Details

analyze76.0ms

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
12.5%	87.4%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.7%	0.1%	6
67.1%	32.8%	0.1%	7
71%	28.9%	0.1%	8
82.3%	17.6%	0.1%	9
84.9%	15%	0.1%	10
90.8%	9.1%	0.1%	11
92.2%	7.7%	0.1%	12
95.3%	4.6%	0.1%	13
96%	3.9%	0.1%	14

sample20.0ms

Algorithm

intervals

Results

6.0ms	193×	body	80	valid
3.0ms	26×	body	640	valid
2.0ms	16×	body	1280	valid
1.0ms	15×	body	320	valid
0.0ms	6×	body	160	valid

simplify242.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (240.0ms)

Iter	Nodes	Cost
0	5206	11

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 14.6b

Counts

2 → 2

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x 1.0) (+ 1.0 y))
0.1b	(* y (/ (- x 1.0) (+ 1.0 y)))
3.2b	(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
41×	`times-frac`
26×	`associate-r`
25×	`add-cube-cbrt`
11×	`distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `associate-/l*` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`flip3-+` `associate-l` `flip-+`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip--`

Counts

3 → 102

Calls

3 calls:

7.0ms	(/ (- x 1.0) (+ 1.0 y))
13.0ms	(* y (/ (- x 1.0) (+ 1.0 y)))
3.0ms	(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

series21.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ (- x 1.0) (+ 1.0 y))
5.0ms	(* y (/ (- x 1.0) (+ 1.0 y)))
10.0ms	(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

simplify58.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	6163	1269

prune185.0ms

Filtered

76 candidates to 111 candidates (-46.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	98	13	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	100	13	113

Merged error: 8.1b

Counts

113 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ 1.0 y))
0.3b	(cbrt (+ 1.0 y))
0.3b	(cbrt (+ 1.0 y))
9.5b	(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y)))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`pow1/3` `distribute-lft-out`
1×	`+-commutative` `sum-log`

Counts

4 → 53

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 y))
3.0ms	(cbrt (+ 1.0 y))
3.0ms	(cbrt (+ 1.0 y))
4.0ms	(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y)))))

series30.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(cbrt (+ 1.0 y))
6.0ms	(cbrt (+ 1.0 y))
6.0ms	(cbrt (+ 1.0 y))
10.0ms	(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y)))))

simplify71.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4914	683
1	4914	683

prune151.0ms

Filtered

50 candidates to 65 candidates (-30.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	64	14	78

Merged error: 8.1b

Counts

78 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
9.8b	(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)
4.0ms	(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

series82.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt y)
22.0ms	(cbrt y)
22.0ms	(cbrt y)
15.0ms	(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

simplify54.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4943	365
1	4943	365

prune87.0ms

Filtered

38 candidates to 56 candidates (-47.4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	56	14	70

Merged error: 8.1b

Counts

70 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (- x 1.0) (+ 1.0 y)))
0.4b	(cbrt (/ (- x 1.0) (+ 1.0 y)))
0.4b	(cbrt (/ (- x 1.0) (+ 1.0 y)))
9.8b	(+ 1.0 (* y (* (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y)))) (cbrt (/ (- x 1.0) (+ 1.0 y))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

88×	`*-un-lft-identity`
78×	`cbrt-prod`
60×	`times-frac`
58×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
15×	`distribute-lft-out`
12×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`+-commutative` `sum-log`

Counts

4 → 116

Calls

4 calls:

7.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))
7.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))
9.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))
4.0ms	(+ 1.0 (* y (* (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y)))) (cbrt (/ (- x 1.0) (+ 1.0 y))))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))
14.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))
15.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))
15.0ms	(+ 1.0 (* y (* (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y)))) (cbrt (/ (- x 1.0) (+ 1.0 y))))))

simplify87.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4923	1974
1	4923	1974

prune259.0ms

Filtered

89 candidates to 128 candidates (-43.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	10	11
Picked	0	1	1
Done	1	1	2
Total	129	13	142

Merged error: 8.1b

Counts

142 → 13

regimes161.0ms

Accuracy

96.8% (0.2b remaining)

Error of 7.7b against oracle of 7.5b and baseline of 15.1b

bsearch32.0ms

Steps

Iters	Range		Point
9	4.6404908239752706e+48	2.0831981418377296e+54	4.6940747658915896e+48
8	-6276803252880.243	-362506761.30292505	-6155885003600.655

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	47
1	69	47

end0.0ms

sample518.0ms

Algorithm

intervals

Results

179.0ms	6072×	body	80	valid
87.0ms	749×	body	640	valid
56.0ms	397×	body	1280	valid
47.0ms	507×	body	320	valid
15.0ms	275×	body	160	valid

Details

analyze76.0ms

sample20.0ms

simplify242.0ms

prune11.0ms

localize7.0ms

rewrite27.0ms

series21.0ms

simplify58.0ms

prune185.0ms

localize11.0ms

rewrite14.0ms

series30.0ms

simplify71.0ms

prune151.0ms

localize13.0ms

rewrite8.0ms

series82.0ms

simplify54.0ms

prune87.0ms

localize11.0ms

rewrite31.0ms

series58.0ms

simplify87.0ms

prune259.0ms

regimes161.0ms

bsearch32.0ms

simplify2.0ms

end0.0ms

sample518.0ms

Profiling