Details

sample142.0ms

Algorithm

intervals

Results

53.0ms	57×	body	1280	valid
26.0ms	48×	body	640	valid
16.0ms	161×	body	80	valid
10.0ms	27×	body	320	valid
8.0ms	103×	body	80	nan
3.0ms	15×	body	160	valid

simplify2.4s

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
6.1b	(pow (/ x (+ x y)) x)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`unpow-prod-down`
7×	`add-exp-log` `distribute-lft-out`
4×	`associate-/r*` `associate-/r/` `add-cbrt-cube`
3×	`pow1` `pow-unpow` `associate-/l*`
2×	`expm1-log1p-u` `flip3-+` `div-exp` `pow-exp` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

2 → 70

Calls

2 calls:

24.0ms	(/ x (+ x y))
18.0ms	(pow (/ x (+ x y)) x)

series417.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ x (+ x y))
358.0ms	(pow (/ x (+ x y)) x)

simplify1.9s

Counts

76 → 76

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	133	864
1	316	808
2	781	780
3	2157	779
done	5001	775

prune283.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize58.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(* (cbrt x) (cbrt x))
1.0b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.2b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

65×	`cbrt-prod`
61×	`unpow-prod-down`
57×	`*-un-lft-identity`
51×	`add-sqr-sqrt`
43×	`add-cube-cbrt` `times-frac`
22×	`add-exp-log`
16×	`cbrt-div`
13×	`pow1`
10×	`associate-/r/`
8×	`flip3-+` `flip-+`
7×	`pow1/3` `pow-exp` `distribute-lft-out`
6×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
5×	`div-exp` `prod-exp`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up` `div-inv` `sqr-pow`
1×	`pow2` `pow-plus` `*-commutative` `cbrt-unprod`

Counts

4 → 156

Calls

4 calls:

7.0ms	(cbrt (+ x y))
30.0ms	(* (cbrt x) (cbrt x))
43.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
37.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series1.3s

Counts

4 → 12

Calls

4 calls:

223.0ms	(cbrt (+ x y))
314.0ms	(* (cbrt x) (cbrt x))
373.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
410.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify1.6s

Counts

168 → 168

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	346	2757
1	802	2531
2	1908	2264
done	5000	2250

prune809.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
1.0b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.8b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

98×	`cbrt-prod`
89×	`*-un-lft-identity`
84×	`times-frac`
61×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`unpow-prod-down` `log-prod`
14×	`distribute-lft-out`
10×	`add-exp-log`
8×	`cbrt-div`
6×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `associate-/r/` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow1/3` `div-exp` `rem-log-exp` `pow-exp` `div-inv`
1×	`pow-to-exp` `log-div` `pow-pow` `log-pow` `sqr-pow`

Counts

4 → 158

Calls

4 calls:

5.0ms	(cbrt (+ x y))
5.0ms	(cbrt (+ x y))
30.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
16.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series882.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(cbrt (+ x y))
151.0ms	(cbrt (+ x y))
409.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
108.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify3.0s

Counts

170 → 170

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	293	2735
1	650	2547
2	1329	2498
3	3354	2454
done	5001	2451

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite27.0ms

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:

25.0ms

(/ (exp (- y)) x)

series30.0ms

Counts

1 → 3

Calls

1 calls:

30.0ms

(/ (exp (- y)) x)

simplify2.7s

Counts

34 → 34

Iterations

Useful iterations: 3 (232.0ms)

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

prune115.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes68.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 5.5b

bsearch147.0ms

Steps

Iters	Range		Point
9	2.9210494299769893e-08	3.811728419345326	3.548587978717038
10	-2.4955120319962723e+20	-128623.8930200133	-2375445713.2073126

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	47
1	34	40
done	34	40

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	1538×	body	1280	valid
730.0ms	1492×	body	640	valid
484.0ms	4916×	body	80	valid
267.0ms	805×	body	320	valid
251.0ms	2973×	body	80	nan
73.0ms	418×	body	160	valid