Details

analyze137.0ms

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
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

sample28.0ms

Algorithm

intervals

Results

20.0ms

256×

body

valid

simplify106.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4906	31
1	4906	31

prune6.0ms

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: 0.2b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0) (.f64 4.0 (+.f64 (.f64 (.f64 a a) (+.f64 1.0 a)) (.f64 (.f64 b b) (-.f64 1.0 (.f64 3.0 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1.0 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0)
0.8b	(.f64 (.f64 b b) (-.f64 1.0 (*.f64 3.0 a)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1_binary64` `add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
7×	`associate-r_binary64`
6×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`associate-*r/_binary64`
3×	`pow-unpow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unpow-prod-down_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `associate-l_binary64` `unswap-sqr_binary64` `flip-+_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `sqr-pow_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 77

Calls

4 calls:

9.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0) (.f64 4.0 (+.f64 (.f64 (.f64 a a) (+.f64 1.0 a)) (.f64 (.f64 b b) (-.f64 1.0 (.f64 3.0 a))))))
8.0ms	(.f64 (.f64 a a) (+.f64 1.0 a))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0)
8.0ms	(.f64 (.f64 b b) (-.f64 1.0 (*.f64 3.0 a)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0) (.f64 4.0 (+.f64 (.f64 (.f64 a a) (+.f64 1.0 a)) (.f64 (.f64 b b) (-.f64 1.0 (.f64 3.0 a))))))
7.0ms	(.f64 (.f64 a a) (+.f64 1.0 a))
26.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0)
11.0ms	(.f64 (.f64 b b) (-.f64 1.0 (*.f64 3.0 a)))

simplify29.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5653	1261

prune107.0ms

Filtered

61 candidates to 89 candidates (-45.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	4	90

Merged error: 0.0b

Counts

90 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b	(.f64 (.f64 b b) (-.f64 1.0 (*.f64 3.0 a)))
9.7b	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2.0) (.f64 4.0 (+.f64 (.f64 (.f64 b b) (-.f64 1.0 (.f64 3.0 a))) (.f64 (.f64 a a) (+.f64 1.0 a))))))
9.7b	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2.0) (.f64 4.0 (+.f64 (.f64 (.f64 b b) (-.f64 1.0 (.f64 3.0 a))) (.f64 (.f64 a a) (+.f64 1.0 a))))))
9.7b	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2.0) (.f64 4.0 (+.f64 (.f64 (.f64 b b) (-.f64 1.0 (.f64 3.0 a))) (.f64 (.f64 a a) (+.f64 1.0 a))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`cbrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `pow1/3_binary64` `prod-exp_binary64` `flip-+_binary64`
2×	`sub-neg_binary64` `associate-*r/_binary64`
1×	`flip3--_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 62

Calls

4 calls:

8.0ms	(.f64 (.f64 b b) (-.f64 1.0 (*.f64 3.0 a)))
7.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2.0) (.f64 4.0 (+.f64 (.f64 (.f64 b b) (-.f64 1.0 (.f64 3.0 a))) (.f64 (.f64 a a) (+.f64 1.0 a))))))
7.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2.0) (.f64 4.0 (+.f64 (.f64 (.f64 b b) (-.f64 1.0 (.f64 3.0 a))) (.f64 (.f64 a a) (+.f64 1.0 a))))))
7.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2.0) (.f64 4.0 (+.f64 (.f64 (.f64 b b) (-.f64 1.0 (.f64 3.0 a))) (.f64 (.f64 a a) (+.f64 1.0 a))))))

series179.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(.f64 (.f64 b b) (-.f64 1.0 (*.f64 3.0 a)))
56.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2.0) (.f64 4.0 (+.f64 (.f64 (.f64 b b) (-.f64 1.0 (.f64 3.0 a))) (.f64 (.f64 a a) (+.f64 1.0 a))))))
57.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2.0) (.f64 4.0 (+.f64 (.f64 (.f64 b b) (-.f64 1.0 (.f64 3.0 a))) (.f64 (.f64 a a) (+.f64 1.0 a))))))
57.0ms	(cbrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2.0) (.f64 4.0 (+.f64 (.f64 (.f64 b b) (-.f64 1.0 (.f64 3.0 a))) (.f64 (.f64 a a) (+.f64 1.0 a))))))

simplify55.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4936	2250
1	4936	2250

prune216.0ms

Filtered

65 candidates to 74 candidates (-13.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	74	4	78

