Details

analyze78.0ms

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

sample19.0ms

Algorithm

intervals

Results

6.0ms	197×	body	80	valid
3.0ms	30×	body	640	valid
1.0ms	8×	body	1280	valid
1.0ms	13×	body	320	valid
0.0ms	8×	body	160	valid

simplify240.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (239.0ms)

Iter	Nodes	Cost
0	5206	11

prune9.0ms

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: 13.7b

Counts

2 → 2

localize10.0ms

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)))
3.1b	(+ 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))
12.0ms	(* y (/ (- x 1.0) (+ 1.0 y)))
3.0ms	(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

series22.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ (- x 1.0) (+ 1.0 y))
6.0ms	(* y (/ (- x 1.0) (+ 1.0 y)))
11.0ms	(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

simplify59.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	6163	1269

prune189.0ms

Filtered

76 candidates to 111 candidates (-46.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	102	9	111
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	103	10	113

Merged error: 7.5b

Counts

113 → 10

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))
9.4b	(+ 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:

6.0ms	(cbrt (+ 1.0 y))
6.0ms	(cbrt (+ 1.0 y))
6.0ms	(cbrt (+ 1.0 y))
11.0ms	(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4914	683
1	4914	683

prune150.0ms

Filtered

50 candidates to 65 candidates (-30.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	64	11	75

Merged error: 7.5b

Counts

75 → 11

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))
9.4b	(+ 1.0 (* y (/ (/ (- x 1.0) (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (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 (/ (/ (- x 1.0) (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (cbrt (+ 1.0 y)))))

series34.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(cbrt (+ 1.0 y))
9.0ms	(cbrt (+ 1.0 y))
7.0ms	(cbrt (+ 1.0 y))
11.0ms	(+ 1.0 (* y (/ (/ (- x 1.0) (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (cbrt (+ 1.0 y)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4918	683
1	4918	683

prune145.0ms

Filtered

48 candidates to 65 candidates (-35.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	64	12	76

Merged error: 7.5b

Counts

76 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (- x 1.0) (+ 1.0 y)))
0.5b	(cbrt (/ (- x 1.0) (+ 1.0 y)))
0.5b	(cbrt (/ (- x 1.0) (+ 1.0 y)))
9.9b	(+ 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))))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))
15.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))
15.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))
16.0ms	(+ 1.0 (* y (* (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y)))) (cbrt (/ (- x 1.0) (+ 1.0 y))))))

simplify86.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4923	1974
1	4923	1974

prune270.0ms

Filtered

90 candidates to 128 candidates (-42.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	125	3	128
Fresh	0	9	9
Picked	1	0	1
Done	0	2	2
Total	126	14	140

Merged error: 7.5b

Counts

140 → 14

regimes453.0ms

Accuracy

95.8% (0.3b remaining)

Error of 7.6b against oracle of 7.3b and baseline of 14.9b

bsearch27.0ms

Steps

Iters	Range		Point
9	0.0135814980420586	6502426.347601415	6384412.93831681
8	-788633544510.412	-33911365.40920275	-773146022775.8846

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	331	31
1	331	31

end0.0ms

sample515.0ms

Algorithm

intervals

Results

181.0ms	6077×	body	80	valid
87.0ms	771×	body	640	valid
58.0ms	380×	body	1280	valid
39.0ms	480×	body	320	valid
16.0ms	292×	body	160	valid

Details

analyze78.0ms

sample19.0ms

simplify240.0ms

prune9.0ms

localize10.0ms

rewrite27.0ms

series22.0ms

simplify59.0ms

prune189.0ms

localize11.0ms

rewrite14.0ms

series30.0ms

simplify72.0ms

prune150.0ms

localize11.0ms

rewrite14.0ms

series34.0ms

simplify65.0ms

prune145.0ms

localize11.0ms

rewrite31.0ms

series62.0ms

simplify86.0ms

prune270.0ms

regimes453.0ms

bsearch27.0ms

simplify7.0ms

end0.0ms

sample515.0ms

Profiling