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	202×	body	80	valid
2.0ms	21×	body	640	valid
1.0ms	10×	body	1280	valid
1.0ms	10×	body	320	valid
1.0ms	13×	body	160	valid

simplify103.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	5726	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: 12.5b

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)))
4.9b	(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

rewrite29.0ms

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))
14.0ms	(* y (/ (- x 1.0) (+ 1.0 y)))
3.0ms	(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

series20.0ms

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))))

simplify44.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5284	1269

prune212.0ms

Filtered

76 candidates to 111 candidates (-46.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	99	12	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	101	12	113

Merged error: 7.4b

Counts

113 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ 1.0 y))
0.2b	(cbrt (+ 1.0 y))
0.2b	(* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))
8.5b	(+ 1.0 (* y (/ (/ (- x 1.0) (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (cbrt (+ 1.0 y)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `swap-sqr` `flip-+`
8×	`pow1/3` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-log-exp`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`+-commutative` `pow2` `pow-plus` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 92

Calls

4 calls:

5.0ms	(cbrt (+ 1.0 y))
3.0ms	(cbrt (+ 1.0 y))
10.0ms	(* (cbrt (+ 1.0 y)) (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))
7.0ms	(* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))
10.0ms	(+ 1.0 (* y (/ (/ (- x 1.0) (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (cbrt (+ 1.0 y)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4944	1168
1	4944	1168

prune244.0ms

Filtered

72 candidates to 104 candidates (-44.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	103	13	116

Merged error: 7.4b

Counts

116 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt y)
0.5b	(cbrt y)
0.5b	(cbrt y)
9.7b	(+ 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))))

series78.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt y)
20.0ms	(cbrt y)
20.0ms	(cbrt y)
15.0ms	(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

simplify67.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4894	362
1	4894	362

prune105.0ms

Filtered

41 candidates to 56 candidates (-36.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	56	13	69

Merged error: 7.4b

Counts

69 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* y (/ (- x 1.0) (+ 1.0 y))))
0.5b	(cbrt (* y (/ (- x 1.0) (+ 1.0 y))))
0.5b	(cbrt (* y (/ (- x 1.0) (+ 1.0 y))))
3.4b	(+ 1.0 (* (* (cbrt (* y (/ (- x 1.0) (+ 1.0 y)))) (cbrt (* y (/ (- x 1.0) (+ 1.0 y))))) (cbrt (* y (/ (- x 1.0) (+ 1.0 y))))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

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

series55.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(cbrt (* y (/ (- x 1.0) (+ 1.0 y))))
14.0ms	(cbrt (* y (/ (- x 1.0) (+ 1.0 y))))
14.0ms	(cbrt (* y (/ (- x 1.0) (+ 1.0 y))))
10.0ms	(+ 1.0 (* (* (cbrt (* y (/ (- x 1.0) (+ 1.0 y)))) (cbrt (* y (/ (- x 1.0) (+ 1.0 y))))) (cbrt (* y (/ (- x 1.0) (+ 1.0 y))))))

simplify45.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4928	658
1	4928	658

prune114.0ms

Filtered

44 candidates to 53 candidates (-20.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	10	10
Picked	1	0	1
Done	0	2	2
Total	53	13	66

Merged error: 7.4b

Counts

66 → 13

regimes175.0ms

Accuracy

97.4% (0.2b remaining)

Error of 7.2b against oracle of 7.0b and baseline of 14.5b

bsearch23.0ms

Steps

Iters	Range		Point
9	1.0000245287059041e+24	2.8553431855315006e+29	1.0535867105030357e+24
4	-35451520218825748.0	-18227636620702732.0	-20918868432909456.0

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	128	39
1	128	39

end0.0ms

sample520.0ms

Algorithm

intervals

Results

194.0ms	6126×	body	80	valid
76.0ms	705×	body	640	valid
53.0ms	371×	body	1280	valid
44.0ms	500×	body	320	valid
19.0ms	298×	body	160	valid

Details

analyze76.0ms

sample20.0ms

simplify103.0ms

prune9.0ms

localize6.0ms

rewrite29.0ms

series20.0ms

simplify44.0ms

prune212.0ms

localize10.0ms

rewrite25.0ms

series29.0ms

simplify64.0ms

prune244.0ms

localize13.0ms

rewrite8.0ms

series78.0ms

simplify67.0ms

prune105.0ms

localize11.0ms

rewrite26.0ms

series55.0ms

simplify45.0ms

prune114.0ms

regimes175.0ms

bsearch23.0ms

simplify2.0ms

end0.0ms

sample520.0ms

Profiling