Details

sample120.0ms

Algorithm

intervals

Results

37.0ms	78×	body	10240	exit
28.0ms	61×	body	1280	valid
20.0ms	331×	body	80	valid
13.0ms	43×	body	640	valid
3.0ms	18×	body	320	valid
2.0ms	15×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	19	29
1	46	29
2	122	29
3	305	27
4	1022	27
5	4217	27
done	5000	27

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (- 1.0 eps) x)))
0.0b	(* (+ 1.0 eps) x)
0.0b	(exp (- (* (+ 1.0 eps) x)))
3.6b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
74×	`exp-neg`
72×	`frac-times`
56×	`neg-sub0` `exp-diff`
38×	`associate-*l/`
36×	`associate-*r/`
28×	`flip3--` `flip3-+` `flip--` `flip-+`
18×	`un-div-inv`
12×	`exp-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`associate-l` `rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 148

Calls

4 calls:

4.0ms	(exp (- (* (- 1.0 eps) x)))
13.0ms	(* (+ 1.0 eps) x)
3.0ms	(exp (- (* (+ 1.0 eps) x)))
28.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series275.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(exp (- (* (- 1.0 eps) x)))
30.0ms	(* (+ 1.0 eps) x)
26.0ms	(exp (- (* (+ 1.0 eps) x)))
192.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify1.2s

Counts

160 → 160

Iterations

Useful iterations: 2 (443.0ms)

Iter	Nodes	Cost
0	368	7406
1	1168	6754
2	3663	6270
done	5000	6270

prune377.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 0.6666666666666667 (pow x 3)) 2.0)
0.1b	(* 0.6666666666666667 (pow x 3))
4.8b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

4.0ms	(+ (* 0.6666666666666667 (pow x 3)) 2.0)
7.0ms	(* 0.6666666666666667 (pow x 3))
32.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series153.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(+ (* 0.6666666666666667 (pow x 3)) 2.0)
39.0ms	(* 0.6666666666666667 (pow x 3))
38.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify2.9s

Counts

65 → 65

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	98	756
1	254	683
2	794	639
3	4619	603
done	5000	603

prune150.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
4.8b	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

rewrite15.0ms

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` `associate-+r+` `sum-log` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 46

Calls

2 calls:

7.0ms	(* 0.6666666666666667 (pow x 3))
7.0ms	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

series75.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(* 0.6666666666666667 (pow x 3))
38.0ms	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (pow x 2))))

simplify2.1s

Counts

52 → 52

Iterations

Useful iterations: 3 (686.0ms)

Iter	Nodes	Cost
0	83	592
1	205	534
2	634	494
3	3628	464
done	5001	464

prune120.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize14.0ms

Local error

Found 4 expressions with local error:

4.8b	(+ (* (* (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))))
41.0b	(cbrt (* 0.6666666666666667 (pow x 3)))
41.0b	(cbrt (* 0.6666666666666667 (pow x 3)))
41.0b	(cbrt (* 0.6666666666666667 (pow x 3)))

rewrite27.0ms

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×	`associate-+r+` `sum-log`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `flip-+`

Counts

4 → 42

Calls

4 calls:

19.0ms	(+ (* (* (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))))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
2.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ (* (* (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))))
38.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
36.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))
38.0ms	(cbrt (* 0.6666666666666667 (pow x 3)))

simplify964.0ms

Counts

54 → 54

Iterations

Useful iterations: 3 (187.0ms)

Iter	Nodes	Cost
0	55	929
1	139	906
2	389	505
3	1863	468
done	5001	468

prune170.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

regimes86.0ms

Accuracy

96.5% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.3b

bsearch135.0ms

Steps

Iters	Range		Point
8	1.1588875362171251	7686.007879781806	95.54164031582988

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	82
1	56	82
2	64	82
done	64	82

end0.0ms

sample3.1s

Algorithm

intervals

Results

878.0ms	1963×	body	10240	exit
824.0ms	1763×	body	1280	valid
602.0ms	9939×	body	80	valid
360.0ms	1288×	body	640	valid
116.0ms	614×	body	320	valid
43.0ms	338×	body	160	valid