Details

analyze999.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.6%	0.1%	6
32.8%	67.1%	0.1%	7
34.3%	65.5%	0.1%	8
38.2%	61.2%	0.5%	9
39.6%	53%	7.4%	10
40.3%	52.4%	7.4%	11
41.6%	49.6%	8.8%	12
42%	39.9%	18.1%	13
42.3%	39.6%	18.2%	14

sample47.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
13.0ms	125×	body	80	invalid
3.0ms	80×	body	80	nan

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4959	13
1	4959	13

prune9.0ms

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: 2.1b

Counts

2 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (*.f64 k (+.f64 k 10)))
0.0b	(*.f64 a (pow.f64 k m))
0.0b	(*.f64 k (+.f64 k 10))
2.1b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log_binary64`
18×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-cbrt-cube_binary64`
11×	`associate-r_binary64` `add-cube-cbrt_binary64`
7×	`prod-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-l_binary64`
4×	`unswap-sqr_binary64` `unpow-prod-down_binary64` `div-exp_binary64`
3×	`flip3-+_binary64` `associate-/r*_binary64` `cbrt-unprod_binary64` `times-frac_binary64` `flip-+_binary64`
2×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64` `associate-+r+_binary64` `pow-exp_binary64` `-commutative_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 86

Calls

4 calls:

4.0ms	(+.f64 1 (*.f64 k (+.f64 k 10)))
5.0ms	(*.f64 a (pow.f64 k m))
6.0ms	(*.f64 k (+.f64 k 10))
7.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+.f64 1 (*.f64 k (+.f64 k 10)))
17.0ms	(*.f64 a (pow.f64 k m))
6.0ms	(*.f64 k (+.f64 k 10))
42.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))

simplify54.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5000	960

prune84.0ms

Filtered

67 candidates to 98 candidates (-46.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	98	2	100

Merged error: 2.1b

Counts

100 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 a (pow.f64 k m))
0.0b	(*.f64 k (+.f64 k 10))
0.1b	(/.f64 1 (/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m))))
2.1b	(/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log_binary64`
36×	`times-frac_binary64`
34×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
26×	`div-exp_binary64`
22×	`add-cbrt-cube_binary64`
16×	`prod-exp_binary64`
11×	`associate-r_binary64`
8×	`associate-/r*_binary64`
7×	`pow1_binary64` `cbrt-undiv_binary64`
6×	`associate-l_binary64` `associate-/l*_binary64` `div-inv_binary64`
5×	`pow-to-exp_binary64` `1-exp_binary64` `rec-exp_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-r/_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `-commutative_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64` `inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 135

Calls

4 calls:

6.0ms	(*.f64 a (pow.f64 k m))
6.0ms	(*.f64 k (+.f64 k 10))
9.0ms	(/.f64 1 (/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m))))
9.0ms	(/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m)))

series92.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(*.f64 a (pow.f64 k m))
6.0ms	(*.f64 k (+.f64 k 10))
33.0ms	(/.f64 1 (/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m))))
36.0ms	(/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m)))

simplify65.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4934	1978
1	4934	1978

prune110.0ms

Filtered

87 candidates to 147 candidates (-69.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	146	3	149

Merged error: 0.0b

Counts

149 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 k (+.f64 k 10))
0.0b	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
15.4b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
15.4b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-sqr-sqrt_binary64`
92×	`times-frac_binary64`
52×	`associate-r_binary64` `sqrt-prod_binary64`
50×	`*-un-lft-identity_binary64`
48×	`add-cube-cbrt_binary64`
30×	`add-exp-log_binary64`
27×	`associate-l_binary64`
24×	`unpow-prod-down_binary64`
22×	`unswap-sqr_binary64`
18×	`add-cbrt-cube_binary64`
12×	`sqr-pow_binary64`
10×	`pow1_binary64` `div-exp_binary64`
9×	`prod-exp_binary64`
8×	`sqrt-div_binary64`
5×	`flip3-+_binary64` `cbrt-unprod_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64`
3×	`associate-*r/_binary64`
2×	`pow-to-exp_binary64` `pow-prod-down_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 170

Calls

4 calls:

