Details

sample36.0ms

Algorithm

intervals

Results

16.0ms	79×	body	1280	valid
6.0ms	57×	body	640	valid
3.0ms	181×	body	80	valid
1.0ms	20×	body	320	valid
1.0ms	14×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3
done	15	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.8b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.1b	(- (exp x) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

24.0ms	(/ (- (exp x) 1.0) x)
10.0ms	(- (exp x) 1.0)

series57.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify72.0ms

Counts

58 → 58

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	222	329
1	625	311
2	2739	309
3	5001	309
done	5001	309

prune114.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.4b	(* 1/6 (pow x 2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`associate-r`
6×	`add-exp-log`
4×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `unswap-sqr`
3×	`associate-l` `prod-exp` `add-cbrt-cube`
2×	`unpow2` `sqr-pow`
1×	`pow1` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

14.0ms

(* 1/6 (pow x 2))

series26.0ms

Counts

1 → 3

Calls

1 calls:

26.0ms

(* 1/6 (pow x 2))

simplify72.0ms

Counts

30 → 30

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	107	99
1	404	87
2	1867	87
3	5002	86
done	5002	86

prune51.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(pow (exp x) 3)
0.0b	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
4.1b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

158×	`add-sqr-sqrt`
90×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
38×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-cbrt-cube`
6×	`add-exp-log`
5×	`pow1` `difference-cubes`
4×	`pow-pow`
3×	`pow-unpow` `exp-prod` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 192

Calls

4 calls:

6.0ms	(+ 1.0 (exp x))
4.0ms	(pow (exp x) 3)
109.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
32.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series166.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ 1.0 (exp x))
27.0ms	(pow (exp x) 3)
94.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))))
36.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify92.0ms

Counts

204 → 204

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	605	2945
1	2678	2881
2	5001	2803
done	5001	2803

prune399.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 3)
0.0b	(pow (exp x) 3)
0.0b	(* (pow (exp x) 3) (pow (exp x) 3))
4.0b	(- (* (pow (exp x) 3) (pow (exp x) 3)) (* (pow 1.0 3) (pow 1.0 3)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
32×	`unpow-prod-down` `cube-prod`
28×	`add-cube-cbrt` `*-un-lft-identity`
18×	`swap-sqr`
16×	`unswap-sqr`
14×	`sqr-pow`
12×	`associate-r` `associate-l`
10×	`add-exp-log`
9×	`prod-exp`
8×	`pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube`
6×	`pow1` `cube-mult` `pow-unpow` `exp-prod` `unpow3` `add-log-exp`
3×	`pow-prod-down`
2×	`rem-cube-cbrt`
1×	`difference-cubes` `pow2` `sub-neg` `flip3--` `diff-log` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 146

Calls

4 calls:

4.0ms	(pow (exp x) 3)
4.0ms	(pow (exp x) 3)
29.0ms	(* (pow (exp x) 3) (pow (exp x) 3))
19.0ms	(- (* (pow (exp x) 3) (pow (exp x) 3)) (* (pow 1.0 3) (pow 1.0 3)))

series132.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (exp x) 3)
23.0ms	(pow (exp x) 3)
33.0ms	(* (pow (exp x) 3) (pow (exp x) 3))
53.0ms	(- (* (pow (exp x) 3) (pow (exp x) 3)) (* (pow 1.0 3) (pow 1.0 3)))

simplify74.0ms

Counts

158 → 158

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	320	726
1	1540	628
2	5001	572
done	5001	572

prune317.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes25.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.2b

bsearch44.0ms

Steps

Iters	Range		Point
10	-0.001391736753177052	-4.1211929036737376e-16	-9.202491378555593e-05

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	27
1	41	27
done	41	27

end0.0ms

sample912.0ms

Algorithm

intervals

Results

375.0ms	2262×	body	1280	valid
172.0ms	1661×	body	640	valid
99.0ms	5474×	body	80	valid
68.0ms	888×	body	320	valid
17.0ms	395×	body	160	valid