Details

sample78.0ms

Algorithm

intervals

Results

29.0ms	52×	body	1280	valid
16.0ms	47×	body	640	valid
10.0ms	155×	body	80	valid
5.0ms	23×	body	320	valid
4.0ms	70×	body	80	nan
2.0ms	14×	body	160	valid

simplify111.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (8.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
8.0b	(log (/ x (+ x y)))

rewrite26.0ms

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:

7.0ms	(/ x (+ x y))
10.0ms	(* x (log (/ x (+ x y))))
3.0ms	(log (/ x (+ x y)))

series27.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ x (+ x y))
14.0ms	(* x (log (/ x (+ x y))))
9.0ms	(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

prune623.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
2.7b	(log (/ (cbrt x) (cbrt (+ x y))))
2.7b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite21.0ms

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:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
6.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(cbrt x)
10.0ms	(cbrt x)
18.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
19.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify75.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 3 (59.0ms)

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

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
29.3b	(log (* (/ 1 (* (cbrt (+ x y)) (cbrt (+ x y)))) (/ x (cbrt (+ x y)))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
20×	`prod-exp`
15×	`div-exp` `rem-log-exp`
13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`pow1` `add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`rec-exp` `1-exp` `add-cbrt-cube` `add-log-exp`
3×	`log-div` `flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`log-pow`
1×	`frac-times` `log-prod` `associate-r/` `pow-prod-down` `associate-l/`

Counts

4 → 70

Calls

4 calls:

4.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
51.0ms	(log (* (/ 1 (* (cbrt (+ x y)) (cbrt (+ x y)))) (/ x (cbrt (+ x y)))))

series90.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (+ x y))
26.0ms	(cbrt (+ x y))
26.0ms	(cbrt (+ x y))
11.0ms	(log (* (/ 1 (* (cbrt (+ x y)) (cbrt (+ x y)))) (/ x (cbrt (+ x y)))))

simplify70.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	171	445
1	545	397
2	2350	361
3	5001	357

prune835.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
30.8b	(log (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))))

rewrite12.0ms

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:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)
8.0ms	(log (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))))

series42.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(cbrt x)
10.0ms	(cbrt x)
9.0ms	(cbrt x)
13.0ms	(log (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))))

simplify34.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (27.0ms)

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

prune779.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

regimes155.0ms

Accuracy

15.1% (4.1b remaining)

Error of 5.0b against oracle of 0.9b and baseline of 5.7b

bsearch111.0ms

Steps

Iters	Range		Point
9	5.003531038945505e+82	4.123826930277484e+87	3.000595354627898e+87
9	0.008244135775532546	16112908.465778163	167.99809592077398

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	30
1	41	30

end0.0ms

sample2.3s

Algorithm

intervals

Results

873.0ms	1572×	body	1280	valid
496.0ms	1447×	body	640	valid
311.0ms	4844×	body	80	valid
194.0ms	825×	body	320	valid
151.0ms	2975×	body	80	nan
67.0ms	455×	body	160	valid