Details

sample30.0ms

Algorithm

intervals

Results

7.0ms	45×	body	1280	valid
5.0ms	45×	body	640	valid
5.0ms	138×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	16	13
3	19	13
4	21	13
5	27	13
6	39	13
7	58	13
8	79	13
9	183	13
10	535	13
11	1706	13
12	3584	13
done	5000	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

44.0ms	(/ (+ x 1.0) (- x 1.0))
18.0ms	(/ x (+ x 1.0))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series284.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(/ (+ x 1.0) (- x 1.0))
52.0ms	(/ x (+ x 1.0))
176.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify961.0ms

Counts

113 → 113

Iterations

Useful iterations: 2 (331.0ms)

Iter	Nodes	Cost
0	176	1584
1	410	1503
2	1795	1427
done	5001	1427

prune265.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ 1 (+ x 1.0))
0.1b	(* x (/ 1 (+ x 1.0)))
5.9b	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
46×	`times-frac`
33×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`associate-r`
13×	`add-cbrt-cube` `distribute-lft-out`
9×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`div-exp` `distribute-lft-out--` `difference-of-squares`
4×	`prod-exp`
3×	`cbrt-undiv` `flip3-+` `associate-l` `flip-+` `div-inv` `unswap-sqr`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `associate-*r/` `clear-num` `un-div-inv` `frac-sub` `flip--` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 137

Calls

4 calls:

34.0ms	(/ (+ x 1.0) (- x 1.0))
14.0ms	(/ 1 (+ x 1.0))
29.0ms	(* x (/ 1 (+ x 1.0)))
52.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (+ x 1.0) (- x 1.0))
35.0ms	(/ 1 (+ x 1.0))
51.0ms	(* x (/ 1 (+ x 1.0)))
182.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

simplify1.7s

Counts

149 → 149

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	211	1874
1	532	1673
2	2600	1472
done	5001	1470

prune326.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1.0))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
0.1b	(* x (/ 1 (+ x 1.0)))
2.7b	(- (* x (/ 1 (+ x 1.0))) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
46×	`times-frac`
39×	`associate-r`
33×	`add-cube-cbrt`
26×	`add-exp-log`
16×	`add-cbrt-cube`
12×	`frac-sub`
10×	`associate-*r/` `un-div-inv`
9×	`pow1`
8×	`prod-exp`
7×	`flip3-+` `associate-l` `flip-+` `distribute-lft-out--` `difference-of-squares`
6×	`frac-times` `div-exp` `associate-*l/` `associate-/r/` `add-log-exp` `unswap-sqr`
5×	`associate-/r*`
4×	`cbrt-unprod` `distribute-lft-out`
3×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `flip--` `div-inv` `associate-/l*`
2×	`pow-prod-down` `*-commutative`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `clear-num` `inv-pow`

Counts

4 → 155

Calls

4 calls:

25.0ms	(/ 1 (- x 1.0))
64.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
38.0ms	(* x (/ 1 (+ x 1.0)))
32.0ms	(- (* x (/ 1 (+ x 1.0))) (* (+ x 1.0) (/ 1 (- x 1.0))))

series339.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1 (- x 1.0))
45.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
49.0ms	(* x (/ 1 (+ x 1.0)))
217.0ms	(- (* x (/ 1 (+ x 1.0))) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify425.0ms

Counts

167 → 167

Iterations

Useful iterations: done (420.0ms)

Iter	Nodes	Cost
0	260	2384
1	749	2073
done	5000	1751

prune400.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (+ 1.0 x) (- x 1.0)) 3))
0.0b	(pow (/ (+ 1.0 x) (- x 1.0)) 3)
0.1b	(* x (/ 1 (+ x 1.0)))
5.9b	(- (* x (/ 1 (+ x 1.0))) (cbrt (pow (/ (+ 1.0 x) (- x 1.0)) 3)))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

134×	`*-un-lft-identity`
94×	`add-sqr-sqrt` `times-frac`
58×	`cbrt-prod`
55×	`add-cube-cbrt`
52×	`unpow-prod-down` `cube-prod`
23×	`distribute-lft-out`
18×	`associate-r`
16×	`add-exp-log` `distribute-lft-out--` `difference-of-squares`
12×	`add-cbrt-cube`
10×	`associate-/r/`
7×	`pow1`
6×	`add-log-exp`
5×	`flip3--` `flip--` `div-inv`
4×	`cube-div` `prod-exp`
3×	`pow-unpow` `cbrt-div` `div-exp` `associate-l` `unswap-sqr`
2×	`cbrt-undiv` `cube-mult` `unpow3` `associate-*r/` `pow-exp` `un-div-inv` `frac-sub` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `rec-exp` `pow-pow` `flip3-+` `pow1/3` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `rem-cbrt-cube` `flip-+`

Counts

4 → 195

Calls

4 calls:

30.0ms	(cbrt (pow (/ (+ 1.0 x) (- x 1.0)) 3))
23.0ms	(pow (/ (+ 1.0 x) (- x 1.0)) 3)
35.0ms	(* x (/ 1 (+ x 1.0)))
108.0ms	(- (* x (/ 1 (+ x 1.0))) (cbrt (pow (/ (+ 1.0 x) (- x 1.0)) 3)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(cbrt (pow (/ (+ 1.0 x) (- x 1.0)) 3))
67.0ms	(pow (/ (+ 1.0 x) (- x 1.0)) 3)
44.0ms	(* x (/ 1 (+ x 1.0)))
186.0ms	(- (* x (/ 1 (+ x 1.0))) (cbrt (pow (/ (+ 1.0 x) (- x 1.0)) 3)))

simplify581.0ms

Counts

207 → 207

Iterations

Useful iterations: done (574.0ms)

Iter	Nodes	Cost
0	308	3785
1	1003	3087
done	5000	2772

prune449.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes30.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.7b

bsearch96.0ms

Steps

Iters	Range		Point
10	15.006088268796836	293663098603.6372	11268.544408709085
8	-28361.394281441724	-101.50163225226844	-10513.461931089661

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	26	57
1	37	42
done	37	42

end0.0ms

sample1.5s

Algorithm

intervals

Results

715.0ms	1750×	body	1280	valid
314.0ms	1258×	body	640	valid
157.0ms	4055×	body	80	valid
105.0ms	613×	body	320	valid
24.0ms	324×	body	160	valid