Details

sample90.0ms

Algorithm

intervals

Results

30.0ms	54×	body	1280	valid
19.0ms	54×	body	640	valid
10.0ms	153×	body	80	valid
6.0ms	30×	body	320	valid
5.0ms	99×	body	80	nan
3.0ms	19×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
6.7b	(pow (/ x (+ x y)) x)

rewrite106.0ms

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×	`div-exp` `associate-/r*` `add-cbrt-cube` `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×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 178

Calls

3 calls:

56.0ms	(/ (pow (/ x (+ x y)) x) x)
16.0ms	(/ x (+ x y))
24.0ms	(pow (/ x (+ x y)) x)

series626.0ms

Counts

3 → 9

Calls

3 calls:

211.0ms	(/ (pow (/ x (+ x y)) x) x)
60.0ms	(/ x (+ x y))
354.0ms	(pow (/ x (+ x y)) x)

simplify1.6s

Counts

187 → 187

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	282	2929
1	545	2745
2	1552	2688
done	5000	2684

prune608.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.1b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.1b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite91.0ms

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` `prod-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `associate-l/` `div-inv` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
28.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
53.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series1.4s

Counts

4 → 12

Calls

4 calls:

291.0ms	(cbrt x)
266.0ms	(cbrt x)
407.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
439.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify3.7s

Counts

136 → 136

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	301	2387
1	695	2215
2	1535	1993
3	4521	1983
done	5000	1980

prune638.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.1b	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) x)
1.1b	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) x)
1.1b	(pow (/ (cbrt x) (cbrt (+ x y))) x)

rewrite48.0ms

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×	`add-exp-log` `pow-unpow`
7×	`pow1`
6×	`distribute-lft-out`
4×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `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:

2.0ms	(cbrt x)
6.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) x)
5.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) x)
26.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)

series712.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(cbrt x)
35.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) x)
51.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) x)
416.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)

simplify3.4s

Counts

128 → 128

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	247	2050
1	541	1914
2	1138	1855
3	2998	1850
done	5001	1843

prune641.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (- y)) x)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log` `associate-/l/`
1×	`pow1` `cbrt-undiv` `neg-sub0` `exp-neg` `expm1-log1p-u` `frac-2neg` `exp-diff` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

24.0ms

(/ (exp (- y)) x)

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

(/ (exp (- y)) x)

simplify2.9s

Counts

34 → 34

Iterations

Useful iterations: 3 (227.0ms)

Iter	Nodes	Cost
0	66	311
1	120	300
2	293	280
3	709	278
4	2815	278
done	5002	278

prune117.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes53.0ms

Accuracy

81.9% (1.0b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 5.4b

bsearch187.0ms

Steps

Iters	Range		Point
9	1.2167838917470026e-32	2.9088581115424155e-25	2.859517489315194e-25
9	-1.1336114390675675e+140	-1.3239866454658551e+135	-1.335604954605443e+135

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	23	55
1	29	48
done	29	48

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	1522×	body	1280	valid
637.0ms	1422×	body	640	valid
439.0ms	4873×	body	80	valid
260.0ms	877×	body	320	valid
235.0ms	3017×	body	80	nan
145.0ms	427×	body	160	valid