Details

sample58.0ms

Algorithm

intervals

Results

18.0ms	64×	body	640	valid
10.0ms	137×	body	80	valid
8.0ms	21×	body	1280	valid
5.0ms	22×	body	320	valid
2.0ms	12×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	18	15
2	31	15
3	41	15
4	88	15
5	135	15
6	162	15
7	211	15
8	441	15
9	1208	15
done	5000	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 2.0 x) (/ 1.0 (+ x 1.0)))
1.6b	(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (/ 1.0 (+ x 1.0))))

rewrite311.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

21.0ms	(/ 1.0 (- x 1.0))
11.0ms	(/ 1.0 (+ x 1.0))
54.0ms	(- (/ 2.0 x) (/ 1.0 (+ x 1.0)))
218.0ms	(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (/ 1.0 (+ x 1.0))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 1.0 (- x 1.0))
48.0ms	(/ 1.0 (+ x 1.0))
54.0ms	(- (/ 2.0 x) (/ 1.0 (+ x 1.0)))
299.0ms	(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (/ 1.0 (+ x 1.0))))

simplify1.4s

Counts

129 → 129

Iterations

Useful iterations: 2 (517.0ms)

Iter	Nodes	Cost
0	218	1924
1	547	1798
2	2164	1714
done	5000	1714

prune415.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.2b	(cbrt (+ x 1.0))
0.2b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
14.5b	(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (* (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (cbrt 1.0) (cbrt (+ x 1.0))))))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
32×	`cbrt-prod`
27×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr` `add-log-exp`
8×	`flip3-+` `pow1/3` `frac-sub` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
5×	`frac-times`
4×	`add-cbrt-cube` `unswap-sqr`
3×	`diff-log` `associate-r/` `associate-l/`
2×	`sub-neg` `flip3--` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip--` `associate--r+` `difference-of-squares`
1×	`pow2` `times-frac` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `associate--r-`

Counts

4 → 105

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))
50.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
129.0ms	(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (* (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (cbrt 1.0) (cbrt (+ x 1.0))))))

series742.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (+ x 1.0))
110.0ms	(cbrt (+ x 1.0))
141.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
374.0ms	(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (* (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (cbrt 1.0) (cbrt (+ x 1.0))))))

simplify2.1s

Counts

117 → 117

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	244	2741
1	657	2539
2	2990	1916
done	5001	1751

prune460.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* x (* (+ x 1.0) 1.0)) (* (- x 1.0) (- (* (+ x 1.0) 2.0) (* x 1.0)))) (* (* (- x 1.0) x) (+ x 1.0)))
0.0b	(- (* (+ x 1.0) 2.0) (* x 1.0))
0.0b	(* (* (- x 1.0) x) (+ x 1.0))
15.8b	(- (* x (* (+ x 1.0) 1.0)) (* (- x 1.0) (- (* (+ x 1.0) 2.0) (* x 1.0))))

rewrite860.0ms

Algorithm

rewrite-expression-head

Rules

56×	`associate-*l/`
44×	`associate-*r/`
33×	`flip3--` `flip--`
32×	`frac-sub`
24×	`frac-times`
22×	`flip3-+` `flip-+`
18×	`add-exp-log` `add-cbrt-cube` `associate-/l/`
9×	`pow1` `*-un-lft-identity`
8×	`associate-/r/` `add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`prod-exp` `cbrt-unprod`
4×	`sub-neg` `associate-r` `associate--r+`
3×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `times-frac` `div-exp` `pow-prod-down` `associate-/l*`
2×	`diff-log`
1×	`frac-2neg` `div-sub` `associate-l` `clear-num` `associate-/r` `-commutative` `div-inv` `distribute-lft-out`

Counts

4 → 123

Calls

4 calls:

255.0ms	(/ (- (* x (* (+ x 1.0) 1.0)) (* (- x 1.0) (- (* (+ x 1.0) 2.0) (* x 1.0)))) (* (* (- x 1.0) x) (+ x 1.0)))
19.0ms	(- (* (+ x 1.0) 2.0) (* x 1.0))
439.0ms	(* (* (- x 1.0) x) (+ x 1.0))
133.0ms	(- (* x (* (+ x 1.0) 1.0)) (* (- x 1.0) (- (* (+ x 1.0) 2.0) (* x 1.0))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (- (* x (* (+ x 1.0) 1.0)) (* (- x 1.0) (- (* (+ x 1.0) 2.0) (* x 1.0)))) (* (* (- x 1.0) x) (+ x 1.0)))
38.0ms	(- (* (+ x 1.0) 2.0) (* x 1.0))
115.0ms	(* (* (- x 1.0) x) (+ x 1.0))
2.0ms	(- (* x (* (+ x 1.0) 1.0)) (* (- x 1.0) (- (* (+ x 1.0) 2.0) (* x 1.0))))

simplify616.0ms

Counts

135 → 135

Iterations

Useful iterations: done (608.0ms)

Iter	Nodes	Cost
0	279	4794
1	1073	4573
done	5001	4223

prune664.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- x 1.0) x)
0.0b	(* (* (- x 1.0) x) (+ x 1.0))
0.5b	(/ 2.0 (* (* (- x 1.0) x) (+ x 1.0)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log` `add-cbrt-cube`
18×	`associate-*l/`
12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`pow1`
8×	`frac-times` `add-cube-cbrt` `associate-/r/`
7×	`flip3--` `associate-r` `prod-exp` `flip--` `cbrt-unprod`
6×	`flip3-+` `associate-l` `flip-+`
4×	`associate-*r/` `pow-prod-down`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*` `add-log-exp`
2×	`*-commutative`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 82

Calls

3 calls:

29.0ms	(* (- x 1.0) x)
80.0ms	(* (* (- x 1.0) x) (+ x 1.0))
60.0ms	(/ 2.0 (* (* (- x 1.0) x) (+ x 1.0)))

series302.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(* (- x 1.0) x)
122.0ms	(* (* (- x 1.0) x) (+ x 1.0))
133.0ms	(/ 2.0 (* (* (- x 1.0) x) (+ x 1.0)))

simplify1.9s

Counts

91 → 91

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	153	1247
1	460	1211
2	3262	1051
done	5001	1039

prune203.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes16.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
done	10	11

end0.0ms

sample1.4s

Algorithm

intervals

Results

466.0ms	1890×	body	640	valid
417.0ms	4197×	body	80	valid
132.0ms	563×	body	1280	valid
127.0ms	916×	body	320	valid
42.0ms	436×	body	160	valid