Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	60×	body	640	valid
4.0ms	132×	body	80	valid
2.0ms	16×	body	1280	valid
2.0ms	25×	body	320	valid
1.0ms	23×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7
done	209	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
1.9b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite359.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

11.0ms	(/ 1.0 (- x 1.0))
11.0ms	(/ 1.0 (+ x 1.0))
59.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
274.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1.0 (- x 1.0))
30.0ms	(/ 1.0 (+ x 1.0))
42.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
220.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify44.0ms

Counts

126 → 126

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	496	865
1	1681	827
2	5002	816
done	5002	816

prune246.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
15.9b	(+ (- (* (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (cbrt 1.0) (cbrt (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite549.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
12×	`cbrt-prod`
9×	`add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
5×	`frac-add`
4×	`pow1` `add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
3×	`pow1/3` `frac-sub`
2×	`associate-+l+` `sum-log`
1×	`+-commutative` `frac-times` `associate-+l-` `sub-neg` `flip3--` `diff-log` `associate-r/` `associate-l/` `flip--`

Counts

4 → 63

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))
536.0ms	(+ (- (* (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (cbrt 1.0) (cbrt (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ x 1.0))
88.0ms	(cbrt (+ x 1.0))
89.0ms	(cbrt (+ x 1.0))
259.0ms	(+ (- (* (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (cbrt 1.0) (cbrt (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify47.0ms

Counts

75 → 75

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	461	1094
1	1598	964
2	5001	843
done	5001	843

prune281.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
1.2b	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
16.3b	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1`
4×	`associate-l` `associate-*l/`
3×	`flip3-+` `times-frac` `associate-r` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-sub` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out`
1×	`+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `frac-add` `clear-num` `associate-/r` `sum-log` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

20.0ms	(* (+ x 1.0) x)
8.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
70.0ms	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
25.0ms	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

series448.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (+ x 1.0) x)
42.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
288.0ms	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
70.0ms	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

simplify55.0ms

Counts

85 → 85

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	457	724
1	1920	638
2	5001	637
done	5001	637

prune168.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
0.0b	(/ 1 (pow x 5))
0.2b	(/ 1 (pow x 3))
0.3b	(/ 1 (pow x 7))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
73×	`*-un-lft-identity`
63×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`unpow-prod-down`
31×	`add-exp-log`
26×	`associate-/r*`
18×	`div-exp`
12×	`cube-prod` `sqr-pow`
10×	`add-cbrt-cube`
9×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
7×	`div-inv` `distribute-lft-out`
6×	`add-log-exp`
4×	`pow1` `cube-mult` `unpow3`
3×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `inv-pow`
1×	`+-commutative` `flip3-+` `frac-add` `sum-log` `flip-+`

Counts

4 → 198

Calls

4 calls:

68.0ms	(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
12.0ms	(/ 1 (pow x 5))
9.0ms	(/ 1 (pow x 3))
8.0ms	(/ 1 (pow x 7))

series249.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
51.0ms	(/ 1 (pow x 5))
34.0ms	(/ 1 (pow x 3))
63.0ms	(/ 1 (pow x 7))

simplify58.0ms

Counts

210 → 210

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	469	961
1	2563	767
2	5002	767
done	5002	767

prune318.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes26.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 24.9b

bsearch113.0ms

Steps

Iters	Range		Point
10	0.00012253353073063669	15794870057.515802	120.10501917782233
9	-3991486314.2924213	-2.7342232818785663	-116.24246562283282

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	19
1	44	19
done	44	19

end0.0ms

sample635.0ms

Algorithm

intervals

Results

197.0ms	1796×	body	640	valid
122.0ms	4215×	body	80	valid
81.0ms	952×	body	320	valid
78.0ms	564×	body	1280	valid
26.0ms	473×	body	160	valid