Details

analyze72.0ms

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
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	50%	6.3%	6
43.7%	43.7%	12.6%	7
59.3%	26.5%	14.1%	8
59.3%	22.6%	18%	9
67.1%	13.7%	19.2%	10
67.1%	11.5%	21.4%	11
71%	6.9%	22%	12
71%	5.8%	23.2%	13
73%	3.5%	23.5%	14

sample14.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
0.0ms	8×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	6	6

prune3.0ms

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: 24.1b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
22.5b	(sqrt (+ (* x x) y))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `add-log-exp`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

2 → 26

Calls

2 calls:

6.0ms	(+ (* x x) y)
4.0ms	(sqrt (+ (* x x) y))

series9.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(+ (* x x) y)
6.0ms	(sqrt (+ (* x x) y))

simplify23.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5020	261

prune42.0ms

Filtered

25 candidates to 32 candidates (-28.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	4	33

Merged error: 0.0b

Counts

33 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (neg x) (* y (/ -1/2 x)))
0.2b	(* y (/ -1/2 x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`pow1`
3×	`associate-l`
2×	`prod-exp` `sum-log` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `neg-log` `-commutative` `flip-+` `div-inv`

Counts

2 → 45

Calls

2 calls:

4.0ms	(+ (neg x) (* y (/ -1/2 x)))
8.0ms	(* y (/ -1/2 x))

series8.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(+ (neg x) (* y (/ -1/2 x)))
3.0ms	(* y (/ -1/2 x))

simplify51.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4975	400
1	4975	400

prune53.0ms

Filtered

35 candidates to 51 candidates (-45.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	51	4	55

Merged error: 0.0b

Counts

55 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x x) y)
7.0b	(- (pow x 4) (* y y))
22.5b	(sqrt (/ (- (pow x 4) (* y y)) (- (* x x) y)))
37.4b	(/ (- (pow x 4) (* y y)) (- (* x x) y))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
49×	`times-frac`
44×	`difference-of-squares`
30×	`sqrt-prod`
27×	`add-cube-cbrt` `*-un-lft-identity`
10×	`unpow-prod-down` `sqr-pow`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `flip3--` `flip--`
4×	`associate-/r*` `associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 119

Calls

4 calls:

4.0ms	(- (* x x) y)
4.0ms	(- (pow x 4) (* y y))
8.0ms	(sqrt (/ (- (pow x 4) (* y y)) (- (* x x) y)))
9.0ms	(/ (- (pow x 4) (* y y)) (- (* x x) y))

series30.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (* x x) y)
6.0ms	(- (pow x 4) (* y y))
11.0ms	(sqrt (/ (- (pow x 4) (* y y)) (- (* x x) y)))
9.0ms	(/ (- (pow x 4) (* y y)) (- (* x x) y))

simplify46.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4960	1958
1	4960	1958

prune180.0ms

Filtered

104 candidates to 131 candidates (-26.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	130	5	135

Merged error: 0b

Counts

135 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (+ y (* x x)) (+ x (sqrt y))) (/ (- (* x x) y) (- x (sqrt y))))
12.7b	(sqrt (* (/ (+ y (* x x)) (+ x (sqrt y))) (/ (- (* x x) y) (- x (sqrt y)))))
12.8b	(/ (- (* x x) y) (- x (sqrt y)))
12.8b	(/ (+ y (* x x)) (+ x (sqrt y)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

105×	`add-sqr-sqrt`
76×	`*-un-lft-identity` `times-frac`
44×	`add-cube-cbrt`
31×	`difference-of-squares`
30×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-l`
10×	`associate-/r*` `sqrt-prod`
9×	`pow1` `distribute-lft-out--`
8×	`associate-/r/`
7×	`distribute-lft-out` `associate-/l*`
6×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
3×	`flip3--` `flip3-+` `sqrt-div` `flip--` `flip-+`
2×	`frac-times` `frac-2neg` `sqrt-pow1` `associate-r/` `pow-prod-down` `associate-l/` `clear-num`
1×	`pow1/2` `div-sub` `*-commutative`

Counts

4 → 172

Calls

4 calls:

27.0ms	(* (/ (+ y (* x x)) (+ x (sqrt y))) (/ (- (* x x) y) (- x (sqrt y))))
14.0ms	(sqrt (* (/ (+ y (* x x)) (+ x (sqrt y))) (/ (- (* x x) y) (- x (sqrt y)))))
9.0ms	(/ (- (* x x) y) (- x (sqrt y)))
7.0ms	(/ (+ y (* x x)) (+ x (sqrt y)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (/ (+ y (* x x)) (+ x (sqrt y))) (/ (- (* x x) y) (- x (sqrt y))))
78.0ms	(sqrt (* (/ (+ y (* x x)) (+ x (sqrt y))) (/ (- (* x x) y) (- x (sqrt y)))))
7.0ms	(/ (- (* x x) y) (- x (sqrt y)))
14.0ms	(/ (+ y (* x x)) (+ x (sqrt y)))

simplify52.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5782	2638

prune161.0ms

Filtered

134 candidates to 184 candidates (-37.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	184	5	189

Merged error: 0b

Counts

189 → 5

regimes247.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 22.3b

bsearch56.0ms

Steps

Iters	Range		Point
7	1.2799898569165748e+116	2.7571051798272293e+117	2.497175538071421e+116
9	-2.54489950956751e+160	-2.766205262501008e+151	-1.3251322205262078e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	29
1	25	29

end0.0ms

analyze73.0ms

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
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	50%	6.3%	6
43.7%	43.7%	12.6%	7
59.3%	26.5%	14.1%	8
59.3%	22.6%	18%	9
67.1%	13.7%	19.2%	10
67.1%	11.5%	21.4%	11
71%	6.9%	22%	12
71%	5.8%	23.2%	13
73%	3.5%	23.5%	14

sample344.0ms

Algorithm

intervals

Results

206.0ms	8000×	body	80	valid
4.0ms	179×	body	80	nan

Details

analyze72.0ms

sample14.0ms

simplify3.0ms

prune3.0ms

localize4.0ms

rewrite10.0ms

series9.0ms

simplify23.0ms

prune42.0ms

localize5.0ms

rewrite14.0ms

series8.0ms

simplify51.0ms

prune53.0ms

localize10.0ms

rewrite29.0ms

series30.0ms

simplify46.0ms

prune180.0ms

localize12.0ms

rewrite64.0ms

series172.0ms

simplify52.0ms

prune161.0ms

regimes247.0ms

bsearch56.0ms

simplify1.0ms

end0.0ms

analyze73.0ms

sample344.0ms

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