Details

sample112.0ms

Algorithm

intervals

Results

38.0ms	52×	body	1280	valid
19.0ms	42×	body	640	valid
12.0ms	153×	body	80	valid
8.0ms	27×	body	320	valid
7.0ms	109×	body	80	nan
3.0ms	18×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	8	11
1	15	11
2	24	9
3	51	9
4	148	9
5	485	9
6	1979	9
done	5000	9

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize24.0ms

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)

rewrite143.0ms

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×	`pow-unpow` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 172

Calls

3 calls:

20.0ms	(/ x (+ x y))
73.0ms	(/ (pow (/ x (+ x y)) x) x)
30.0ms	(pow (/ x (+ x y)) x)

series691.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(/ x (+ x y))
224.0ms	(/ (pow (/ x (+ x y)) x) x)
401.0ms	(pow (/ x (+ x y)) x)

simplify2.0s

Counts

181 → 181

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	276	2881
1	649	2711
2	2839	2657
done	5000	2654

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.0b

localize14.0ms

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` `frac-2neg` `exp-diff` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

25.0ms

(/ (exp (- y)) x)

series41.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

(/ (exp (- y)) x)

simplify3.8s

Counts

32 → 32

Iterations

Useful iterations: 3 (891.0ms)

Iter	Nodes	Cost
0	64	299
1	125	289
2	488	271
3	3657	267
done	5001	267

prune173.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
53×	`times-frac`
39×	`*-un-lft-identity`
37×	`add-cube-cbrt`
28×	`associate-r`
22×	`unpow-prod-down`
19×	`add-exp-log`
11×	`add-cbrt-cube` `add-log-exp`
8×	`associate-/l*` `unpow2` `sqr-pow`
6×	`pow1` `div-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`associate-r/` `associate-l` `associate-/r` `frac-sub`
2×	`cbrt-undiv` `pow-to-exp` `flip3-+` `diff-log` `frac-add` `pow-exp` `sum-log` `cbrt-unprod` `flip-+` `div-inv` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow-prod-down` `associate--l+` `clear-num` `*-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 133

Calls

4 calls:

27.0ms	(+ (* 1/2 (/ (pow y 2) x)) (/ 1 x))
37.0ms	(* 1/2 (/ (pow y 2) x))
229.0ms	(- (+ (* 1/2 (/ (pow y 2) x)) (/ 1 x)) (/ y x))
20.0ms	(/ (pow y 2) x)

series205.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+ (* 1/2 (/ (pow y 2) x)) (/ 1 x))
47.0ms	(* 1/2 (/ (pow y 2) x))
55.0ms	(- (+ (* 1/2 (/ (pow y 2) x)) (/ 1 x)) (/ y x))
37.0ms	(/ (pow y 2) x)

simplify1.7s

Counts

145 → 145

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	207	1997
1	525	1811
2	2261	1625
done	5001	1618

prune830.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.0b

localize45.0ms

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)

rewrite72.0ms

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×	`flip3-+` `add-cbrt-cube` `flip-+` `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 → 84

Calls

4 calls:

7.0ms	(cbrt (+ x y))
8.0ms	(cbrt (+ x y))
9.0ms	(cbrt (+ x y))
43.0ms	(pow (/ x (cbrt (+ x y))) x)

series850.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(cbrt (+ x y))
225.0ms	(cbrt (+ x y))
229.0ms	(cbrt (+ x y))
180.0ms	(pow (/ x (cbrt (+ x y))) x)

simplify1.8s

Counts

96 → 96

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	207	1387
1	633	1298
2	2306	1262
done	5000	1253

prune799.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes220.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch256.0ms

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

sample4.8s

Algorithm

intervals

Results

1.4s	1497×	body	1280	valid
1.2s	4807×	body	80	valid
832.0ms	1495×	body	640	valid
350.0ms	855×	body	320	valid
253.0ms	2953×	body	80	nan
162.0ms	444×	body	160	valid