Details

analyze575.0ms

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
0%	99.9%	0.1%	4
6.2%	93.7%	0.1%	5
6.2%	90.5%	3.2%	6
21.9%	67.1%	11%	7
23.4%	64.8%	11.8%	8
32%	52.7%	15.3%	9
33.2%	51.3%	15.5%	10
37.7%	45.2%	17.2%	11
38.3%	44.4%	17.2%	12
40.6%	41.3%	18%	13
41%	41%	18%	14

sample44.0ms

Algorithm

intervals

Results

9.0ms	177×	body	80	valid
6.0ms	24×	body	1280	valid
5.0ms	34×	body	640	nan
4.0ms	24×	body	1280	nan
4.0ms	21×	body	640	valid
2.0ms	19×	body	320	valid
1.0ms	15×	body	160	valid
1.0ms	9×	body	320	nan
1.0ms	10×	body	160	nan
0.0ms	5×	body	80	nan

simplify112.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	5039	12

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 19.4b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
3.4b	(- 1.0 (/ (- x y) (- 1.0 y)))
5.0b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
28×	`times-frac`
19×	`difference-of-squares`
18×	`add-cube-cbrt`
17×	`distribute-lft-out--`
12×	`log-prod`
7×	`add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `add-cbrt-cube` `flip--` `associate--r+`
5×	`associate-/r` `associate-/l`
4×	`log-div`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 106

Calls

4 calls:

16.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
8.0ms	(/ (- x y) (- 1.0 y))
13.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
17.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series44.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
6.0ms	(/ (- x y) (- 1.0 y))
9.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
12.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify42.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5428	1660

prune222.0ms

Filtered

93 candidates to 118 candidates (-26.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	114	4	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	4	119

Merged error: 0.2b

Counts

119 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 y))
0.3b	(cbrt (- 1.0 y))
5.0b	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
13.8b	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
14×	`cbrt-prod`
12×	`times-frac` `difference-of-squares`
9×	`log-prod`
7×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1` `add-exp-log`
4×	`cbrt-div` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out--`
2×	`log-div` `pow1/3` `div-sub`
1×	`sub-neg` `diff-log` `rem-log-exp` `log-pow` `associate--r-`

Counts

4 → 68

Calls

4 calls:

3.0ms	(cbrt (- 1.0 y))
3.0ms	(cbrt (- 1.0 y))
39.0ms	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
42.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

series33.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (- 1.0 y))
6.0ms	(cbrt (- 1.0 y))
12.0ms	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
9.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

simplify50.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	6060	1211

prune174.0ms

Filtered

67 candidates to 80 candidates (-19.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	80	4	84

Merged error: 0.2b

Counts

84 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (- 1.0 (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))) (log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y)))))))
3.3b	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
13.0b	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
13.3b	(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
48×	`difference-of-squares`
39×	`log-prod`
38×	`*-un-lft-identity`
36×	`unpow-prod-down` `cube-prod`
20×	`sqr-pow`
16×	`times-frac`
14×	`distribute-lft-out--`
11×	`pow1`
8×	`log-div` `add-log-exp`
7×	`add-cube-cbrt` `log-pow`
6×	`add-exp-log` `distribute-lft-out`
4×	`add-cbrt-cube`
3×	`associate-+l+` `associate-+r+` `flip3--` `flip3-+` `flip--` `flip-+`
2×	`difference-cubes` `associate-+r-` `sub-neg` `diff-log` `rem-log-exp` `sum-log` `associate--r-`
1×	`+-commutative` `associate-+l-`

Counts

4 → 126

Calls

4 calls:

26.0ms	(+ (- 1.0 (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))) (log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y)))))))
45.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
43.0ms	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
20.0ms	(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))

series225.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ (- 1.0 (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))) (log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y)))))))
51.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
61.0ms	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
34.0ms	(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))

simplify44.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5104	4087

prune368.0ms

Filtered

92 candidates to 138 candidates (-50.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	137	5	142

Merged error: 0.2b

Counts

142 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (+ (/ x y) (* (/ 1.0 y) (+ (/ x y) -1)))))
0.1b	(* (/ 1.0 y) (+ (/ x y) -1))
1.8b	(+ (/ x y) (* (/ 1.0 y) (+ (/ x y) -1)))
2.2b	(log (+ (/ x y) (* (/ 1.0 y) (+ (/ x y) -1))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
15×	`frac-add`
14×	`add-cube-cbrt` `log-div`
13×	`associate-l`
11×	`flip3-+` `times-frac` `flip-+`
10×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1` `frac-times` `associate-*r/`
7×	`associate--r-` `add-log-exp`
6×	`log-prod` `associate-r`
4×	`associate-*l/`
3×	`associate--r+`
2×	`difference-of-sqr--1` `distribute-rgt-in` `associate-+r+` `distribute-lft-in` `prod-exp` `log-pow` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `sum-log` `*-commutative` `flip--` `div-inv` `distribute-lft-out` `difference-of-squares`

Counts

4 → 102

Calls

4 calls:

9.0ms	(- 1.0 (log (+ (/ x y) (* (/ 1.0 y) (+ (/ x y) -1)))))
12.0ms	(* (/ 1.0 y) (+ (/ x y) -1))
9.0ms	(+ (/ x y) (* (/ 1.0 y) (+ (/ x y) -1)))
7.0ms	(log (+ (/ x y) (* (/ 1.0 y) (+ (/ x y) -1))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- 1.0 (log (+ (/ x y) (* (/ 1.0 y) (+ (/ x y) -1)))))
6.0ms	(* (/ 1.0 y) (+ (/ x y) -1))
10.0ms	(+ (/ x y) (* (/ 1.0 y) (+ (/ x y) -1)))
12.0ms	(log (+ (/ x y) (* (/ 1.0 y) (+ (/ x y) -1))))

simplify53.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5006	2043

prune169.0ms

Filtered

96 candidates to 114 candidates (-18.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	111	8	119

Merged error: 0.2b

Counts

119 → 8

regimes292.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 17.1b

bsearch117.0ms

Steps

Iters	Range		Point
7	5.300874665106141e+51	1.975225859588203e+53	5.362376023934354e+51
8	-69214650689.57396	-1865465.991685719	-54595547.19675808

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	140	48
1	140	48

end0.0ms

sample1.3s

Algorithm

intervals

Results

282.0ms	5659×	body	80	valid
198.0ms	801×	body	1280	valid
149.0ms	823×	body	640	valid
137.0ms	721×	body	1280	nan
125.0ms	815×	body	640	nan
58.0ms	434×	body	320	valid
47.0ms	433×	body	320	nan
25.0ms	283×	body	160	valid
18.0ms	251×	body	160	nan
13.0ms	351×	body	80	nan

Details

analyze575.0ms

sample44.0ms

simplify112.0ms

prune6.0ms

localize9.0ms

rewrite57.0ms

series44.0ms

simplify42.0ms

prune222.0ms

localize13.0ms

rewrite92.0ms

series33.0ms

simplify50.0ms

prune174.0ms

localize21.0ms

rewrite141.0ms

series225.0ms

simplify44.0ms

prune368.0ms

localize10.0ms

rewrite40.0ms

series43.0ms

simplify53.0ms

prune169.0ms

regimes292.0ms

bsearch117.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling