Details

analyze772.0ms

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%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

sample64.0ms

Algorithm

intervals

Results

15.0ms	173×	body	80	valid
9.0ms	26×	body	1280	valid
8.0ms	30×	body	640	valid
5.0ms	21×	body	640	nan
5.0ms	15×	body	1280	nan
3.0ms	44×	body	80	nan
3.0ms	15×	body	320	valid
2.0ms	11×	body	320	nan
2.0ms	12×	body	160	valid
1.0ms	5×	body	160	nan

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5004	27

prune3.0ms

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: 41.7b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
0.4b	(*.f64 (sqrt.f64 2) t)
11.9b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
21.2b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`sqrt-div_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

21.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
5.0ms	(*.f64 (sqrt.f64 2) t)
16.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
16.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
4.0ms	(*.f64 (sqrt.f64 2) t)
63.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
228.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

simplify63.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4974	2007
1	4974	2007

prune125.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	4	92

Merged error: 3.4b

Counts

92 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

4.0b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
5.5b	(/.f64 (*.f64 l l) x)
7.8b	(/.f64 (*.f64 t t) x)
26.3b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-*r/_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `times-frac_binary64`
5×	`pow1_binary64`
4×	`flip3-+_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `div-exp_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`sqrt-prod_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `associate-+r+_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 74

Calls

4 calls:

9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
5.0ms	(/.f64 (*.f64 l l) x)
5.0ms	(/.f64 (*.f64 t t) x)
9.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
4.0ms	(/.f64 (*.f64 l l) x)
4.0ms	(/.f64 (*.f64 t t) x)
29.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

simplify28.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5022	1324

prune76.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	81	9	90

Merged error: 1.7b

Counts

90 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

1.4b	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
4.0b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
7.8b	(/.f64 (*.f64 t t) x)
26.3b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `associate-*r/_binary64` `add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
4×	`frac-add_binary64` `sqrt-div_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64` `sum-log_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 64

Calls

4 calls:

5.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
5.0ms	(/.f64 (*.f64 t t) x)
9.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
17.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
4.0ms	(/.f64 (*.f64 t t) x)
29.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

simplify28.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5126	1346

prune65.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	76	9	85

Merged error: 1.7b

Counts

85 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

4.0b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (.f64 l l) (/.f64 1 x)))))
5.5b	(.f64 (.f64 l l) (/.f64 1 x))
7.8b	(/.f64 (*.f64 t t) x)
26.3b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (.f64 l l) (/.f64 1 x))))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
21×	`add-cbrt-cube_binary64`
19×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64` `times-frac_binary64`
13×	`associate-r_binary64` `prod-exp_binary64`
10×	`pow1_binary64`
9×	`associate-*r/_binary64`
7×	`cbrt-unprod_binary64`
6×	`add-log-exp_binary64` `div-exp_binary64`
4×	`flip3-+_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `associate-/r*_binary64` `unswap-sqr_binary64` `sqrt-prod_binary64`
2×	`1-exp_binary64` `rec-exp_binary64` `div-inv_binary64` `associate-+r+_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `un-div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 94

Calls

4 calls:

9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (.f64 l l) (/.f64 1 x)))))
10.0ms	(.f64 (.f64 l l) (/.f64 1 x))
5.0ms	(/.f64 (*.f64 t t) x)
9.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (.f64 l l) (/.f64 1 x))))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (.f64 l l) (/.f64 1 x)))))
4.0ms	(.f64 (.f64 l l) (/.f64 1 x))
4.0ms	(/.f64 (*.f64 t t) x)
32.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (.f64 l l) (/.f64 1 x))))))

simplify32.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5084	1463

prune57.0ms

Filtered

66 candidates to 106 candidates (-60.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	106	9	115

Merged error: 1.7b

Counts

115 → 9

regimes396.0ms

Accuracy

73.8% (6.2b remaining)

Error of 10.0b against oracle of 3.7b and baseline of 27.6b

bsearch766.0ms

Steps

Iters	Range		Point
6	4.883418031490245e+39	4.587804681121891e+40	4.476892235675878e+40
6	1.0244890097125646e-156	9.156454977210159e-156	1.0390836696447033e-156
9	3.016349471432922e-254	8.569748972996248e-246	8.444142802464952e-246
11	1.185622087390319e-299	5.594627680061196e-278	1.1976647284219064e-299
6	-1.2561431465120803e-266	-1.9545198516610967e-267	-1.994070347116178e-267
9	-4.535792502090446e-196	-1.4229804189555175e-201	-4.459218330231056e-196
10	-6.544816625833973e-166	-1.2335522561798778e-182	-1.2539860067398703e-182
6	-1.3471082874682217e+43	-1.8685414241321426e+42	-1.3221287020936742e+43

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	174	267
1	174	267

end0.0ms

sample2.0s

Algorithm

intervals

Results

369.0ms	5143×	body	80	valid
302.0ms	860×	body	1280	valid
282.0ms	1021×	body	640	valid
199.0ms	595×	body	1280	nan
170.0ms	637×	body	640	nan
127.0ms	618×	body	320	valid
98.0ms	1434×	body	80	nan
74.0ms	368×	body	320	nan
49.0ms	358×	body	160	valid
23.0ms	172×	body	160	nan

Details

analyze772.0ms

sample64.0ms

simplify60.0ms

prune3.0ms

localize16.0ms

rewrite60.0ms

series402.0ms

simplify63.0ms

prune125.0ms

localize14.0ms

rewrite31.0ms

series57.0ms

simplify28.0ms

prune76.0ms

localize17.0ms

rewrite31.0ms

series61.0ms

simplify28.0ms

prune65.0ms

localize16.0ms

rewrite37.0ms

series56.0ms

simplify32.0ms

prune57.0ms

regimes396.0ms

bsearch766.0ms

simplify4.0ms

end0.0ms

sample2.0s

Profiling