Details

analyze235.0ms

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

sample75.0ms

Algorithm

intervals

Results

35.0ms	62×	body	1280	valid
13.0ms	36×	body	640	valid
10.0ms	130×	body	80	valid
5.0ms	22×	body	320	valid
1.0ms	6×	body	160	valid
1.0ms	9×	body	80	invalid
0.0ms	6×	body	80	overflowed

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5443	27

prune7.0ms

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: 29.2b

Counts

2 → 1

localize18.0ms

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)))
0.2b	(-.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)))))

rewrite45.0ms

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)
3.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
4.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
19.0ms	(-.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)))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(*.f64 (+.f64 1 eps) x)
6.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
6.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
37.0ms	(-.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)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5438	5373

prune214.0ms

Filtered

85 candidates to 159 candidates (-87.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	156	3	159
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	3	160

Merged error: 0.2b

Counts

160 → 3

localize9.0ms

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))

series11.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify48.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4882	457
1	4882	457

prune58.0ms

Filtered

32 candidates to 51 candidates (-59.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	50	4	54

Merged error: 0.2b

Counts

54 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
6.4b	(-.f64 (+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (.f64 x 2/3)) 2) (.f64 x x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`add-log-exp_binary64`
8×	`pow1/3_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `diff-log_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `flip--_binary64` `pow2_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 76

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
13.0ms	(-.f64 (+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (.f64 x 2/3)) 2) (.f64 x x))

series72.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
18.0ms	(cbrt.f64 x)
19.0ms	(cbrt.f64 x)
10.0ms	(-.f64 (+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (.f64 x 2/3)) 2) (.f64 x x))

simplify51.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4945	581
1	4945	581

prune96.0ms

Filtered

66 candidates to 88 candidates (-33.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	87	5	92

Merged error: 0.2b

Counts

92 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 2/3)
0.1b	(*.f64 (pow.f64 x 3) 2/3)
10.4b	(-.f64 (.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)) (pow.f64 x 4))
10.8b	(/.f64 (-.f64 (.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (+.f64 (.f64 (pow.f64 x 3) 2/3) 2)) (pow.f64 x 4)) (+.f64 (.f64 x x) (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
24×	`associate-l_binary64`
23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`times-frac_binary64`
16×	`add-exp-log_binary64`
15×	`difference-of-squares_binary64`
13×	`unpow-prod-down_binary64`
10×	`add-cbrt-cube_binary64`
9×	`sqr-pow_binary64`
8×	`unswap-sqr_binary64` `cube-prod_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `prod-exp_binary64` `associate-/l*_binary64`
4×	`pow1_binary64`
3×	`associate-/r*_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `associate--l+_binary64` `*-commutative_binary64` `cube-mult_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 122

Calls

4 calls:

6.0ms	(*.f64 (pow.f64 x 3) 2/3)
6.0ms	(*.f64 (pow.f64 x 3) 2/3)
16.0ms	(-.f64 (.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)) (pow.f64 x 4))
25.0ms	(/.f64 (-.f64 (.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (+.f64 (.f64 (pow.f64 x 3) 2/3) 2)) (pow.f64 x 4)) (+.f64 (.f64 x x) (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(*.f64 (pow.f64 x 3) 2/3)
6.0ms	(*.f64 (pow.f64 x 3) 2/3)
7.0ms	(-.f64 (.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)) (pow.f64 x 4))
12.0ms	(/.f64 (-.f64 (.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (+.f64 (.f64 (pow.f64 x 3) 2/3) 2)) (pow.f64 x 4)) (+.f64 (.f64 x x) (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)))

simplify46.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5569	2731

prune239.0ms

Filtered

96 candidates to 134 candidates (-39.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	134	5	139

Merged error: 0.2b

Counts

139 → 5

regimes134.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.5b

bsearch73.0ms

Steps

Iters	Range		Point
9	69.96252274476456	299340061.5779964	312.8937051629594

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	162	64
1	162	64

end0.0ms

sample2.1s

Algorithm

intervals

Results

922.0ms	1667×	body	1280	valid
448.0ms	1263×	body	640	valid
329.0ms	4089×	body	80	valid
154.0ms	644×	body	320	valid
52.0ms	337×	body	160	valid
23.0ms	249×	body	80	invalid
15.0ms	194×	body	80	overflowed
10.0ms	17×	body	1280	invalid
6.0ms	16×	body	640	invalid
2.0ms	8×	body	320	invalid
1.0ms	4×	body	160	invalid

Details

analyze235.0ms

sample75.0ms

simplify74.0ms

prune7.0ms

localize18.0ms

rewrite45.0ms

series53.0ms

simplify66.0ms

prune214.0ms

localize9.0ms

rewrite16.0ms

series11.0ms

simplify48.0ms

prune58.0ms

localize12.0ms

rewrite24.0ms

series72.0ms

simplify51.0ms

prune96.0ms

localize16.0ms

rewrite58.0ms

series35.0ms

simplify46.0ms

prune239.0ms

regimes134.0ms

bsearch73.0ms

simplify5.0ms

end0.0ms

sample2.1s

Profiling