Details

sample39.0ms

Algorithm

intervals

Results

12.0ms	75×	body	1280	valid
9.0ms	94×	body	10240	exit
5.0ms	53×	body	640	valid
2.0ms	29×	body	320	valid
2.0ms	84×	body	80	valid
1.0ms	15×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	8	4
2	8	4
done	8	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
4.7b	(- (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-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 51

Calls

2 calls:

22.0ms	(/ (exp x) (- (exp x) 1.0))
11.0ms	(- (exp x) 1.0)

series43.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(/ (exp x) (- (exp x) 1.0))
15.0ms	(- (exp x) 1.0)

simplify68.0ms

Counts

57 → 57

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	180	378
1	542	357
2	2210	354
3	5001	354
done	5001	354

prune131.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp x) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
0.1b	(* (pow x 2) (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `associate-l`
9×	`times-frac` `add-cbrt-cube`
6×	`associate-r`
5×	`pow1` `unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`associate-/r` `associate-/l` `add-log-exp`
2×	`flip3-+` `associate-r/` `associate-/r/` `-commutative` `cbrt-unprod` `flip-+` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `frac-2neg` `distribute-lft-in` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `div-inv`

Counts

3 → 78

Calls

3 calls:

31.0ms	(/ (exp x) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
32.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
7.0ms	(* x 1/6)

series120.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ (exp x) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
66.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
15.0ms	(* x 1/6)

simplify57.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	401	620
1	1835	574
2	5001	572
done	5001	572

prune211.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
0.0b	(+ (* 1/12 x) (/ 1 x))
0.3b	(* 1/12 x)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
7×	`add-sqr-sqrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`sum-log`
3×	`associate-r` `associate-l`
2×	`+-commutative` `flip3-+` `flip-+`
1×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

3 → 43

Calls

3 calls:

35.0ms	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
13.0ms	(+ (* 1/12 x) (/ 1 x))
7.0ms	(* 1/12 x)

series75.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
45.0ms	(+ (* 1/12 x) (/ 1 x))
15.0ms	(* 1/12 x)

simplify106.0ms

Counts

52 → 52

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	200	216
1	705	205
2	3820	204
3	5002	204
done	5002	204

prune84.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 1/12 x) (/ 1 x))) (cbrt (+ (* 1/12 x) (/ 1 x))))
0.5b	(cbrt (+ (* 1/12 x) (/ 1 x)))
0.5b	(cbrt (+ (* 1/12 x) (/ 1 x)))
0.5b	(cbrt (+ (* 1/12 x) (/ 1 x)))

rewrite125.0ms

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:

88.0ms	(* (cbrt (+ (* 1/12 x) (/ 1 x))) (cbrt (+ (* 1/12 x) (/ 1 x))))
10.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))
10.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))
14.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (cbrt (+ (* 1/12 x) (/ 1 x))) (cbrt (+ (* 1/12 x) (/ 1 x))))
111.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))
114.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))
120.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))

simplify51.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	361	1208
1	1237	1135
2	5001	1081
done	5001	1081

prune277.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes57.0ms

Accuracy

0% (0.6b remaining)

Error of 0.9b against oracle of 0.3b and baseline of 0.9b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7
done	15	7

end0.0ms

sample1.1s

Algorithm

intervals

Results

372.0ms	2263×	body	1280	valid
269.0ms	2511×	body	10240	exit
175.0ms	1710×	body	640	valid
56.0ms	794×	body	320	valid
53.0ms	2801×	body	80	valid
19.0ms	433×	body	160	valid