Details

sample151.0ms

Algorithm

intervals

Results

43.0ms	73×	body	10240	exit
32.0ms	61×	body	1280	valid
26.0ms	340×	body	80	valid
15.0ms	42×	body	640	valid
4.0ms	20×	body	320	valid
2.0ms	13×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	19	29
1	46	29
2	122	29
3	335	27
4	933	27
5	4084	27
done	5000	27

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 eps) x)
0.0b	(exp (* (- 1.0 eps) x))
0.0b	(exp (* (+ 1.0 eps) x))
1.9b	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
14×	`add-log-exp`
12×	`times-frac`
7×	`distribute-lft-out--`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`exp-to-pow` `associate-l` `difference-of-squares`
3×	`associate-r` `distribute-lft-out`
2×	`exp-prod` `diff-log` `associate-*l/` `rem-exp-log`
1×	`sub-neg` `flip3--` `flip3-+` `div-sub` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `flip-+` `associate--r-` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

36.0ms	(* (+ 1.0 eps) x)
9.0ms	(exp (* (- 1.0 eps) x))
7.0ms	(exp (* (+ 1.0 eps) x))
290.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (+ 1.0 eps) x)
36.0ms	(exp (* (- 1.0 eps) x))
21.0ms	(exp (* (+ 1.0 eps) x))
245.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify2.2s

Counts

78 → 78

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	145	1386
1	342	1340
2	988	1240
3	3573	1201
done	5000	1201

prune395.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(* (* x x) (- (* x 0.6666666666666667) 1.0))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `add-cube-cbrt` `sub-neg` `-un-lft-identity` `distribute-lft-in` `associate-r/`
1×	`flip3--` `associate-l` `*-commutative` `flip--` `add-log-exp` `unswap-sqr`

Counts

1 → 25

Calls

1 calls:

84.0ms

(* (* x x) (- (* x 0.6666666666666667) 1.0))

series133.0ms

Counts

1 → 3

Calls

1 calls:

133.0ms

(* (* x x) (- (* x 0.6666666666666667) 1.0))

simplify1.9s

Counts

28 → 28

Iterations

Useful iterations: 2 (145.0ms)

Iter	Nodes	Cost
0	57	367
1	156	344
2	563	294
3	2164	294
done	5000	294

prune82.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (- (* x 0.6666666666666667) 1.0)) (cbrt (- (* x 0.6666666666666667) 1.0)))
0.1b	(cbrt (- (* x 0.6666666666666667) 1.0))
0.1b	(cbrt (- (* x 0.6666666666666667) 1.0))
0.1b	(cbrt (- (* x 0.6666666666666667) 1.0))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

109.0ms	(* (cbrt (- (* x 0.6666666666666667) 1.0)) (cbrt (- (* x 0.6666666666666667) 1.0)))
16.0ms	(cbrt (- (* x 0.6666666666666667) 1.0))
8.0ms	(cbrt (- (* x 0.6666666666666667) 1.0))
7.0ms	(cbrt (- (* x 0.6666666666666667) 1.0))

series754.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(* (cbrt (- (* x 0.6666666666666667) 1.0)) (cbrt (- (* x 0.6666666666666667) 1.0)))
209.0ms	(cbrt (- (* x 0.6666666666666667) 1.0))
195.0ms	(cbrt (- (* x 0.6666666666666667) 1.0))
162.0ms	(cbrt (- (* x 0.6666666666666667) 1.0))

simplify3.4s

Counts

99 → 99

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	183	2139
1	438	2008
2	1314	1905
3	4766	1623
done	5000	1545

prune439.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
0.1b	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
0.1b	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
0.2b	(pow (cbrt (cbrt (- (* x 0.6666666666666667) 1.0))) 4)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-div`
9×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `flip3--` `flip--`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

14.0ms	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
9.0ms	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
7.0ms	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
14.0ms	(pow (cbrt (cbrt (- (* x 0.6666666666666667) 1.0))) 4)

series1.0s

Counts

4 → 12

Calls

4 calls:

235.0ms	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
193.0ms	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
194.0ms	(cbrt (cbrt (- (* x 0.6666666666666667) 1.0)))
388.0ms	(pow (cbrt (cbrt (- (* x 0.6666666666666667) 1.0))) 4)

simplify1.0s

Counts

84 → 84

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	188	1804
1	452	1685
2	1362	1603
done	5000	1470

prune485.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

regimes124.0ms

Accuracy

97% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.5b

bsearch286.0ms

Steps

Iters	Range		Point
11	9.104077427347524e-22	110.15968793260775	1.714530635609196

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	39	90
1	50	90
done	50	90

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.2s	1927×	body	10240	exit
1.1s	1737×	body	1280	valid
843.0ms	9990×	body	80	valid
481.0ms	1228×	body	640	valid
172.0ms	670×	body	320	valid
55.0ms	333×	body	160	valid