Details

sample137.0ms

Algorithm

intervals

Results

44.0ms	52×	body	1280	valid
22.0ms	42×	body	640	valid
14.0ms	153×	body	80	valid
10.0ms	27×	body	320	valid
8.0ms	109×	body	80	nan
4.0ms	18×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	8	11
1	15	11
2	24	9
3	51	9
4	150	9
5	501	9
6	2070	9
done	5000	9

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x y))
0.0b	(/ (pow (/ x (+ x y)) x) x)
7.7b	(pow (/ x (+ x y)) x)

rewrite171.0ms

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:

25.0ms	(/ x (+ x y))
95.0ms	(/ (pow (/ x (+ x y)) x) x)
29.0ms	(pow (/ x (+ x y)) x)

series921.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(/ x (+ x y))
310.0ms	(/ (pow (/ x (+ x y)) x) x)
521.0ms	(pow (/ x (+ x y)) x)

simplify3.0s

Counts

187 → 187

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	282	2929
1	664	2748
2	2884	2692
done	5001	2690

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.0b

localize23.0ms

Local error

Found 1 expressions with local error:

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

rewrite30.0ms

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:

28.0ms

(/ (exp (- y)) x)

series48.0ms

Counts

1 → 3

Calls

1 calls:

48.0ms

(/ (exp (- y)) x)

simplify4.5s

Counts

34 → 34

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	66	311
1	128	300
2	473	282
3	3443	278
done	5001	278

prune240.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/2 (/ (pow y 2) x) (/ 1 x))
2.4b	(- (fma 1/2 (/ (pow y 2) x) (/ 1 x)) (/ y x))
3.8b	(/ (pow y 2) x)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
55×	`add-cube-cbrt`
52×	`times-frac`
39×	`prod-diff`
12×	`unpow-prod-down`
8×	`add-exp-log` `associate-/l*`
5×	`add-cbrt-cube` `add-log-exp`
4×	`div-inv` `unpow2` `sqr-pow`
3×	`pow1` `expm1-log1p-u` `fma-neg` `div-exp` `associate-/r*` `log1p-expm1-u`
2×	`fma-udef` `difference-of-squares`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-exp` `associate--l+` `clear-num` `flip--` `distribute-lft-out--`

Counts

3 → 121

Calls

3 calls:

1.0ms	(fma 1/2 (/ (pow y 2) x) (/ 1 x))
29.0ms	(- (fma 1/2 (/ (pow y 2) x) (/ 1 x)) (/ y x))
20.0ms	(/ (pow y 2) x)

series223.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(fma 1/2 (/ (pow y 2) x) (/ 1 x))
76.0ms	(- (fma 1/2 (/ (pow y 2) x) (/ 1 x)) (/ y x))
57.0ms	(/ (pow y 2) x)

simplify3.4s

Counts

130 → 130

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	238	3396
1	572	3105
2	2590	2455
done	5002	1950

prune745.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
1.2b	(pow (/ x (cbrt (+ x y))) x)

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
27×	`unpow-prod-down`
24×	`cbrt-prod`
22×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`times-frac`
8×	`cbrt-div`
7×	`add-exp-log`
6×	`distribute-lft-out`
5×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`pow-exp` `associate-/r/`
1×	`pow-to-exp` `pow-pow` `div-exp` `div-inv` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

9.0ms	(cbrt (+ x y))
9.0ms	(cbrt (+ x y))
9.0ms	(cbrt (+ x y))
45.0ms	(pow (/ x (cbrt (+ x y))) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

310.0ms	(cbrt (+ x y))
314.0ms	(cbrt (+ x y))
318.0ms	(cbrt (+ x y))
249.0ms	(pow (/ x (cbrt (+ x y))) x)

simplify2.6s

Counts

104 → 104

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	211	1435
1	650	1331
2	2429	1297
done	5003	1280

prune956.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes214.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 12.5b

bsearch297.0ms

Steps

Iters	Range		Point
11	4.735830173312099e-12	453261925.93168354	35.40231590631766
10	-906041723027795.1	-2.7801956145632056	-11.131115373710125

simplify9.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	28	64
1	36	60
done	36	60

end0.0ms

sample5.2s

Algorithm

intervals

Results

1.5s	4807×	body	80	valid
1.4s	1497×	body	1280	valid
795.0ms	1495×	body	640	valid
324.0ms	2953×	body	80	nan
301.0ms	855×	body	320	valid
154.0ms	444×	body	160	valid