Details

sample62.0ms

Algorithm

intervals

Results

19.0ms	43×	body	1280	valid
13.0ms	51×	body	640	valid
7.0ms	154×	body	80	valid
6.0ms	107×	body	80	nan
5.0ms	28×	body	320	valid
2.0ms	17×	body	160	valid

simplify116.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (9.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	108	6
4	310	4
5	792	4
6	4183	4
7	5001	4

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 11.8b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
10.4b	(log (/ x (+ x y)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
54×	`log-prod`
48×	`times-frac`
42×	`add-sqr-sqrt`
40×	`add-cube-cbrt`
18×	`distribute-rgt-in` `distribute-lft-in`
14×	`distribute-lft-out`
10×	`add-exp-log` `log-div`
8×	`associate-/r` `associate-/r/` `associate-/l`
7×	`pow1` `add-cbrt-cube`
4×	`flip3-+` `associate-r` `log-rec` `clear-num` `flip-+` `div-inv`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `div-exp` `rem-log-exp` `log-pow` `distribute-rgt-neg-out`
1×	`cbrt-undiv` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 136

Calls

3 calls:

5.0ms	(/ x (+ x y))
9.0ms	(* x (log (/ x (+ x y))))
6.0ms	(log (/ x (+ x y)))

series172.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ x (+ x y))
80.0ms	(* x (log (/ x (+ x y))))
52.0ms	(log (/ x (+ x y)))

simplify52.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	316	938
1	1333	868
2	5002	848

prune215.0ms

Filtered

145 candidates to 90 candidates (62.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	143	3	146

Merged error: 0.7b

Counts

146 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
4.1b	(log (/ (cbrt x) (cbrt (+ x y))))
4.1b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

110×	`cbrt-prod`
98×	`*-un-lft-identity`
96×	`log-prod`
84×	`times-frac`
68×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`log-div`
14×	`associate-/r` `distribute-lft-out` `associate-/l`
10×	`add-exp-log`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `rem-log-exp` `log-rec` `clear-num` `associate-/r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `flip3-+` `pow1/3` `div-exp` `log-pow` `flip-+` `div-inv`

Counts

4 → 182

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))))

series497.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt x)
174.0ms	(cbrt x)
73.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
75.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify106.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	346	1788
1	890	1730
2	3104	1690
3	5001	1614

prune555.0ms

Filtered

194 candidates to 132 candidates (68.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	193	4	197

Merged error: 0.2b

Counts

197 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
0.6b	(cbrt (cbrt x))
4.1b	(log (/ (cbrt x) (cbrt (+ x y))))
27.9b	(log (/ (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))) (cbrt (+ x y))))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

1914×	`cbrt-prod`
1482×	`add-sqr-sqrt`
754×	`log-prod`
742×	`times-frac`
648×	`unswap-sqr`
598×	`*-un-lft-identity`
403×	`associate-l`
378×	`add-cube-cbrt`
144×	`swap-sqr` `associate-r`
126×	`log-div`
110×	`associate-/l*`
108×	`distribute-lft-out`
40×	`*-commutative`
17×	`add-exp-log`
14×	`associate-/r*`
6×	`pow1` `rem-log-exp` `log-rec`
4×	`expm1-log1p-u` `cbrt-div` `div-exp` `clear-num` `associate-/r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp`
2×	`frac-2neg` `flip3-+` `pow1/3` `log-pow` `flip-+` `div-inv`

Counts

4 → 944

Calls

4 calls:

2.0ms	(cbrt (cbrt x))
2.0ms	(cbrt (cbrt x))
9.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
80.0ms	(log (/ (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))) (cbrt (+ x y))))

series840.0ms

Counts

4 → 12

Calls

4 calls:

446.0ms	(cbrt (cbrt x))
246.0ms	(cbrt (cbrt x))
72.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
75.0ms	(log (/ (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))) (cbrt (+ x y))))

simplify226.0ms

Algorithm

egg-herbie

Counts

956 → 956

Iterations

Useful iterations: 1 (56.0ms)

Iter	Nodes	Cost
0	3630	21046
1	5001	20966

prune2.7s

Filtered

956 candidates to 480 candidates (50.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	956	0	956
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	956	4	960

Merged error: 0.2b

Counts

960 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
38.6b	(log (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

1428×	`times-frac`
1032×	`*-un-lft-identity`
924×	`add-sqr-sqrt`
812×	`cbrt-prod`
775×	`log-prod`
692×	`add-cube-cbrt`
175×	`associate-l`
174×	`swap-sqr` `associate-r`
169×	`distribute-lft-out`
116×	`unswap-sqr`
58×	`log-div`
34×	`associate-/r*`
33×	`associate-/l*`
29×	`*-commutative` `div-inv`
17×	`add-exp-log`
15×	`associate-/r/`
6×	`div-exp`
5×	`pow1` `rem-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `log-rec` `clear-num`
2×	`frac-2neg` `prod-exp` `associate-/l/`
1×	`flip3-+` `log-pow` `flip-+`

Counts

4 → 890

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
65.0ms	(log (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))))

series626.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(cbrt x)
182.0ms	(cbrt x)
188.0ms	(cbrt x)
67.0ms	(log (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))))

simplify207.0ms

Algorithm

egg-herbie

Counts

902 → 902

Iterations

Useful iterations: 1 (69.0ms)

Iter	Nodes	Cost
0	3897	15796
1	5001	15790

prune2.1s

Filtered

902 candidates to 507 candidates (56.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	902	0	902
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	902	4	906

Merged error: 0.2b

Counts

906 → 4

regimes50.0ms

Accuracy

32.9% (3.2b remaining)

Error of 4.4b against oracle of 1.2b and baseline of 5.9b

bsearch52.0ms

Steps

Iters	Range		Point
6	1.0543316325738937e+25	8.37173053923323e+25	1.0769375439169042e+25

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	41
1	41	41
2	41	41

end0.0ms

sample1.7s

Algorithm

intervals

Results

636.0ms	1451×	body	1280	valid
362.0ms	1440×	body	640	valid
215.0ms	4892×	body	80	valid
136.0ms	842×	body	320	valid
94.0ms	3059×	body	80	nan
49.0ms	487×	body	160	valid