Details

sample199.0ms

Algorithm

intervals

Results

78.0ms	57×	body	10240	exit
34.0ms	320×	body	80	valid
33.0ms	53×	body	1280	valid
16.0ms	35×	body	640	valid
6.0ms	19×	body	320	valid
1.0ms	6×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	19	29
1	46	29
2	122	29
3	377	27
4	2267	27
done	5000	27

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.1b	(exp (- (* (+ 1.0 eps) x)))
0.1b	(exp (- (* (- 1.0 eps) x)))
2.2b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
78×	`exp-neg`
76×	`frac-times`
59×	`neg-sub0` `exp-diff`
38×	`associate-r/` `associate-l/`
31×	`flip3--` `flip--`
27×	`flip3-+` `flip-+`
19×	`un-div-inv`
15×	`add-sqr-sqrt`
12×	`exp-prod`
10×	`*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `associate-l` `add-cbrt-cube`
5×	`add-exp-log`
4×	`rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log` `difference-of-squares`
1×	`sub-neg` `times-frac` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 157

Calls

4 calls:

111.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
14.0ms	(exp (- (* (+ 1.0 eps) x)))
19.0ms	(exp (- (* (- 1.0 eps) x)))
66.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
37.0ms	(exp (- (* (+ 1.0 eps) x)))
51.0ms	(exp (- (* (- 1.0 eps) x)))
282.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify633.0ms

Counts

169 → 169

Iterations

Useful iterations: done (625.0ms)

Iter	Nodes	Cost
0	369	7824
1	1171	7122
done	5001	6820

prune758.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
8.0b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-r`
7×	`add-exp-log` `add-log-exp`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `diff-log` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `unpow3` `pow-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod`

Counts

2 → 45

Calls

2 calls:

13.0ms	(* 0.6666666666666667 (pow x 3))
99.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series122.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(* 0.6666666666666667 (pow x 3))
50.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify767.0ms

Counts

51 → 51

Iterations

Useful iterations: done (763.0ms)

Iter	Nodes	Cost
0	84	590
1	222	548
2	908	500
done	5000	462

prune211.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize36.0ms

Local error

Found 4 expressions with local error:

8.0b	(- (+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
40.4b	(cbrt (* 0.6666666666666667 (pow x 3)))
40.4b	(cbrt (* 0.6666666666666667 (pow x 3)))
40.4b	(cbrt (* 0.6666666666666667 (pow x 3)))

rewrite337.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cbrt-prod` `pow1/3`
2×	`diff-log`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

4 → 41

Calls

4 calls:

306.0ms	(- (+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
10.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
10.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
10.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(- (+ (* (* (cbrt (* 0.6666666666666667 (pow x 3))) (cbrt (* 0.6666666666666667 (pow x 3)))) (cbrt (* 0.6666666666666667 (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
70.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
63.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
49.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))

simplify2.5s

Counts

53 → 53

Iterations

Useful iterations: 3 (834.0ms)

Iter	Nodes	Cost
0	56	882
1	137	861
2	535	561
3	3235	469
done	5003	469

prune297.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize52.0ms

Local error

Found 4 expressions with local error:

40.4b	(cbrt (* 0.6666666666666667 (pow x 3)))
40.4b	(cbrt (* 0.6666666666666667 (pow x 3)))
40.4b	(cbrt (* 0.6666666666666667 (pow x 3)))
40.4b	(cbrt (* 0.6666666666666667 (pow x 3)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

5.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
5.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
9.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
10.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
56.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
69.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
76.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))

simplify1.9s

Counts

48 → 48

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	21	360
1	38	344
2	84	296
3	189	284
4	372	284
5	814	284
6	2234	284
done	5000	284

prune328.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

regimes71.0ms

Accuracy

96.7% (0.5b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.7b

bsearch261.0ms

Steps

Iters	Range		Point
8	1.4124627081995123	1575.9184687212278	14.67295150394162

simplify18.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	39	98
1	60	98
2	70	98
done	70	98

end0.0ms

sample8.3s

Algorithm

intervals

Results

2.5s	1697×	body	1280	valid
2.5s	1858×	body	10240	exit
1.8s	10005×	body	80	valid
666.0ms	1244×	body	640	valid
210.0ms	640×	body	320	valid
63.0ms	309×	body	160	valid