Details

analyze234.0ms

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

sample16.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
1.0ms	16×	body	80	invalid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	112	16
1	112	16

prune1.0ms

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: 7.0b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

3.6b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
4.5b	(.f64 y (+.f64 1 (.f64 z z)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac_binary64`
26×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
12×	`div-exp_binary64`
6×	`cbrt-undiv_binary64`
5×	`prod-exp_binary64`
4×	`pow1_binary64` `associate-*r/_binary64`
3×	`cbrt-unprod_binary64` `associate-r_binary64` `associate-l_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `add-log-exp_binary64` `1-exp_binary64` `associate-/r/_binary64` `rec-exp_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-/r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

2 → 74

Calls

2 calls:

9.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
5.0ms	(.f64 y (+.f64 1 (.f64 z z)))

series96.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
45.0ms	(.f64 y (+.f64 1 (.f64 z z)))

simplify98.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5018	1317

prune73.0ms

Filtered

51 candidates to 80 candidates (-56.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	72	8	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	8	81

Merged error: 6.1b

Counts

81 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z))))
3.6b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z)))))
18.2b	(sqrt.f64 (+.f64 1 (*.f64 z z)))
18.2b	(sqrt.f64 (+.f64 1 (*.f64 z z)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log_binary64`
31×	`times-frac_binary64`
30×	`add-cbrt-cube_binary64`
28×	`sqrt-div_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`div-exp_binary64`
16×	`associate-*r/_binary64`
15×	`prod-exp_binary64`
14×	`flip3-+_binary64` `flip-+_binary64`
13×	`associate-/l*_binary64`
11×	`pow1_binary64`
9×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-prod_binary64`
8×	`associate-/r/_binary64` `frac-times_binary64`
6×	`associate-r_binary64`
4×	`add-log-exp_binary64` `associate-*l/_binary64`
3×	`pow-prod-down_binary64` `1-exp_binary64` `rec-exp_binary64` `div-inv_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`associate-/l/_binary64` `associate-/r_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 123

Calls

4 calls:

11.0ms	(.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z))))
15.0ms	(/.f64 (/.f64 1 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z)))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

series131.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z))))
58.0ms	(/.f64 (/.f64 1 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z)))))
16.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
18.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

simplify99.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4933	2530
1	4933	2530

prune104.0ms

Filtered

89 candidates to 135 candidates (-51.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	135	8	143

Merged error: 6.1b

Counts

143 → 8

localize7.0ms

Local error

Found 3 expressions with local error:

0.4b	(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
3.3b	(.f64 (.f64 y (+.f64 1 (*.f64 z z))) x)
4.5b	(.f64 y (+.f64 1 (.f64 z z)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
19×	`add-cbrt-cube_binary64`
16×	`pow1_binary64`
13×	`prod-exp_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`pow-prod-down_binary64` `cbrt-unprod_binary64`
6×	`associate-r_binary64` `associate-*r/_binary64` `div-exp_binary64`
4×	`associate-l_binary64` `associate-*l/_binary64`
3×	`flip3-+_binary64` `add-log-exp_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `associate-/l*_binary64` `times-frac_binary64` `pow-flip_binary64` `flip-+_binary64`
2×	`associate-/r/_binary64` `*-commutative_binary64`
1×	`associate-/r*_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

3 → 77

Calls

3 calls:

8.0ms	(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
7.0ms	(.f64 (.f64 y (+.f64 1 (*.f64 z z))) x)
6.0ms	(.f64 y (+.f64 1 (.f64 z z)))

series126.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/.f64 1 (.f64 (.f64 y (+.f64 1 (*.f64 z z))) x))
43.0ms	(.f64 (.f64 y (+.f64 1 (*.f64 z z))) x)
37.0ms	(.f64 y (+.f64 1 (.f64 z z)))

simplify105.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5152	1234

prune51.0ms

Filtered

49 candidates to 86 candidates (-75.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	86	8	94

Merged error: 6.1b

Counts

94 → 8

localize7.0ms

Local error

Found 3 expressions with local error:

0.6b	(/.f64 1 (.f64 y (+.f64 1 (.f64 z z))))
3.1b	(/.f64 (/.f64 1 (.f64 y (+.f64 1 (.f64 z z)))) x)
4.5b	(.f64 y (+.f64 1 (.f64 z z)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

42×	`times-frac_binary64`
35×	`add-exp-log_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`add-cbrt-cube_binary64`
15×	`div-exp_binary64`
12×	`associate-r/_binary64` `associate-/l_binary64`
10×	`associate-/r/_binary64`
8×	`pow1_binary64`
7×	`cbrt-undiv_binary64` `prod-exp_binary64`
6×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
4×	`associate-/r*_binary64` `1-exp_binary64` `rec-exp_binary64`
3×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`pow-prod-down_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-flip_binary64`
1×	`associate-/l/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `inv-pow_binary64` `*-commutative_binary64`

Counts

3 → 112

Calls

3 calls:

6.0ms	(/.f64 1 (.f64 y (+.f64 1 (.f64 z z))))
9.0ms	(/.f64 (/.f64 1 (.f64 y (+.f64 1 (.f64 z z)))) x)
6.0ms	(.f64 y (+.f64 1 (.f64 z z)))

series133.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/.f64 1 (.f64 y (+.f64 1 (.f64 z z))))
46.0ms	(/.f64 (/.f64 1 (.f64 y (+.f64 1 (.f64 z z)))) x)
38.0ms	(.f64 y (+.f64 1 (.f64 z z)))

simplify95.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4946	2211
1	4946	2211

prune70.0ms

Filtered

75 candidates to 121 candidates (-61.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	121	8	129

Merged error: 6.1b

Counts

129 → 8

regimes136.0ms

Accuracy

0% (1.5b remaining)

Error of 6.4b against oracle of 4.9b and baseline of 6.4b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	16
1	14	16

end0.0ms

sample463.0ms

Algorithm

intervals

Results

279.0ms	8000×	body	80	valid
15.0ms	458×	body	80	invalid

Details

analyze234.0ms

sample16.0ms

simplify15.0ms

prune1.0ms

localize7.0ms

rewrite17.0ms

series96.0ms

simplify98.0ms

prune73.0ms

localize9.0ms

rewrite36.0ms

series131.0ms

simplify99.0ms

prune104.0ms

localize7.0ms

rewrite24.0ms

series126.0ms

simplify105.0ms

prune51.0ms

localize7.0ms

rewrite24.0ms

series133.0ms

simplify95.0ms

prune70.0ms

regimes136.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample463.0ms

Profiling