Details

sample72.0ms

Algorithm

intervals

Results

27.0ms	51×	body	1280	valid
13.0ms	44×	body	640	valid
8.0ms	162×	body	80	valid
4.0ms	22×	body	320	valid
4.0ms	103×	body	80	nan
2.0ms	15×	body	160	valid

simplify110.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (7.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	106	6
4	304	4
5	774	4
6	4142	4
7	5001	4

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
8.3b	(log (/ x (+ x y)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
54×	`log-prod`
48×	`times-frac`
40×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
18×	`distribute-rgt-in` `distribute-lft-in`
13×	`distribute-lft-out`
10×	`add-exp-log`
8×	`associate-/r/`
7×	`pow1` `add-cbrt-cube`
4×	`flip3-+` `associate-r` `associate-/r*` `flip-+` `div-inv`
3×	`associate-l` `associate-/l*` `add-log-exp`
2×	`div-exp` `rem-log-exp` `log-pow`
1×	`cbrt-undiv` `log-div` `frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 117

Calls

3 calls:

5.0ms	(/ x (+ x y))
8.0ms	(* x (log (/ x (+ x y))))
5.0ms	(log (/ x (+ x y)))

series164.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ x (+ x y))
76.0ms	(* x (log (/ x (+ x y))))
47.0ms	(log (/ x (+ x y)))

simplify104.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	293	850
1	1237	789
2	4806	759
3	5001	759

prune243.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
3.1b	(log (/ (cbrt x) (cbrt (+ x y))))
3.1b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod` `log-prod`
84×	`*-un-lft-identity` `times-frac`
60×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`distribute-lft-out`
10×	`add-exp-log`
6×	`pow1`
4×	`cbrt-div` `rem-log-exp` `associate-/r/` `add-cbrt-cube` `add-log-exp`
2×	`log-div` `flip3-+` `pow1/3` `div-exp` `log-pow` `flip-+` `div-inv`

Counts

4 → 140

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series499.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
174.0ms	(cbrt x)
70.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
73.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify74.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	311	1470
1	757	1424
2	2319	1392
3	5001	1324

prune502.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt (cbrt x))
3.1b	(log (/ (cbrt x) (cbrt (+ x y))))
14.5b	(log (/ (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt (+ x y))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

61×	`cbrt-prod` `log-prod`
51×	`*-un-lft-identity`
49×	`times-frac`
37×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`add-exp-log`
7×	`distribute-lft-out`
6×	`pow1`
5×	`rem-log-exp`
4×	`cbrt-div` `associate-/r/` `add-cbrt-cube` `add-log-exp`
3×	`div-exp`
2×	`log-div` `flip3-+` `pow1/3` `log-pow` `flip-+` `div-inv`
1×	`prod-exp`

Counts

4 → 109

Calls

4 calls:

1.0ms	(cbrt x)
2.0ms	(cbrt (cbrt x))
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
7.0ms	(log (/ (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt (+ x y))))

series566.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt x)
242.0ms	(cbrt (cbrt x))
73.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
75.0ms	(log (/ (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt (+ x y))))

simplify83.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	376	1181
1	901	1118
2	2879	1099
3	5001	1058

prune504.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
33.0b	(log (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
35×	`*-un-lft-identity`
33×	`log-prod`
23×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`cbrt-prod`
17×	`add-exp-log`
6×	`div-exp` `distribute-lft-out`
5×	`pow1` `rem-log-exp`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`prod-exp` `div-inv`
1×	`log-div` `associate-/r/` `log-pow`

Counts

4 → 80

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
11.0ms	(log (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))))

series622.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt x)
184.0ms	(cbrt x)
182.0ms	(cbrt x)
72.0ms	(log (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))))

simplify45.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	303	706
1	1140	664
2	5001	635

prune290.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.7b

regimes53.0ms

Accuracy

24.8% (2.8b remaining)

Error of 4.7b against oracle of 1.9b and baseline of 5.7b

bsearch63.0ms

Steps

Iters	Range		Point
7	8.309509795626052e-40	6.362239778674672e-38	6.2479584586387e-38

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	38
1	37	38

end0.0ms

sample1.7s

Algorithm

intervals

Results

637.0ms	1484×	body	1280	valid
360.0ms	1443×	body	640	valid
219.0ms	4971×	body	80	valid
126.0ms	765×	body	320	valid
88.0ms	3008×	body	80	nan
46.0ms	452×	body	160	valid