Details

sample94.0ms

Algorithm

intervals

Results

27.0ms	43×	body	1280	valid
25.0ms	59×	body	640	valid
11.0ms	150×	body	80	valid
6.0ms	23×	body	320	valid
5.0ms	87×	body	80	nan
2.0ms	13×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	2074
5	506
4	151
3	52
2	24
1	15
0	8

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ y x)) x) x)
0.0b	(/ x (+ y x))
7.3b	(pow (/ x (+ y x)) x)

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`associate-/r*` `add-cbrt-cube` `div-exp` `div-inv`
6×	`flip3-+` `flip-+`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `cbrt-undiv` `clear-num` `frac-2neg`
1×	`pow-pow`

Counts

3 → 178

Calls

3 calls:

51.0ms	(/ (pow (/ x (+ y x)) x) x)
9.0ms	(/ x (+ y x))
11.0ms	(pow (/ x (+ y x)) x)

series982.0ms

Counts

3 → 9

Calls

3 calls:

172.0ms	(/ (pow (/ x (+ y x)) x) x)
53.0ms	(/ x (+ y x))
757.0ms	(pow (/ x (+ y x)) x)

simplify1.7s

Counts

187 → 187

Iterations

Iter	Nodes
done	5002
2	2899
1	667
0	282

prune844.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize62.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.8b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.0b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ y x)) (cbrt (+ y x)))) x)

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

61×	`unpow-prod-down`
51×	`cbrt-prod`
48×	`*-un-lft-identity`
43×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
14×	`cbrt-div`
10×	`associate-/r/`
7×	`flip3-+` `pow-exp` `flip-+`
6×	`pow1` `pow-unpow` `distribute-lft-out`
5×	`div-exp`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `prod-exp` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `associate-l/` `associate-r/` `div-inv` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
26.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
53.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ y x)) (cbrt (+ y x)))) x)

series1.4s

Counts

4 → 12

Calls

4 calls:

293.0ms	(cbrt x)
318.0ms	(cbrt x)
388.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
440.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ y x)) (cbrt (+ y x)))) x)

simplify1.9s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
2	3395
1	1035
0	319

prune927.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.8b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
0.8b	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) x)
0.8b	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) x)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

54×	`unpow-prod-down`
49×	`*-un-lft-identity`
48×	`cbrt-prod`
42×	`times-frac`
37×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`pow-unpow` `add-exp-log`
7×	`pow1`
6×	`distribute-lft-out`
4×	`expm1-log1p-u` `add-cbrt-cube` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `sqr-pow`
2×	`cbrt-div` `associate-/r/`
1×	`flip3-+` `pow1/3` `div-exp` `flip-+` `div-inv`

Counts

4 → 116

Calls

4 calls:

1.0ms	(cbrt x)
22.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) x)
2.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) x)

series756.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(cbrt x)
399.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
59.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) x)
35.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) x)

simplify1.3s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	2452
1	760
0	247

prune744.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (pow (/ x (+ y x)) x) (/ 1 x))
0.0b	(/ x (+ y x))
7.3b	(pow (/ x (+ y x)) x)

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
56×	`times-frac`
44×	`add-exp-log`
42×	`unpow-prod-down`
37×	`add-cube-cbrt`
22×	`associate-l`
16×	`prod-exp`
14×	`div-exp`
13×	`associate-r`
12×	`unswap-sqr`
10×	`add-cbrt-cube` `pow-exp` `distribute-lft-out`
6×	`associate-/r/`
5×	`pow-to-exp` `sqr-pow`
4×	`pow1` `rec-exp` `associate-/r*` `1-exp` `div-inv`
3×	`expm1-log1p-u` `pow-unpow` `flip3-+` `flip-+` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`cbrt-undiv` `cbrt-unprod`
1×	`clear-num` `pow-pow` `frac-2neg` `associate-r/` `un-div-inv` `-commutative`

Counts

3 → 147

Calls

3 calls:

78.0ms	(* (pow (/ x (+ y x)) x) (/ 1 x))
18.0ms	(/ x (+ y x))
21.0ms	(pow (/ x (+ y x)) x)

series557.0ms

Counts

3 → 9

Calls

3 calls:

158.0ms	(* (pow (/ x (+ y x)) x) (/ 1 x))
53.0ms	(/ x (+ y x))
346.0ms	(pow (/ x (+ y x)) x)

simplify4.1s

Counts

156 → 156

Iterations

Iter	Nodes
done	5001
2	4174
1	753
0	234

prune556.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes126.0ms

Accuracy

87.5% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 5.7b

bsearch110.0ms

Steps

Iters	Range		Point
5	1.2985943333401616e-18	3.4680268680189636e-18	3.4273149668109094e-18
8	-1.9592666963809983e+96	-1.8808133542610653e+93	-1.9012472550965265e+93

simplify2.0ms

Iterations

Iter	Nodes
done	25
1	25
0	21

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	1523×	body	1280	valid
734.0ms	1526×	body	640	valid
393.0ms	4803×	body	80	valid
324.0ms	3024×	body	80	nan
274.0ms	835×	body	320	valid
123.0ms	461×	body	160	valid