6.0ms	(*.f64 k (+.f64 k 10))
33.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(*.f64 k (+.f64 k 10))
39.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
6.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

simplify44.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5123	3772

prune188.0ms

Filtered

117 candidates to 182 candidates (-55.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	182	3	185

Merged error: 0.0b

Counts

185 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (pow.f64 k (neg.f64 m)) a)
0.0b	(+.f64 (/.f64 10 a) (/.f64 k a))
0.1b	(*.f64 (/.f64 k (pow.f64 k m)) (+.f64 (/.f64 10 a) (/.f64 k a)))
0.1b	(/.f64 1 (+.f64 (/.f64 (pow.f64 k (neg.f64 m)) a) (*.f64 (/.f64 k (pow.f64 k m)) (+.f64 (/.f64 10 a) (/.f64 k a)))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac_binary64`
63×	`*-un-lft-identity_binary64`
57×	`add-sqr-sqrt_binary64`
47×	`add-cube-cbrt_binary64`
25×	`associate-l_binary64`
23×	`add-exp-log_binary64`
22×	`unpow-prod-down_binary64`
13×	`add-cbrt-cube_binary64`
12×	`frac-add_binary64`
10×	`associate-/l*_binary64`
9×	`associate-/r/_binary64`
8×	`distribute-lft-out_binary64` `associate-r_binary64` `sqr-pow_binary64` `div-exp_binary64`
7×	`pow1_binary64` `div-inv_binary64`
6×	`flip3-+_binary64` `associate-/r_binary64` `add-log-exp_binary64` `associate-r/_binary64` `flip-+_binary64` `frac-times_binary64`
4×	`unswap-sqr_binary64` `prod-exp_binary64`
3×	`cbrt-undiv_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `distribute-rgt-out_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `1-exp_binary64` `neg-sub0_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-sub_binary64` `inv-pow_binary64` `rec-exp_binary64` `pow-neg_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 165

Calls

4 calls:

5.0ms	(/.f64 (pow.f64 k (neg.f64 m)) a)
12.0ms	(+.f64 (/.f64 10 a) (/.f64 k a))
22.0ms	(*.f64 (/.f64 k (pow.f64 k m)) (+.f64 (/.f64 10 a) (/.f64 k a)))
15.0ms	(/.f64 1 (+.f64 (/.f64 (pow.f64 k (neg.f64 m)) a) (*.f64 (/.f64 k (pow.f64 k m)) (+.f64 (/.f64 10 a) (/.f64 k a)))))

series129.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/.f64 (pow.f64 k (neg.f64 m)) a)
5.0ms	(+.f64 (/.f64 10 a) (/.f64 k a))
33.0ms	(*.f64 (/.f64 k (pow.f64 k m)) (+.f64 (/.f64 10 a) (/.f64 k a)))
71.0ms	(/.f64 1 (+.f64 (/.f64 (pow.f64 k (neg.f64 m)) a) (*.f64 (/.f64 k (pow.f64 k m)) (+.f64 (/.f64 10 a) (/.f64 k a)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5427	3068

prune168.0ms

Filtered

135 candidates to 177 candidates (-31.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	175	5	180

Merged error: 0b

Counts

180 → 5

regimes165.0ms

Accuracy

93.5% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 2.1b

bsearch15.0ms

Steps

Iters	Range		Point
5	2.88696532579728e+144	7.861322747078371e+144	3.408471258283922e+144

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	41
1	38	41

end0.0ms

sample1.2s

Algorithm

intervals

Results

516.0ms	8000×	body	80	valid
269.0ms	3285×	body	80	invalid
88.0ms	1965×	body	80	nan

Details

analyze999.0ms

sample47.0ms

simplify101.0ms

prune9.0ms

localize9.0ms

rewrite25.0ms

series68.0ms

simplify54.0ms

prune84.0ms

localize10.0ms

rewrite34.0ms

series92.0ms

simplify65.0ms

prune110.0ms

localize11.0ms

rewrite53.0ms

series56.0ms

simplify44.0ms

prune188.0ms

localize16.0ms

rewrite62.0ms

series129.0ms

simplify51.0ms

prune168.0ms

regimes165.0ms

bsearch15.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling