Details

sample95.0ms

Algorithm

intervals

Results

38.0ms	57×	body	1280	valid
19.0ms	51×	body	640	valid
11.0ms	154×	body	80	valid
8.0ms	32×	body	320	valid
6.0ms	120×	body	80	nan
2.0ms	15×	body	160	valid

simplify108.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
8.5b	(log (/ x (+ x y)))

rewrite28.0ms

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:

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

series166.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ x (+ x y))
80.0ms	(* x (log (/ x (+ x y))))
47.0ms	(log (/ x (+ x y)))

simplify111.0ms

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

prune247.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize14.0ms

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))))

rewrite24.0ms

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)
6.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
10.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series512.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt x)
185.0ms	(cbrt x)
68.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
77.0ms	(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

prune695.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
36.4b	(log (/ (* (cbrt x) (cbrt x)) (/ (+ x y) (cbrt x))))

rewrite13.0ms

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

series590.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt x)
173.0ms	(cbrt x)
173.0ms	(cbrt x)
66.0ms	(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

prune281.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
37.4b	(log (/ (/ x (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y))))

rewrite41.0ms

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×	`rem-log-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
1×	`log-div` `prod-exp` `log-pow`

Counts

4 → 166

Calls

4 calls:

2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
21.0ms	(log (/ (/ x (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(cbrt (+ x y))
135.0ms	(cbrt (+ x y))
130.0ms	(cbrt (+ x y))
78.0ms	(log (/ (/ x (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y))))

simplify68.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	863	2865
1	2484	2812
2	5001	2708

prune537.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.7b

regimes62.0ms

Accuracy

9.8% (4.3b remaining)

Error of 5.8b against oracle of 1.6b and baseline of 6.3b

bsearch185.0ms

Steps

Iters	Range		Point
6	6.6397013411054035e+146	7.929518348033325e+147	6.751416967699413e+146
3	3.634260247071152e+81	4.4615371318470405e+81	3.906185484315914e+81
8	1.5562990904748346e+66	7.2484695024147705e+68	3.174668474364579e+67
5	189475072901.19046	661184882896.0549	193392245631.92206

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	71
1	54	71

end0.0ms

sample2.5s

Algorithm

intervals

Results

868.0ms	1479×	body	1280	valid
548.0ms	1488×	body	640	valid
353.0ms	4831×	body	80	valid
218.0ms	869×	body	320	valid
154.0ms	2996×	body	80	nan
70.0ms	445×	body	160	valid