Details

sample90.0ms

Algorithm

intervals

Results

30.0ms	51×	body	1280	valid
18.0ms	53×	body	640	valid
9.0ms	145×	body	80	valid
7.0ms	19×	body	160	valid
6.0ms	26×	body	320	valid
4.0ms	88×	body	80	nan

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
7	2012
6	545
5	216
4	91
3	41
2	22
1	15
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x (log (/ x (+ x y)))))
0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
8.0b	(log (/ x (+ x y)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

93×	`*-un-lft-identity`
90×	`log-prod`
72×	`times-frac`
57×	`add-sqr-sqrt`
55×	`add-cube-cbrt`
36×	`distribute-rgt-in` `distribute-lft-in` `exp-sum`
19×	`distribute-lft-out`
12×	`associate-/r/`
11×	`add-exp-log`
8×	`pow1` `add-cbrt-cube`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r` `associate-r*` `log1p-expm1-u`
3×	`associate-l` `associate-/l*`
2×	`div-exp` `rem-log-exp` `log-pow`
1×	`cbrt-undiv` `log-div` `exp-prod` `clear-num` `frac-2neg` `exp-to-pow` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 171

Calls

4 calls:

29.0ms	(exp (* x (log (/ x (+ x y)))))
18.0ms	(/ x (+ x y))
32.0ms	(* x (log (/ x (+ x y))))
6.0ms	(log (/ x (+ x y)))

series591.0ms

Counts

4 → 12

Calls

4 calls:

340.0ms	(exp (* x (log (/ x (+ x y)))))
68.0ms	(/ x (+ x y))
114.0ms	(* x (log (/ x (+ x y))))
69.0ms	(log (/ x (+ x y)))

simplify3.1s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
3	4394
2	1236
1	559
0	256

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow (exp x) (log (/ x (+ x y)))) x)
0.0b	(/ x (+ x y))
0.1b	(pow (exp x) (log (/ x (+ x y))))
8.0b	(log (/ x (+ x y)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
142×	`*-un-lft-identity`
108×	`log-prod`
98×	`add-sqr-sqrt` `add-cube-cbrt`
90×	`unpow-prod-up`
28×	`associate-/l*`
22×	`distribute-lft-out`
15×	`unpow-prod-down`
14×	`associate-/r/`
13×	`add-exp-log`
8×	`add-cbrt-cube` `div-inv`
7×	`pow1` `associate-/r*` `flip3-+` `flip-+`
5×	`div-exp` `sqr-pow`
4×	`expm1-log1p-u` `pow-unpow` `pow-pow` `log1p-expm1-u` `add-log-exp`
3×	`log-div` `exp-prod`
2×	`pow-to-exp` `cbrt-undiv` `clear-num` `frac-2neg` `rem-log-exp` `pow-exp` `log-pow` `pow-sub`
1×	`associate-/l/`

Counts

4 → 228

Calls

4 calls:

27.0ms	(/ (pow (exp x) (log (/ x (+ x y)))) x)
9.0ms	(/ x (+ x y))
13.0ms	(pow (exp x) (log (/ x (+ x y))))
10.0ms	(log (/ x (+ x y)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (pow (exp x) (log (/ x (+ x y)))) x)
55.0ms	(/ x (+ x y))
189.0ms	(pow (exp x) (log (/ x (+ x y))))
91.0ms	(log (/ x (+ x y)))

simplify2.0s

Counts

240 → 240

Iterations

Iter	Nodes
done	5008
2	2045
1	736
0	339

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
8.0b	(log (/ x (+ x y)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
18×	`log-prod`
15×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
9×	`cbrt-prod`
7×	`add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
2×	`rem-log-exp` `associate-/r/`
1×	`log-div` `flip3-+` `div-exp` `log-pow` `flip-+` `div-inv`

Counts

4 → 70

Calls

4 calls:

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

series800.0ms

Counts

4 → 12

Calls

4 calls:

271.0ms	(cbrt x)
235.0ms	(cbrt x)
225.0ms	(cbrt x)
69.0ms	(log (/ x (+ x y)))

simplify2.5s

Counts

82 → 82

Iterations

Iter	Nodes
done	5027
4	3792
3	1040
2	394
1	202
0	105

prune531.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

2.9b	(log (sqrt (/ x (+ x y))))
2.9b	(log (sqrt (/ x (+ x y))))
5.0b	(sqrt (/ x (+ x y)))
5.0b	(sqrt (/ x (+ x y)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
62×	`*-un-lft-identity`
50×	`times-frac`
44×	`add-sqr-sqrt`
42×	`log-prod`
38×	`add-cube-cbrt`
12×	`distribute-lft-out`
10×	`pow1`
8×	`associate-/r/`
6×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `sqrt-div` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 134

Calls

4 calls:

6.0ms	(log (sqrt (/ x (+ x y))))
6.0ms	(log (sqrt (/ x (+ x y))))
16.0ms	(sqrt (/ x (+ x y)))
18.0ms	(sqrt (/ x (+ x y)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(log (sqrt (/ x (+ x y))))
100.0ms	(log (sqrt (/ x (+ x y))))
107.0ms	(sqrt (/ x (+ x y)))
79.0ms	(sqrt (/ x (+ x y)))

simplify3.1s

Counts

146 → 146

Iterations

Iter	Nodes
done	5001
5	2378
4	1100
3	478
2	288
1	183
0	126

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes141.0ms

Accuracy

98.9% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 6.1b

bsearch151.0ms

Steps

Iters	Range		Point
11	1.4622773167296954e-11	37605091470.942024	6.903129057972267
8	-1.8275688213906753e+41	-2.70728775310249e+38	-2.738716592497185e+38

simplify29.0ms

Iterations

Iter	Nodes
done	25
1	25
0	20

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.6s	1520×	body	1280	valid
635.0ms	1500×	body	640	valid
463.0ms	4767×	body	80	valid
303.0ms	878×	body	320	valid
296.0ms	3005×	body	80	nan
76.0ms	440×	body	160	valid