Details

sample56.0ms

Algorithm

intervals

Results

21.0ms	48×	body	1280	valid
9.0ms	39×	body	640	valid
7.0ms	173×	body	80	valid
4.0ms	27×	body	320	valid
2.0ms	75×	body	80	nan
1.0ms	13×	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	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))))
8.1b	(log (/ x (+ x y)))

rewrite24.0ms

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:

5.0ms	(/ x (+ x y))
11.0ms	(* x (log (/ x (+ x y))))
4.0ms	(log (/ x (+ x y)))

series162.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ x (+ x y))
75.0ms	(* x (log (/ x (+ x y))))
50.0ms	(log (/ x (+ x y)))

simplify110.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (33.0ms)

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

prune264.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
3.0b	(log (/ (cbrt x) (cbrt (+ x y))))
3.0b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite20.0ms

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:

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

series494.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt x)
175.0ms	(cbrt x)
70.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
76.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify85.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 3 (66.0ms)

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

prune545.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)
32.3b	(log (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (+ x y))))

rewrite19.0ms

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:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
1.0ms	(cbrt x)
16.0ms	(log (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (+ x y))))

series618.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt x)
187.0ms	(cbrt x)
182.0ms	(cbrt x)
69.0ms	(log (* (* (cbrt x) (cbrt x)) (/ (cbrt x) (+ x y))))

simplify98.0ms

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

prune230.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
32.8b	(log (/ (/ x (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
111×	`log-prod`
92×	`cbrt-div`
88×	`*-un-lft-identity`
72×	`cbrt-prod`
58×	`associate-/r/`
52×	`add-sqr-sqrt` `add-cube-cbrt`
46×	`flip3-+` `flip-+`
28×	`frac-times`
18×	`distribute-lft-out`
14×	`add-exp-log` `associate-r/` `associate-l/`
8×	`div-inv`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `rem-log-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`log-div` `prod-exp` `log-pow`

Counts

4 → 174

Calls

4 calls:

2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
18.0ms	(log (/ (/ x (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(cbrt (+ x y))
127.0ms	(cbrt (+ x y))
127.0ms	(cbrt (+ x y))
77.0ms	(log (/ (/ x (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y))))

simplify77.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	871	2905
1	2517	2849
2	5002	2745

prune578.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.7b

regimes53.0ms

Accuracy

18.6% (4.1b remaining)

Error of 5.2b against oracle of 1.1b and baseline of 6.1b

bsearch127.0ms

Steps

Iters	Range		Point
8	5.363269104146834e+93	2.6216430800597077e+98	4.937389794231227e+97
8	1050.8208076513	11297247.164780367	1077.461896878142

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	34
1	38	34

end0.0ms

sample1.7s

Algorithm

intervals

Results

636.0ms	1461×	body	1280	valid
362.0ms	1466×	body	640	valid
210.0ms	4868×	body	80	valid
140.0ms	875×	body	320	valid
92.0ms	3061×	body	80	nan
51.0ms	465×	body	160	valid