Details

analyze1.8s

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

sample186.0ms

Algorithm

intervals

Results

101.0ms	125×	body	2048	valid
34.0ms	74×	body	1024	valid
10.0ms	36×	body	512	valid
6.0ms	10×	body	2048	overflowed
6.0ms	311×	pre	128	true
5.0ms	17×	body	1024	overflowed
2.0ms	11×	body	512	overflowed
2.0ms	15×	body	128	valid
1.0ms	6×	body	256	valid
1.0ms	6×	body	256	overflowed
1.0ms	11×	body	128	overflowed

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5217	37

prune3.0ms

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:

0.5b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
3.2b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
3.3b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
5.8b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite33.0ms

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

series274.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
45.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
44.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
80.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify71.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4979	1893
1	4979	1893

prune99.0ms

Filtered

70 candidates to 93 candidates (-32.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	4	94

Merged error: 51.4b

Counts

94 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

4.0b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps)))))))
4.9b	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
5.8b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
13.4b	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
26×	`add-cbrt-cube_binary64`
14×	`prod-exp_binary64`
11×	`pow1_binary64` `add-sqr-sqrt_binary64`
10×	`cbrt-unprod_binary64`
9×	`*-un-lft-identity_binary64`
8×	`associate-/r/_binary64`
6×	`add-log-exp_binary64` `associate-*r/_binary64` `add-cube-cbrt_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64` `flip-+_binary64` `frac-times_binary64`
2×	`associate-/l/_binary64` `difference-of-squares_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`pow-to-exp_binary64` `associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `difference-of-sqr-1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `div-inv_binary64` `pow-exp_binary64`

Counts

4 → 88

Calls

4 calls:

16.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps)))))))
6.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
13.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))

series8.2s

Counts

4 → 12

Calls

4 calls:

7.9s	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps)))))))
86.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
71.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
176.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))

simplify84.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4961	3679
1	4961	3679

prune150.0ms

Filtered

65 candidates to 100 candidates (-53.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	102	2	104

Merged error: 0.1b

Counts

104 → 2

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:

13.0ms

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

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify63.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4953	287
1	4953	287

prune18.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	21	3	24

Merged error: 0.1b

Counts

24 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
0.6b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.6b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.6b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity_binary64`
114×	`cbrt-prod_binary64`
81×	`distribute-lft-out_binary64`
60×	`div-inv_binary64`
42×	`times-frac_binary64`
37×	`add-sqr-sqrt_binary64`
33×	`cbrt-div_binary64` `swap-sqr_binary64`
29×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64` `associate-l_binary64`
11×	`flip3-+_binary64` `pow1_binary64` `frac-add_binary64` `flip-+_binary64`
9×	`pow1/3_binary64` `frac-times_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 159

Calls

4 calls:

37.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
13.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
13.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
13.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
148.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
132.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
142.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

simplify102.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4909	3950
1	4909	3950

prune182.0ms

Filtered

96 candidates to 171 candidates (-78.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	170	4	174

Merged error: 0.1b

Counts

174 → 4

regimes45.0ms

Accuracy

0% (3.3b remaining)

Error of 3.4b against oracle of 0.1b and baseline of 3.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	8	10

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.4s	3988×	body	2048	valid
1.1s	2464×	body	1024	valid
222.0ms	397×	body	2048	overflowed
200.0ms	593×	body	1024	overflowed
196.0ms	9759×	pre	128	true
192.0ms	750×	body	512	valid
70.0ms	316×	body	512	overflowed
41.0ms	254×	body	256	valid
39.0ms	534×	body	128	valid
23.0ms	163×	body	256	overflowed
21.0ms	288×	body	128	overflowed
16.0ms	10×	body	4096	valid
2.0ms	2×	body	2048	invalid

Details

analyze1.8s

sample186.0ms

simplify23.0ms

prune3.0ms

localize17.0ms

rewrite33.0ms

series274.0ms

simplify71.0ms

prune99.0ms

localize30.0ms

rewrite53.0ms

series8.2s

simplify84.0ms

prune150.0ms

localize5.0ms

rewrite15.0ms

series19.0ms

simplify63.0ms

prune18.0ms

localize9.0ms

rewrite97.0ms

series605.0ms

simplify102.0ms

prune182.0ms

regimes45.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample5.8s

Profiling