Details

sample61.0ms

Algorithm

intervals

Results

23.0ms	56×	body	1280	valid
11.0ms	47×	body	640	valid
6.0ms	148×	body	80	valid
4.0ms	24×	body	320	valid
2.0ms	83×	body	80	nan
1.0ms	15×	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.3b

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)))

rewrite43.0ms

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:

10.0ms	(/ x (+ x y))
22.0ms	(* x (log (/ x (+ x y))))
6.0ms	(log (/ x (+ x y)))

series154.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ x (+ x y))
71.0ms	(* x (log (/ x (+ x y))))
42.0ms	(log (/ x (+ x y)))

simplify103.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (31.0ms)

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

prune245.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
3.5b	(log (/ (cbrt x) (cbrt (+ x y))))
3.5b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite25.0ms

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))))

series477.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt x)
175.0ms	(cbrt x)
61.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
67.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify72.0ms

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

prune508.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
3.5b	(log (/ (cbrt x) (cbrt (+ x y))))
16.1b	(log (/ (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt (+ x y))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

61×	`log-prod`
55×	`cbrt-prod`
50×	`*-un-lft-identity`
49×	`times-frac`
36×	`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 → 106

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
9.0ms	(log (/ (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt (+ x y))))

series480.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
168.0ms	(cbrt x)
67.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
62.0ms	(log (/ (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt (+ x y))))

simplify76.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	345	1146
1	838	1085
2	2673	1066
3	5001	1027

prune476.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
3.5b	(log (/ (cbrt x) (cbrt (+ x y))))
16.1b	(log (/ (* (cbrt (* (cbrt x) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))) (cbrt (cbrt x))) (cbrt (+ x y))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

61×	`log-prod`
55×	`cbrt-prod`
50×	`*-un-lft-identity`
49×	`times-frac`
36×	`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 → 106

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
9.0ms	(log (/ (* (cbrt (* (cbrt x) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))) (cbrt (cbrt x))) (cbrt (+ x y))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(cbrt x)
165.0ms	(cbrt x)
64.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
66.0ms	(log (/ (* (cbrt (* (cbrt x) (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))))) (cbrt (cbrt x))) (cbrt (+ x y))))

simplify92.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	373	1314
1	925	1235
2	2950	1216
3	5001	1177

prune518.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

regimes65.0ms

Accuracy

50.8% (1.7b remaining)

Error of 3.8b against oracle of 2.1b and baseline of 5.6b

bsearch63.0ms

Steps

Iters	Range		Point
9	2.983864905276105e+17	4.246926653605731e+23	3.041201228711916e+17

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	39
1	36	39

end0.0ms

sample1.7s

Algorithm

intervals

Results

618.0ms	1527×	body	1280	valid
334.0ms	1420×	body	640	valid
188.0ms	4780×	body	80	valid
125.0ms	840×	body	320	valid
80.0ms	2984×	body	80	nan
42.0ms	463×	body	160	valid