Details

sample52.0ms

Algorithm

intervals

Results

16.0ms	39×	body	1280	valid
10.0ms	43×	body	640	valid
7.0ms	172×	body	80	valid
3.0ms	22×	body	320	valid
2.0ms	71×	body	80	nan
2.0ms	17×	body	160	valid

simplify113.0ms

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	108	6
4	310	4
5	792	4
6	4192	4
7	5002	4

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
9.7b	(log (/ x (+ x y)))

rewrite51.0ms

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×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `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 → 123

Calls

3 calls:

11.0ms	(/ x (+ x y))
29.0ms	(* x (log (/ x (+ x y))))
6.0ms	(log (/ x (+ x y)))

series173.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ x (+ x y))
81.0ms	(* x (log (/ x (+ x y))))
48.0ms	(log (/ x (+ x y)))

simplify107.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	302	874
1	1266	813
2	4974	783
3	5001	783

prune255.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
3.6b	(log (/ (cbrt x) (cbrt (+ x y))))
3.6b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite26.0ms

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×	`expm1-log1p-u` `cbrt-div` `rem-log-exp` `associate-/r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `flip3-+` `pow1/3` `div-exp` `log-pow` `flip-+` `div-inv`

Counts

4 → 148

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
9.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
9.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series506.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt x)
174.0ms	(cbrt x)
76.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
77.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify83.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	318	1502
1	772	1456
2	2360	1424
3	5002	1350

prune534.0ms

Pruning

4 alts after pruning (3 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))
32.9b	(log (* (/ 1 (* (cbrt (+ x y)) (cbrt (+ x y)))) (/ x (cbrt (+ x y)))))

rewrite112.0ms

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×	`expm1-log1p-u` `rec-exp` `1-exp` `add-cbrt-cube` `log1p-expm1-u` `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 → 78

Calls

4 calls:

4.0ms	(cbrt (+ x y))
4.0ms	(cbrt (+ x y))
6.0ms	(cbrt (+ x y))
96.0ms	(log (* (/ 1 (* (cbrt (+ x y)) (cbrt (+ x y)))) (/ x (cbrt (+ x y)))))

series491.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (+ x y))
136.0ms	(cbrt (+ x y))
133.0ms	(cbrt (+ x y))
80.0ms	(log (* (/ 1 (* (cbrt (+ x y)) (cbrt (+ x y)))) (/ x (cbrt (+ x y)))))

simplify76.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	179	487
1	582	436
2	2472	400
3	5001	395

prune311.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
30.3b	(log (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (+ x y))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
10×	`pow1`
9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`prod-exp`
5×	`rem-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `pow-prod-down` `log-pow`
2×	`div-exp`
1×	`log-div` `log-prod` `associate-*r/`

Counts

4 → 58

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
34.0ms	(log (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (+ x y))))

series633.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt x)
189.0ms	(cbrt x)
193.0ms	(cbrt x)
66.0ms	(log (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (+ x y))))

simplify96.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (22.0ms)

Iter	Nodes	Cost
0	75	278
1	163	249
2	535	234
3	3110	223
4	5001	223

prune214.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

regimes54.0ms

Accuracy

17.8% (3.7b remaining)

Error of 4.6b against oracle of 0.9b and baseline of 5.4b

bsearch102.0ms

Steps

Iters	Range		Point
4	1.3103672088424093e+146	1.9153874764585364e+146	1.480529159109445e+146
9	0.0058045631009331555	994.2830895116298	227.45691516776162

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	29
1	39	29

end0.0ms

sample1.8s

Algorithm

intervals

Results

631.0ms	1486×	body	1280	valid
362.0ms	1497×	body	640	valid
207.0ms	4951×	body	80	valid
130.0ms	818×	body	320	valid
85.0ms	3017×	body	80	nan
39.0ms	407×	body	160	valid