Details

analyze236.0ms

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

sample73.0ms

Algorithm

intervals

Results

31.0ms	72×	body	1024	valid
11.0ms	113×	body	128	valid
11.0ms	43×	body	512	valid
7.0ms	9×	body	2048	valid
3.0ms	19×	body	256	valid
1.0ms	10×	body	128	overflowed
1.0ms	7×	body	128	invalid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5465	41

prune5.0ms

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: 34.8b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
0.0b	(*.f64 (+.f64 1 eps) x)
1.7b	(-.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)))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub_binary64`
80×	`exp-neg_binary64` `frac-times_binary64`
60×	`neg-sub0_binary64` `exp-diff_binary64`
42×	`associate-*l/_binary64`
40×	`associate-*r/_binary64`
31×	`flip3-+_binary64` `flip3--_binary64` `add-sqr-sqrt_binary64` `flip--_binary64` `flip-+_binary64`
24×	`*-un-lft-identity_binary64`
23×	`associate-l_binary64`
20×	`un-div-inv_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64`
8×	`add-exp-log_binary64`
6×	`add-log-exp_binary64` `difference-of-squares_binary64` `times-frac_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
2×	`distribute-lft-out--_binary64` `div-inv_binary64`
1×	`sub-neg_binary64` `diff-log_binary64`

Counts

4 → 180

Calls

4 calls:

15.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
18.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
7.0ms	(*.f64 (+.f64 1 eps) x)
23.0ms	(-.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)))))

series421.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
71.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
33.0ms	(*.f64 (+.f64 1 eps) x)
265.0ms	(-.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)))))

simplify139.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5038	9587

prune433.0ms

Filtered

149 candidates to 192 candidates (-28.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	190	2	192
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	191	2	193

Merged error: 0.6b

Counts

193 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 2/3)
5.2b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

rewrite19.0ms

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))

series84.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(*.f64 (pow.f64 x 3) 2/3)
38.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

simplify54.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4860	681
1	4860	681

prune45.0ms

Filtered

32 candidates to 51 candidates (-59.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	50	3	53

Merged error: 0.6b

Counts

53 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(*.f64 x 2/3)
5.2b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 x 3)) (cbrt.f64 (pow.f64 x 3))) (.f64 x 2/3)) 2) (.f64 x x))
43.2b	(cbrt.f64 (pow.f64 x 3))
43.2b	(cbrt.f64 (pow.f64 x 3))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod_binary64`
15×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`add-log-exp_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`rem-cbrt-cube_binary64` `diff-log_binary64` `pow1/3_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `flip--_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 74

Calls

4 calls:

4.0ms	(*.f64 x 2/3)
17.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 x 3)) (cbrt.f64 (pow.f64 x 3))) (.f64 x 2/3)) 2) (.f64 x x))
3.0ms	(cbrt.f64 (pow.f64 x 3))
3.0ms	(cbrt.f64 (pow.f64 x 3))

series122.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(*.f64 x 2/3)
55.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 x 3)) (cbrt.f64 (pow.f64 x 3))) (.f64 x 2/3)) 2) (.f64 x x))
20.0ms	(cbrt.f64 (pow.f64 x 3))
21.0ms	(cbrt.f64 (pow.f64 x 3))

simplify75.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4896	761
1	4896	761

prune70.0ms

Filtered

51 candidates to 86 candidates (-68.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	86	3	89

Merged error: 0.6b

Counts

89 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (*.f64 x 2/3))
5.2b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 x 3)) (cbrt.f64 (pow.f64 x 3))) (.f64 (.f64 (cbrt.f64 (.f64 x 2/3)) (cbrt.f64 (.f64 x 2/3))) (cbrt.f64 (.f64 x 2/3)))) 2) (.f64 x x))
43.2b	(cbrt.f64 (pow.f64 x 3))
43.2b	(cbrt.f64 (pow.f64 x 3))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`add-log-exp_binary64`
6×	`unpow-prod-down_binary64` `cube-prod_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64`
2×	`rem-cbrt-cube_binary64` `diff-log_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 65

Calls

4 calls:

2.0ms	(cbrt.f64 (*.f64 x 2/3))
31.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 x 3)) (cbrt.f64 (pow.f64 x 3))) (.f64 (.f64 (cbrt.f64 (.f64 x 2/3)) (cbrt.f64 (.f64 x 2/3))) (cbrt.f64 (.f64 x 2/3)))) 2) (.f64 x x))
3.0ms	(cbrt.f64 (pow.f64 x 3))
5.0ms	(cbrt.f64 (pow.f64 x 3))

series284.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt.f64 (*.f64 x 2/3))
71.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 x 3)) (cbrt.f64 (pow.f64 x 3))) (.f64 (.f64 (cbrt.f64 (.f64 x 2/3)) (cbrt.f64 (.f64 x 2/3))) (cbrt.f64 (.f64 x 2/3)))) 2) (.f64 x x))
20.0ms	(cbrt.f64 (pow.f64 x 3))
20.0ms	(cbrt.f64 (pow.f64 x 3))

simplify71.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5052	701

prune79.0ms

Filtered

47 candidates to 77 candidates (-63.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	77	3	80

Merged error: 0.6b

Counts

80 → 3

regimes39.0ms

Accuracy

96.6% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.8b

bsearch71.0ms

Steps

Iters	Range		Point
7	7.065108351657321	1275.238021944567	389.54422545557793

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	308	109
1	308	109

end0.0ms

sample2.0s

Algorithm

intervals

Results

935.0ms	2079×	body	1024	valid
355.0ms	4231×	body	128	valid
256.0ms	968×	body	512	valid
168.0ms	225×	body	2048	valid
82.0ms	497×	body	256	valid
18.0ms	198×	body	128	invalid
14.0ms	172×	body	128	overflowed
10.0ms	18×	body	1024	invalid
6.0ms	13×	body	512	invalid
1.0ms	5×	body	256	invalid

Details

analyze236.0ms

sample73.0ms

simplify50.0ms

prune5.0ms

localize18.0ms

rewrite99.0ms

series421.0ms

simplify139.0ms

prune433.0ms

localize8.0ms

rewrite19.0ms

series84.0ms

simplify54.0ms

prune45.0ms

localize12.0ms

rewrite33.0ms

series122.0ms

simplify75.0ms

prune70.0ms

localize16.0ms

rewrite49.0ms

series284.0ms

simplify71.0ms

prune79.0ms

regimes39.0ms

bsearch71.0ms

simplify7.0ms

end0.0ms

sample2.0s

Profiling