Details

sample276.0ms

Algorithm

intervals

Results

160.0ms	110×	body	1280	valid
70.0ms	73×	body	640	valid
22.0ms	51×	body	320	valid
9.0ms	256×	pre	80	true
3.0ms	15×	body	160	valid
1.0ms	7×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	11
2	11
1	10
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.4b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1 x)) (log (+ 1 x)))
4.7b	(log (+ 1 x))
4.8b	(log (- 1 x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`times-frac`
15×	`pow1` `add-cube-cbrt`
12×	`log-pow`
10×	`log-prod`
7×	`add-exp-log`
6×	`log-div`
5×	`add-cbrt-cube`
4×	`associate-/r` `associate-/l`
3×	`insert-posit16` `add-log-exp`
2×	`flip3--` `div-sub` `rem-log-exp` `flip--` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--`

Counts

3 → 73

Calls

3 calls:

22.0ms	(/ (log (- 1 x)) (log (+ 1 x)))
5.0ms	(log (+ 1 x))
7.0ms	(log (- 1 x))

series143.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (log (- 1 x)) (log (+ 1 x)))
22.0ms	(log (+ 1 x))
40.0ms	(log (- 1 x))

simplify1.4s

Counts

82 → 82

Iterations

Iter	Nodes
3	3507
2	1069
1	388
0	178

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 1 expressions with local error:

0.0b	(- (- -1 (* x (* x 1/2))) x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
3×	`add-sqr-sqrt` `*-un-lft-identity` `diff-log`
2×	`sub-neg` `associate--l+`
1×	`associate--l-` `pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 19

Calls

1 calls:

20.0ms

(- (- -1 (* x (* x 1/2))) x)

series34.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

(- (- -1 (* x (* x 1/2))) x)

simplify1.6s

Counts

22 → 22

Iterations

Iter	Nodes
4	3885
3	806
2	249
1	99
0	48

prune178.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (- (- -1 (* x (* x 1/2))) x)) (cbrt (- (- -1 (* x (* x 1/2))) x)))
0.0b	(cbrt (- (- -1 (* x (* x 1/2))) x))
0.0b	(cbrt (- (- -1 (* x (* x 1/2))) x))
0.0b	(cbrt (- (- -1 (* x (* x 1/2))) x))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
37×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 105

Calls

4 calls:

115.0ms	(* (cbrt (- (- -1 (* x (* x 1/2))) x)) (cbrt (- (- -1 (* x (* x 1/2))) x)))
9.0ms	(cbrt (- (- -1 (* x (* x 1/2))) x))
15.0ms	(cbrt (- (- -1 (* x (* x 1/2))) x))
19.0ms	(cbrt (- (- -1 (* x (* x 1/2))) x))

series420.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (cbrt (- (- -1 (* x (* x 1/2))) x)) (cbrt (- (- -1 (* x (* x 1/2))) x)))
99.0ms	(cbrt (- (- -1 (* x (* x 1/2))) x))
86.0ms	(cbrt (- (- -1 (* x (* x 1/2))) x))
110.0ms	(cbrt (- (- -1 (* x (* x 1/2))) x))

simplify973.0ms

Counts

117 → 117

Iterations

Iter	Nodes
3	2180
2	847
1	350
0	161

prune999.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (cbrt -1) (+ (* 2/3 (* (cbrt -1) x)) (cbrt -1))) (* (* (* (cbrt -1) x) (* (cbrt -1) x)) 2/9))
0.0b	(cbrt (- (- -1 (* x (* x 1/2))) x))
0.2b	(* (* (* (cbrt -1) x) (* (cbrt -1) x)) 2/9)
0.4b	(* 2/3 (* (cbrt -1) x))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1` `add-exp-log`
22×	`add-cbrt-cube`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`cbrt-prod`
4×	`associate-r` `associate-l` `insert-posit16`
2×	`associate-+l+` `cbrt-div` `*-commutative`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `flip3-+` `flip3--` `pow1/3` `flip-+` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

79.0ms	(+ (* (cbrt -1) (+ (* 2/3 (* (cbrt -1) x)) (cbrt -1))) (* (* (* (cbrt -1) x) (* (cbrt -1) x)) 2/9))
17.0ms	(cbrt (- (- -1 (* x (* x 1/2))) x))
113.0ms	(* (* (* (cbrt -1) x) (* (cbrt -1) x)) 2/9)
20.0ms	(* 2/3 (* (cbrt -1) x))

series524.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(+ (* (cbrt -1) (+ (* 2/3 (* (cbrt -1) x)) (cbrt -1))) (* (* (* (cbrt -1) x) (* (cbrt -1) x)) 2/9))
91.0ms	(cbrt (- (- -1 (* x (* x 1/2))) x))
159.0ms	(* (* (* (cbrt -1) x) (* (cbrt -1) x)) 2/9)
90.0ms	(* 2/3 (* (cbrt -1) x))

simplify10.3s

Counts

90 → 90

Iterations

Iter	Nodes
3	11375
2	1987
1	489
0	186

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes37.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	9
1	9
0	7

end0.0ms

sample8.9s

Algorithm

intervals

Results

5.6s	3315×	body	1280	valid
2.1s	2594×	body	640	valid
532.0ms	1260×	body	320	valid
351.0ms	8000×	pre	80	true
158.0ms	616×	body	160	valid
25.0ms	215×	body	80	valid