-cbrt-cube_binary64`
19×	`prod-exp_binary64`
16×	`unswap-sqr_binary64`
15×	`associate-l_binary64`
14×	`unpow-prod-down_binary64` `cube-prod_binary64`
13×	`-un-lft-identity_binary64` `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` `unpow3_binary64` `associate-l/_binary64` `-commutative_binary64` `cube-mult_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `div-inv_binary64`

Counts

4 → 124

Calls

4 calls:

21.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1.0)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1.0) (+.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)) 1.0)
8.0ms	(.f64 b (.f64 1/2 (*.f64 eps eps)))
12.0ms	(*.f64 (pow.f64 eps 3) (pow.f64 b 3))

series978.0ms

Counts

4 → 12

Calls

4 calls:

941.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1.0)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1.0) (+.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))))))))
15.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1.0)
9.0ms	(.f64 b (.f64 1/2 (*.f64 eps eps)))
13.0ms	(*.f64 (pow.f64 eps 3) (pow.f64 b 3))

simplify64.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5169	2567

prune198.0ms

Filtered

87 candidates to 136 candidates (-56.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	133	6	139

Merged error: 0.0b

Counts

139 → 6

localize4.0ms

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:

15.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify77.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4881	196
1	4881	196

prune34.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	22	6	28

Merged error: 0.0b

Counts

28 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1 b) (/.f64 1 a))
0.1b	(sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.1b	(sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.3b	(*.f64 (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

138×	`*-un-lft-identity_binary64`
106×	`sqrt-prod_binary64`
81×	`distribute-lft-out_binary64`
60×	`div-inv_binary64`
42×	`add-sqr-sqrt_binary64` `times-frac_binary64`
35×	`swap-sqr_binary64`
30×	`sqrt-div_binary64`
28×	`add-cube-cbrt_binary64`
21×	`pow1_binary64`
13×	`associate-r_binary64` `associate-l_binary64`
11×	`flip3-+_binary64` `frac-add_binary64` `flip-+_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
9×	`frac-times_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-up_binary64`
4×	`unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
2×	`rem-sqrt-square_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 170

Calls

4 calls:

15.0ms	(+.f64 (/.f64 1 b) (/.f64 1 a))
12.0ms	(sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
12.0ms	(sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
32.0ms	(*.f64 (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))

series30.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+.f64 (/.f64 1 b) (/.f64 1 a))
10.0ms	(sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
10.0ms	(sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
6.0ms	(*.f64 (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))

simplify46.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5074	2012

prune112.0ms

Filtered

84 candidates to 182 candidates (-116.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	182	6	188

Merged error: 0.0b

Counts

188 → 6

regimes171.0ms

Accuracy

0% (3.4b remaining)

Error of 3.5b against oracle of 0.1b and baseline of 3.5b

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	2523×	body	2560	valid
2.0s	3458×	body	1280	valid
354.0ms	1052×	body	640	valid
268.0ms	626×	body	1280	overflowed
209.0ms	9695×	pre	80	true
118.0ms	179×	body	2560	overflowed
110.0ms	383×	body	640	overflowed
81.0ms	352×	body	320	valid
37.0ms	175×	body	320	overflowed
35.0ms	467×	body	80	valid
23.0ms	148×	body	160	valid
18.0ms	247×	body	80	overflowed
11.0ms	83×	body	160	overflowed
1.0ms	1×	body	2560	invalid
0.0ms	1×	body	1280	invalid

Details

analyze1.7s

sample197.0ms

simplify47.0ms

prune6.0ms

localize15.0ms

rewrite26.0ms

series48.0ms

simplify37.0ms

prune99.0ms

localize24.0ms

rewrite50.0ms

series978.0ms

simplify64.0ms

prune198.0ms

localize4.0ms

rewrite15.0ms

series3.0ms

simplify77.0ms

prune34.0ms

localize9.0ms

rewrite81.0ms

series30.0ms

simplify46.0ms

prune112.0ms

regimes171.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.2s

Profiling