Details

analyze136.0ms

Algorithm

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

sample38.0ms

Algorithm

intervals

Results

12.0ms	209×	body	80	valid
6.0ms	256×	pre	80	true
4.0ms	13×	body	1280	valid
3.0ms	15×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	6×	body	160	valid

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5221	29

prune9.0ms

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: 25.7b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
0.1b	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
1.6b	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
21.4b	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64` `times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
28×	`add-cube-cbrt_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
12×	`distribute-lft-out_binary64`
10×	`associate-/l*_binary64`
9×	`associate-/l/_binary64`
8×	`frac-times_binary64`
7×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `flip--_binary64`
5×	`associate-r_binary64`
4×	`associate-r/_binary64` `associate-l_binary64` `associate-l/_binary64`
3×	`cbrt-unprod_binary64` `prod-exp_binary64`
2×	`sub-neg_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 142

Calls

4 calls:

12.0ms	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
22.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
34.0ms	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
15.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

series197.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
73.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
97.0ms	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
19.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

simplify52.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4968	3892
1	4968	3892

prune253.0ms

Filtered

114 candidates to 154 candidates (-35.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	144	10	154
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	10	155

Merged error: 5.2b

Counts

155 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
1.2b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
2.3b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

321×	`times-frac_binary64`
290×	`*-un-lft-identity_binary64`
211×	`add-sqr-sqrt_binary64`
140×	`add-cube-cbrt_binary64`
90×	`associate-r_binary64`
44×	`distribute-lft-out_binary64`
31×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
26×	`associate-/l*_binary64`
24×	`associate-/r/_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
12×	`div-inv_binary64`
7×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
4×	`associate-l_binary64`
3×	`associate-/l/_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `div-sub_binary64` `prod-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r/_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 295

Calls

4 calls:

11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
20.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
39.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
31.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

series229.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
42.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
73.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
98.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

simplify100.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5049	8873

prune479.0ms

Filtered

201 candidates to 307 candidates (-52.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	300	7	307
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	305	12	317

Merged error: 5.1b

Counts

317 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.2b	(.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
2.3b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
3.3b	(log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

191×	`times-frac_binary64`
181×	`*-un-lft-identity_binary64`
134×	`add-sqr-sqrt_binary64`
110×	`log-pow_binary64`
106×	`associate-r_binary64`
105×	`exp-prod_binary64`
91×	`add-cube-cbrt_binary64`
26×	`distribute-lft-out_binary64`
19×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
14×	`associate-/r/_binary64`
11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`flip3-+_binary64` `flip-+_binary64`
7×	`div-inv_binary64`
6×	`add-log-exp_binary64`
5×	`associate-/l*_binary64`
4×	`associate-l_binary64`
3×	`associate-/r*_binary64` `log-prod_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-sub_binary64` `prod-exp_binary64` `div-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `rem-log-exp_binary64` `associate-r/_binary64` `exp-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 215

Calls

4 calls:

11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
45.0ms	(.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
34.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
13.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

series202.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
74.0ms	(.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
95.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
17.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5236	4904

prune357.0ms

Filtered

164 candidates to 227 candidates (-38.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	227	12	239

Merged error: 5.1b

Counts

239 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
0.1b	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
1.2b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
2.3b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac_binary64`
275×	`*-un-lft-identity_binary64`
196×	`add-sqr-sqrt_binary64`
133×	`add-cube-cbrt_binary64`
90×	`associate-r_binary64`
44×	`distribute-lft-out_binary64`
27×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
22×	`associate-/r/_binary64`
21×	`associate-/l*_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
12×	`cbrt-prod_binary64`
11×	`div-inv_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`associate-/r_binary64` `associate-l*_binary64`
3×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `prod-exp_binary64` `cube-prod_binary64`
2×	`cbrt-div_binary64` `cube-div_binary64` `div-sub_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `rem-cbrt-cube_binary64` `associate-r/_binary64` `pow1/3_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `unpow3_binary64` `sum-log_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 278

Calls

4 calls:

20.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
28.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
41.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
28.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

series307.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
94.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
71.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
99.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

simplify85.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4993	9182
1	4993	9182

prune462.0ms

Filtered

186 candidates to 290 candidates (-55.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	281	9	290
Fresh	7	3	10
Picked	1	0	1
Done	1	0	1
Total	290	12	302

Merged error: 5.1b

Counts

302 → 12

regimes332.0ms

Accuracy

0% (6.4b remaining)

Error of 12.5b against oracle of 6.1b and baseline of 12.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	63
1	38	63

end0.0ms

sample1.1s

Algorithm

intervals

Results

372.0ms	6343×	body	80	valid
185.0ms	8000×	pre	80	true
164.0ms	549×	body	1280	valid
130.0ms	555×	body	640	valid
62.0ms	356×	body	320	valid
23.0ms	197×	body	160	valid

Details

analyze136.0ms

sample38.0ms

simplify55.0ms

prune9.0ms

localize14.0ms

rewrite89.0ms

series197.0ms

simplify52.0ms

prune253.0ms

localize13.0ms

rewrite122.0ms

series229.0ms

simplify100.0ms

prune479.0ms

localize17.0ms

rewrite121.0ms

series202.0ms

simplify59.0ms

prune357.0ms

localize16.0ms

rewrite134.0ms

series307.0ms

simplify85.0ms

prune462.0ms

regimes332.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling