Details

analyze483.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	93.6%	6.4%	7
3.1%	84.2%	12.7%	8
12.5%	67.1%	20.5%	9
16%	63.5%	20.5%	10
17.9%	57.7%	24.4%	11
22.6%	48.7%	28.7%	12
28.7%	37.8%	33.6%	13
30.4%	35.9%	33.7%	14

sample27.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	92×	body	80	nan
1.0ms	25×	body	80	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	8
1	14	8

prune4.0ms

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: 20.2b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

1.2b	(* c0 (sqrt (/ A (* V l))))
4.0b	(/ A (* V l))
18.5b	(sqrt (/ A (* V l)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`sqrt-prod`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log` `associate-r` `add-cbrt-cube`
9×	`times-frac`
6×	`pow1`
3×	`associate-l` `div-inv` `associate-/l*` `add-log-exp`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `*-commutative`

Counts

3 → 66

Calls

3 calls:

8.0ms	(* c0 (sqrt (/ A (* V l))))
4.0ms	(/ A (* V l))
4.0ms	(sqrt (/ A (* V l)))

series30.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(* c0 (sqrt (/ A (* V l))))
5.0ms	(/ A (* V l))
12.0ms	(sqrt (/ A (* V l)))

simplify52.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4959	561
1	4959	561

prune145.0ms

Filtered

57 candidates to 75 candidates (-31.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	61	14	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	15	76

Merged error: 7.4b

Counts

76 → 15

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(* c0 (sqrt (/ (* (cbrt A) (cbrt A)) (* V (/ l (cbrt A))))))
1.8b	(* V (/ l (cbrt A)))
1.9b	(/ (* (cbrt A) (cbrt A)) (* V (/ l (cbrt A))))
18.5b	(sqrt (/ (* (cbrt A) (cbrt A)) (* V (/ l (cbrt A)))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
32×	`add-exp-log`
31×	`associate-r`
23×	`times-frac` `add-cbrt-cube`
22×	`add-cube-cbrt` `*-un-lft-identity`
13×	`sqrt-prod`
10×	`cbrt-prod` `prod-exp` `cbrt-unprod`
9×	`pow1` `cbrt-undiv` `div-exp`
6×	`associate-l`
5×	`associate-*r/` `unswap-sqr`
4×	`div-inv` `add-log-exp`
3×	`associate-/r/`
2×	`sqrt-div` `pow-prod-down` `*-commutative`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 111

Calls

4 calls:

12.0ms	(* c0 (sqrt (/ (* (cbrt A) (cbrt A)) (* V (/ l (cbrt A))))))
8.0ms	(* V (/ l (cbrt A)))
10.0ms	(/ (* (cbrt A) (cbrt A)) (* V (/ l (cbrt A))))
10.0ms	(sqrt (/ (* (cbrt A) (cbrt A)) (* V (/ l (cbrt A)))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* c0 (sqrt (/ (* (cbrt A) (cbrt A)) (* V (/ l (cbrt A))))))
18.0ms	(* V (/ l (cbrt A)))
8.0ms	(/ (* (cbrt A) (cbrt A)) (* V (/ l (cbrt A))))
12.0ms	(sqrt (/ (* (cbrt A) (cbrt A)) (* V (/ l (cbrt A)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4952	948
1	4952	948

prune171.0ms

Filtered

83 candidates to 123 candidates (-48.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	3	10	13
Picked	1	0	1
Done	0	1	1
Total	121	17	138

Merged error: 4.1b

Counts

138 → 17

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt A)
1.2b	(* c0 (/ (fabs (cbrt A)) (sqrt (* V (/ l (cbrt A))))))
1.8b	(* V (/ l (cbrt A)))
12.9b	(sqrt (* V (/ l (cbrt A))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
39×	`associate-r`
33×	`times-frac`
28×	`add-cube-cbrt` `*-un-lft-identity`
14×	`add-exp-log`
13×	`cbrt-prod` `add-cbrt-cube`
11×	`pow1`
6×	`associate-l`
5×	`unswap-sqr`
4×	`associate-*r/` `prod-exp` `sqrt-prod` `cbrt-unprod` `add-log-exp`
3×	`pow-prod-down`
2×	`cbrt-undiv` `sqrt-pow1` `sqrt-div` `div-exp` `*-commutative` `div-inv`
1×	`pow1/2` `pow1/3` `associate-/r/`

Counts

4 → 101

Calls

4 calls:

1.0ms	(cbrt A)
11.0ms	(* c0 (/ (fabs (cbrt A)) (sqrt (* V (/ l (cbrt A))))))
8.0ms	(* V (/ l (cbrt A)))
4.0ms	(sqrt (* V (/ l (cbrt A))))

series109.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt A)
44.0ms	(* c0 (/ (fabs (cbrt A)) (sqrt (* V (/ l (cbrt A))))))
18.0ms	(* V (/ l (cbrt A)))
24.0ms	(sqrt (* V (/ l (cbrt A))))

simplify55.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5005	1037

prune188.0ms

Filtered

85 candidates to 113 candidates (-32.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	106	7	113
Fresh	4	11	15
Picked	1	0	1
Done	1	0	1
Total	112	18	130

Merged error: 3.4b

Counts

130 → 18

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt A)
0.6b	(cbrt A)
1.2b	(* c0 (/ (fabs (cbrt A)) (sqrt (* (* V (* (/ (cbrt l) (cbrt (cbrt A))) (/ (cbrt l) (cbrt (cbrt A))))) (/ (cbrt l) (cbrt (cbrt A)))))))
12.9b	(sqrt (* (* V (* (/ (cbrt l) (cbrt (cbrt A))) (/ (cbrt l) (cbrt (cbrt A))))) (/ (cbrt l) (cbrt (cbrt A)))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

23×	`associate-r`
20×	`add-sqr-sqrt`
19×	`associate-*r/`
16×	`pow1`
15×	`add-cube-cbrt` `*-un-lft-identity`
14×	`sqrt-div`
13×	`times-frac`
10×	`frac-times` `associate-*l/`
9×	`add-exp-log` `add-cbrt-cube`
7×	`pow-prod-down` `associate-/r/`
6×	`cbrt-prod`
4×	`sqrt-pow1` `sqrt-prod` `add-log-exp`
3×	`associate-l`
2×	`pow1/3` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `pow1/2` `div-exp` `*-commutative` `div-inv`

Counts

4 → 84

Calls

4 calls:

1.0ms	(cbrt A)
1.0ms	(cbrt A)
30.0ms	(* c0 (/ (fabs (cbrt A)) (sqrt (* (* V (* (/ (cbrt l) (cbrt (cbrt A))) (/ (cbrt l) (cbrt (cbrt A))))) (/ (cbrt l) (cbrt (cbrt A)))))))
22.0ms	(sqrt (* (* V (* (/ (cbrt l) (cbrt (cbrt A))) (/ (cbrt l) (cbrt (cbrt A))))) (/ (cbrt l) (cbrt (cbrt A)))))

series149.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt A)
22.0ms	(cbrt A)
73.0ms	(* c0 (/ (fabs (cbrt A)) (sqrt (* (* V (* (/ (cbrt l) (cbrt (cbrt A))) (/ (cbrt l) (cbrt (cbrt A))))) (/ (cbrt l) (cbrt (cbrt A)))))))
31.0ms	(sqrt (* (* V (* (/ (cbrt l) (cbrt (cbrt A))) (/ (cbrt l) (cbrt (cbrt A))))) (/ (cbrt l) (cbrt (cbrt A)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5008	1003

prune95.0ms

Filtered

69 candidates to 96 candidates (-39.1%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	93	21	114

Merged error: 2.8b

Counts

114 → 21

regimes1.2s

Accuracy

40.8% (5.6b remaining)

Error of 8.7b against oracle of 3.1b and baseline of 12.5b

bsearch524.0ms

Steps

Iters	Range		Point
10	-1.3969248317787982e-293	-1.6799042247353052e-304	-1.6960457929493363e-304

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	41
1	29	41

end0.0ms

analyze474.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	93.6%	6.4%	7
3.1%	84.2%	12.7%	8
12.5%	67.1%	20.5%	9
16%	63.5%	20.5%	10
17.9%	57.7%	24.4%	11
22.6%	48.7%	28.7%	12
28.7%	37.8%	33.6%	13
30.4%	35.9%	33.7%	14

sample695.0ms

Algorithm

intervals

Results

293.0ms	8000×	body	80	valid
98.0ms	2835×	body	80	nan
31.0ms	889×	body	80	invalid

Details

analyze483.0ms

sample27.0ms

simplify3.0ms

prune4.0ms

localize7.0ms

rewrite17.0ms

series30.0ms

simplify52.0ms

prune145.0ms

localize11.0ms

rewrite43.0ms

series58.0ms

simplify72.0ms

prune171.0ms

localize14.0ms

rewrite29.0ms

series109.0ms

simplify55.0ms

prune188.0ms

localize21.0ms

rewrite58.0ms

series149.0ms

simplify53.0ms

prune95.0ms

regimes1.2s

bsearch524.0ms

simplify1.0ms

end0.0ms

analyze474.0ms

sample695.0ms

Profiling