Merged error: 0.0b

Counts

78 → 4

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 b b) (.f64 a a))))
0.0b	(.f64 2 (.f64 (.f64 b b) (.f64 a a)))
2.6b	(.f64 (.f64 b b) (*.f64 a a))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1_binary64`
33×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`pow-prod-down_binary64`
21×	`cbrt-unprod_binary64` `prod-exp_binary64`
5×	`add-log-exp_binary64`
4×	`-un-lft-identity_binary64` `pow-prod-up_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `pow-plus_binary64` `add-sqr-sqrt_binary64`
2×	`associate-r_binary64` `pow-sqr_binary64` `pow2_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 67

Calls

3 calls:

6.0ms	(+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 b b) (.f64 a a))))
12.0ms	(.f64 2 (.f64 (.f64 b b) (.f64 a a)))
9.0ms	(.f64 (.f64 b b) (*.f64 a a))

series32.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 b b) (.f64 a a))))
9.0ms	(.f64 2 (.f64 (.f64 b b) (.f64 a a)))
8.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify32.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5466	665

prune61.0ms

Filtered

39 candidates to 76 candidates (-94.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	76	4	80

Merged error: 0.0b

Counts

80 → 4

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 4.0 (+.f64 (.f64 (.f64 a a) (+.f64 1.0 a)) (.f64 (.f64 b b) (-.f64 1.0 (.f64 3.0 a)))))
0.1b	(.f64 (.f64 a a) (+.f64 1.0 a))
0.3b	(pow.f64 (/.f64 1 a) -4.0)
0.8b	(.f64 (.f64 b b) (-.f64 1.0 (*.f64 3.0 a)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`-un-lft-identity_binary64` `pow1_binary64` `associate-r/_binary64`
16×	`add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
13×	`unpow-prod-down_binary64`
10×	`associate-r_binary64`
9×	`times-frac_binary64`
7×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
5×	`associate-l_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `frac-add_binary64` `flip-+_binary64` `pow-exp_binary64`
3×	`pow-unpow_binary64` `flip3--_binary64` `pow-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `flip--_binary64` `*-commutative_binary64`
2×	`sub-neg_binary64` `div-exp_binary64`
1×	`pow-to-exp_binary64` `distribute-lft-out_binary64` `1-exp_binary64` `sqr-pow_binary64` `inv-pow_binary64` `rec-exp_binary64` `div-inv_binary64` `pow-flip_binary64`

Counts

4 → 105

Calls

4 calls:

13.0ms	(.f64 4.0 (+.f64 (.f64 (.f64 a a) (+.f64 1.0 a)) (.f64 (.f64 b b) (-.f64 1.0 (.f64 3.0 a)))))
8.0ms	(.f64 (.f64 a a) (+.f64 1.0 a))
8.0ms	(pow.f64 (/.f64 1 a) -4.0)
14.0ms	(.f64 (.f64 b b) (-.f64 1.0 (*.f64 3.0 a)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(.f64 4.0 (+.f64 (.f64 (.f64 a a) (+.f64 1.0 a)) (.f64 (.f64 b b) (-.f64 1.0 (.f64 3.0 a)))))
13.0ms	(.f64 (.f64 a a) (+.f64 1.0 a))
27.0ms	(pow.f64 (/.f64 1 a) -4.0)
9.0ms	(.f64 (.f64 b b) (-.f64 1.0 (*.f64 3.0 a)))

simplify74.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4961	1476
1	4961	1476

prune122.0ms

Filtered

74 candidates to 117 candidates (-58.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	117	4	121

Merged error: 0.0b

Counts

121 → 4

regimes197.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	31
1	61	31

end0.0ms

sample682.0ms

Algorithm

intervals

Results

545.0ms	8000×	body	80	valid
0.0ms	2×	body	80	invalid

Details

analyze137.0ms

sample28.0ms

simplify106.0ms

prune6.0ms

localize16.0ms

rewrite33.0ms

series75.0ms

simplify29.0ms

prune107.0ms

localize24.0ms

rewrite31.0ms

series179.0ms

simplify55.0ms

prune216.0ms

localize11.0ms

rewrite30.0ms

series32.0ms

simplify32.0ms

prune61.0ms

localize28.0ms

rewrite46.0ms

series77.0ms

simplify74.0ms

prune122.0ms

regimes197.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample682.0ms

Profiling