Details

analyze74.0ms

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

5.0ms	188×	body	80	valid
3.0ms	29×	body	640	valid
2.0ms	20×	body	320	valid
1.0ms	11×	body	1280	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

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: 16.1b

Counts

2 → 2

localize6.0ms

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)))
4.6b	(+ 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))))

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))))

simplify59.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	6163	1269

prune179.0ms

Filtered

76 candidates to 111 candidates (-46.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	100	11	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	102	11	113

Merged error: 8.0b

Counts

113 → 11

localize10.0ms

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))
11.4b	(+ 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)))))

series29.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify60.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4918	683
1	4918	683

prune151.0ms

Filtered

48 candidates to 65 candidates (-35.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	63	13	76

Merged error: 8.0b

Counts

76 → 13

localize15.0ms

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))
12.2b	(+ 1.0 (* y (/ (/ (- x 1.0) (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (* (* (cbrt (cbrt (+ 1.0 y))) (cbrt (cbrt (+ 1.0 y)))) (cbrt (cbrt (+ 1.0 y)))))))

rewrite17.0ms

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:

5.0ms	(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 (cbrt (+ 1.0 y))) (cbrt (cbrt (+ 1.0 y)))) (cbrt (cbrt (+ 1.0 y)))))))

series29.0ms

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

simplify33.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4928	683
1	4928	683

prune206.0ms

Filtered

50 candidates to 65 candidates (-30.0%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	65	13	78

Merged error: 8.0b

Counts

78 → 13

localize10.0ms

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)))
10.0b	(+ 1.0 (* (* y (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y))))) (cbrt (/ (- x 1.0) (+ 1.0 y)))))

rewrite29.0ms

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)))
6.0ms	(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)))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))
15.0ms	(cbrt (/ (- x 1.0) (+ 1.0 y)))
17.0ms	(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)))))

simplify73.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4947	2010
1	4947	2010

prune272.0ms

Filtered

90 candidates to 128 candidates (-42.2%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	125	3	128
Fresh	2	8	10
Picked	0	1	1
Done	0	2	2
Total	127	14	141

Merged error: 8.0b

Counts

141 → 14

regimes210.0ms

Accuracy

96.8% (0.2b remaining)

Error of 7.6b against oracle of 7.4b and baseline of 14.9b

bsearch26.0ms

Steps

Iters	Range		Point
7	1.5856726680705946e+45	3.343236924937976e+47	3.1571612471339895e+45
7	-1.0352769975432956e+22	-2.521372178098138e+20	-2.8008884576821015e+20

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	39
1	61	39

end0.0ms

sample496.0ms

Algorithm

intervals

Results

178.0ms	6094×	body	80	valid
84.0ms	727×	body	640	valid
54.0ms	380×	body	1280	valid
41.0ms	510×	body	320	valid
16.0ms	289×	body	160	valid

Details

analyze74.0ms

sample19.0ms

simplify240.0ms

prune11.0ms

localize6.0ms

rewrite27.0ms

series21.0ms

simplify59.0ms

prune179.0ms

localize10.0ms

rewrite14.0ms

series29.0ms

simplify60.0ms

prune151.0ms

localize15.0ms

rewrite17.0ms

series29.0ms

simplify33.0ms

prune206.0ms

localize10.0ms

rewrite29.0ms

series61.0ms

simplify73.0ms

prune272.0ms

regimes210.0ms

bsearch26.0ms

simplify2.0ms

end0.0ms

sample496.0ms

Profiling