Details

sample141.0ms

Algorithm

intervals

Results

44.0ms	47×	body	1280	valid
26.0ms	38×	body	320	valid
23.0ms	43×	body	640	valid
15.0ms	160×	body	80	valid
8.0ms	109×	body	80	nan
3.0ms	15×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	8	11
1	15	11
2	24	9
3	49	9
4	107	9
5	245	9
6	580	9
7	1850	9
done	5000	9

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
7.2b	(log (/ x (+ x y)))

rewrite68.0ms

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:

12.0ms	(/ x (+ x y))
34.0ms	(* x (log (/ x (+ x y))))
14.0ms	(log (/ x (+ x y)))

series277.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(/ x (+ x y))
131.0ms	(* x (log (/ x (+ x y))))
85.0ms	(log (/ x (+ x y)))

simplify1.6s

Counts

132 → 132

Iterations

Useful iterations: 3 (989.0ms)

Iter	Nodes	Cost
0	173	1644
1	303	1553
2	662	1464
3	1717	1425
done	5002	1425

prune340.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
4.2b	(log (/ (cbrt x) (cbrt (+ x y))))
4.2b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite37.0ms

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)
11.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
15.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series715.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(cbrt x)
239.0ms	(cbrt x)
121.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
112.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify2.0s

Counts

160 → 160

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	177	2306
1	321	2146
2	578	2060
3	1115	1986
4	2482	1982
done	5000	1976

prune829.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
33.1b	(log (/ (/ x (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y))))

rewrite86.0ms

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:

8.0ms	(cbrt (+ x y))
7.0ms	(cbrt (+ x y))
7.0ms	(cbrt (+ x y))
43.0ms	(log (/ (/ x (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y))))

series747.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt (+ x y))
224.0ms	(cbrt (+ x y))
219.0ms	(cbrt (+ x y))
126.0ms	(log (/ (/ x (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (+ x y))))

simplify2.2s

Counts

186 → 186

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	396	4946
1	875	4650
2	1819	4389
3	4172	4083
done	5001	4032

prune824.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.2b	(log1p (expm1 (cbrt x)))
3.4b	(log (/ (log1p (expm1 (cbrt x))) (cbrt (+ x y))))
4.2b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

75×	`log-prod`
64×	`*-un-lft-identity`
63×	`times-frac`
60×	`cbrt-prod`
46×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log`
9×	`distribute-lft-out`
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-+` `div-exp` `log-pow` `flip-+` `div-inv`
1×	`log1p-udef` `pow1/3` `log1p-expm1`

Counts

4 → 125

Calls

4 calls:

2.0ms	(cbrt x)
1.0ms	(log1p (expm1 (cbrt x)))
15.0ms	(log (/ (log1p (expm1 (cbrt x))) (cbrt (+ x y))))
14.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series1.2s

Counts

4 → 12

Calls

4 calls:

318.0ms	(cbrt x)
535.0ms	(log1p (expm1 (cbrt x)))
215.0ms	(log (/ (log1p (expm1 (cbrt x))) (cbrt (+ x y))))
122.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify2.4s

Counts

137 → 137

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	251	2025
1	396	1750
2	653	1680
3	1197	1616
4	2574	1613
done	5000	1609

prune807.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.3b

regimes104.0ms

Accuracy

16.8% (3.7b remaining)

Error of 4.9b against oracle of 1.2b and baseline of 5.6b

bsearch243.0ms

Steps

Iters	Range		Point
10	3.860152561141286e+185	1.343754371366865e+197	8.906285416665826e+185
10	2.3498104185213125e-09	3991008.2413703846	165.0208082342575

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	90
1	47	90
done	47	90

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.2s	1463×	body	1280	valid
1.0s	4915×	body	80	valid
668.0ms	1452×	body	640	valid
228.0ms	833×	body	320	valid
214.0ms	3035×	body	80	nan
77.0ms	456×	body	160	valid