Details

analyze600.0ms

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
3.1%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

sample63.0ms

Algorithm

intervals

Results

23.0ms	47×	body	1280	valid
12.0ms	42×	body	640	valid
9.0ms	133×	body	80	valid
4.0ms	21×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	5×	body	640	invalid
1.0ms	3×	body	1280	invalid
1.0ms	6×	body	320	invalid
0.0ms	4×	body	160	invalid
0.0ms	7×	body	80	invalid
0.0ms	2×	body	80	nan

simplify90.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4959	13
1	4959	13

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 11.6b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
0.0b	(/.f64 x (+.f64 x y))
5.6b	(pow.f64 (/.f64 x (+.f64 x y)) x)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac_binary64`
118×	`*-un-lft-identity_binary64`
90×	`unpow-prod-down_binary64`
80×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
25×	`associate-/l*_binary64`
19×	`distribute-lft-out_binary64`
16×	`add-exp-log_binary64`
12×	`associate-/r/_binary64`
7×	`associate-/r*_binary64` `add-cbrt-cube_binary64` `div-inv_binary64` `div-exp_binary64`
6×	`flip3-+_binary64` `flip-+_binary64`
5×	`sqr-pow_binary64`
4×	`pow1_binary64` `pow-exp_binary64`
3×	`pow-unpow_binary64` `add-log-exp_binary64`
2×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64`

Counts

3 → 172

Calls

3 calls:

11.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
5.0ms	(/.f64 x (+.f64 x y))
7.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

series333.0ms

Counts

3 → 9

Calls

3 calls:

133.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
29.0ms	(/.f64 x (+.f64 x y))
172.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

simplify120.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4946	4029
1	4946	4029

prune113.0ms

Filtered

131 candidates to 181 candidates (-38.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	179	3	182

Merged error: 0.3b

Counts

182 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.9b	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
1.9b	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

61×	`unpow-prod-down_binary64`
51×	`cbrt-prod_binary64`
48×	`*-un-lft-identity_binary64`
43×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
20×	`add-exp-log_binary64`
14×	`cbrt-div_binary64`
10×	`associate-/r/_binary64`
7×	`flip3-+_binary64` `flip-+_binary64` `pow-exp_binary64`
6×	`pow-unpow_binary64` `pow1_binary64` `distribute-lft-out_binary64`
5×	`div-exp_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `prod-exp_binary64` `frac-times_binary64`
2×	`pow-to-exp_binary64` `associate-r/_binary64` `pow1/3_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-inv_binary64` `associate-l/_binary64`

Counts

4 → 116

Calls

4 calls:

1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
11.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
16.0ms	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)

series641.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(cbrt.f64 x)
87.0ms	(cbrt.f64 x)
228.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
241.0ms	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)

simplify95.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5563	3131

prune115.0ms

Filtered

98 candidates to 128 candidates (-30.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	129	2	131

Merged error: 0.0b

Counts

131 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.9b	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
3.0b	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod_binary64`
85×	`*-un-lft-identity_binary64`
84×	`times-frac_binary64`
61×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
48×	`log-prod_binary64` `unpow-prod-down_binary64`
12×	`distribute-lft-out_binary64`
10×	`add-exp-log_binary64`
6×	`pow1_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
3×	`pow-unpow_binary64`
2×	`flip3-+_binary64` `rem-log-exp_binary64` `pow1/3_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `pow-pow_binary64` `log-pow_binary64` `sqr-pow_binary64` `log-div_binary64`

Counts

4 → 144

Calls

4 calls:

1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
11.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
10.0ms	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(cbrt.f64 x)
86.0ms	(cbrt.f64 x)
231.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
72.0ms	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))

simplify92.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4926	3711
1	4926	3711

prune148.0ms

Filtered

124 candidates to 156 candidates (-25.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	156	2	158

Merged error: 0.0b

Counts

158 → 2

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(/.f64 (exp.f64 (neg.f64 y)) x)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64`
3×	`associate-/r_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `add-exp-log_binary64`
1×	`add-log-exp_binary64` `pow1_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `exp-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `exp-neg_binary64`

Counts

1 → 29

Calls

1 calls:

5.0ms

(/.f64 (exp.f64 (neg.f64 y)) x)

series24.0ms

Counts

1 → 3

Calls

1 calls:

24.0ms

(/.f64 (exp.f64 (neg.f64 y)) x)

simplify74.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4886	435
1	4886	435

prune17.0ms

Filtered

24 candidates to 32 candidates (-33.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	31	1	32
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	32	2	34

Merged error: 0b

Counts

34 → 2

regimes30.0ms

Accuracy

94% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 5.5b

bsearch66.0ms

Steps

Iters	Range		Point
6	2.2209263942109523e-18	1.48493567820076e-17	1.4546893430040697e-17
10	-4.8982121753079465e+26	-3733572718855.876	-2.318046369106234e+17

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	63
1	36	63

end0.0ms

sample1.9s

Algorithm

intervals

Results

715.0ms	1422×	body	1280	valid
364.0ms	1199×	body	640	valid
246.0ms	4428×	body	80	valid
126.0ms	633×	body	320	valid
66.0ms	219×	body	640	invalid
40.0ms	318×	body	160	valid
38.0ms	85×	body	1280	invalid
37.0ms	192×	body	320	invalid
11.0ms	92×	body	160	invalid
9.0ms	155×	body	80	invalid
7.0ms	179×	body	80	nan

Details

analyze600.0ms

sample63.0ms

simplify90.0ms

prune3.0ms

localize6.0ms

rewrite32.0ms

series333.0ms

simplify120.0ms

prune113.0ms

localize16.0ms

rewrite34.0ms

series641.0ms

simplify95.0ms

prune115.0ms

localize16.0ms

rewrite32.0ms

series472.0ms

simplify92.0ms

prune148.0ms

localize4.0ms

rewrite6.0ms

series24.0ms

simplify74.0ms

prune17.0ms

regimes30.0ms

bsearch66.0ms

simplify4.0ms

end0.0ms

sample1.9s

Profiling