Details

analyze233.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

sample80.0ms

Algorithm

intervals

Results

34.0ms	58×	body	1280	valid
15.0ms	45×	body	640	valid
9.0ms	118×	body	80	valid
5.0ms	23×	body	320	valid
2.0ms	12×	body	160	valid
1.0ms	9×	body	80	invalid
0.0ms	5×	body	80	overflowed
0.0ms	1×	body	640	invalid
0.0ms	1×	body	160	invalid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5473	41

prune15.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 32.3b

Counts

2 → 2

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 1 eps) x)
0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
2.2b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub_binary64`
74×	`exp-neg_binary64`
72×	`frac-times_binary64`
56×	`neg-sub0_binary64` `exp-diff_binary64`
38×	`associate-*l/_binary64`
36×	`associate-*r/_binary64`
28×	`flip3-+_binary64` `flip3--_binary64` `flip--_binary64` `flip-+_binary64`
18×	`un-div-inv_binary64`
12×	`exp-prod_binary64`
10×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-l_binary64` `rem-exp-log_binary64`
3×	`associate-r_binary64`
2×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 147

Calls

4 calls:

6.0ms	(*.f64 (+.f64 1 eps) x)
4.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
3.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
22.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

series187.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(*.f64 (+.f64 1 eps) x)
19.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
21.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
128.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

simplify138.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5322	8469

prune667.0ms

Filtered

127 candidates to 159 candidates (-25.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	156	3	159
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	158	3	161

Merged error: 0.7b

Counts

161 → 3

localize17.0ms

Local error

Found 2 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 2/3)
6.4b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
7×	`add-log-exp_binary64` `add-exp-log_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
3×	`associate-r_binary64` `prod-exp_binary64`
2×	`pow1_binary64` `diff-log_binary64` `sqr-pow_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `difference-of-squares_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

2 → 45

Calls

2 calls:

6.0ms	(*.f64 (pow.f64 x 3) 2/3)
9.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

series49.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(*.f64 (pow.f64 x 3) 2/3)
19.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

simplify70.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4940	693
1	4940	693

prune151.0ms

Filtered

34 candidates to 51 candidates (-50.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	49	5	54

Merged error: 0.7b

Counts

54 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

6.4b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 x 3) 2/3)) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) 2) (.f64 x x))
43.6b	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
43.6b	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
43.6b	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64` `cbrt-prod_binary64`
2×	`diff-log_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 41

Calls

4 calls:

13.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 x 3) 2/3)) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) 2) (.f64 x x))
4.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
4.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
8.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))

series105.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 x 3) 2/3)) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) 2) (.f64 x x))
23.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
23.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
27.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))

simplify83.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5465	701

prune178.0ms

Filtered

40 candidates to 53 candidates (-32.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	53	5	58

Merged error: 0.7b

Counts

58 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

6.4b	(+.f64 (-.f64 2 (.f64 x x)) (.f64 (pow.f64 x 3) 2/3))
10.2b	(cbrt.f64 (+.f64 (-.f64 2 (.f64 x x)) (.f64 (pow.f64 x 3) 2/3)))
10.2b	(cbrt.f64 (+.f64 (-.f64 2 (.f64 x x)) (.f64 (pow.f64 x 3) 2/3)))
10.2b	(cbrt.f64 (+.f64 (-.f64 2 (.f64 x x)) (.f64 (pow.f64 x 3) 2/3)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp_binary64` `cbrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`cbrt-div_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
3×	`pow1/3_binary64`
2×	`sum-log_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `+-commutative_binary64`

Counts

4 → 53

Calls

4 calls:

6.0ms	(+.f64 (-.f64 2 (.f64 x x)) (.f64 (pow.f64 x 3) 2/3))
5.0ms	(cbrt.f64 (+.f64 (-.f64 2 (.f64 x x)) (.f64 (pow.f64 x 3) 2/3)))
6.0ms	(cbrt.f64 (+.f64 (-.f64 2 (.f64 x x)) (.f64 (pow.f64 x 3) 2/3)))
5.0ms	(cbrt.f64 (+.f64 (-.f64 2 (.f64 x x)) (.f64 (pow.f64 x 3) 2/3)))

series140.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+.f64 (-.f64 2 (.f64 x x)) (.f64 (pow.f64 x 3) 2/3))
41.0ms	(cbrt.f64 (+.f64 (-.f64 2 (.f64 x x)) (.f64 (pow.f64 x 3) 2/3)))
37.0ms	(cbrt.f64 (+.f64 (-.f64 2 (.f64 x x)) (.f64 (pow.f64 x 3) 2/3)))
44.0ms	(cbrt.f64 (+.f64 (-.f64 2 (.f64 x x)) (.f64 (pow.f64 x 3) 2/3)))

simplify66.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5738	1848

prune355.0ms

Filtered

57 candidates to 65 candidates (-14.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	61	4	65
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	63	7	70

Merged error: 0.7b

Counts

70 → 7

regimes221.0ms

Accuracy

96.8% (0.5b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.3b

bsearch76.0ms

Steps

Iters	Range		Point
8	175760362218427/549755813888	6347482879018185/4294967296	337.94709420177713

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	183	93
1	183	93

end0.0ms

sample2.2s

Algorithm

intervals

Results

970.0ms	1770×	body	1280	valid
430.0ms	1217×	body	640	valid
336.0ms	4083×	body	80	valid
141.0ms	607×	body	320	valid
50.0ms	323×	body	160	valid
19.0ms	227×	body	80	invalid
13.0ms	175×	body	80	overflowed
9.0ms	19×	body	640	invalid
9.0ms	16×	body	1280	invalid
4.0ms	16×	body	320	invalid
0.0ms	2×	body	160	invalid

Details

analyze233.0ms

sample80.0ms

simplify59.0ms

prune15.0ms

localize30.0ms

rewrite44.0ms

series187.0ms

simplify138.0ms

prune667.0ms

localize17.0ms

rewrite16.0ms

series49.0ms

simplify70.0ms

prune151.0ms

localize21.0ms

rewrite30.0ms

series105.0ms

simplify83.0ms

prune178.0ms

localize19.0ms

rewrite24.0ms

series140.0ms

simplify66.0ms

prune355.0ms

regimes221.0ms

bsearch76.0ms

simplify6.0ms

end0.0ms

sample2.2s

Profiling