Details

sample64.0ms

Algorithm

intervals

Results

21.0ms	50×	body	1280	valid
12.0ms	137×	body	80	valid
11.0ms	33×	body	640	valid
5.0ms	21×	body	320	valid
2.0ms	15×	body	160	valid

simplify243.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	168
15	168
14	165
13	136
12	114
11	99
10	89
9	69
8	53
7	42
6	32
5	26
4	23
3	22
2	19
1	15
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ (+ x 1) (- x 1))
4.1b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity`
60×	`times-frac`
57×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
20×	`distribute-lft-out`
18×	`distribute-lft-out--`
14×	`difference-of-squares`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`difference-of-sqr-1` `add-log-exp`
4×	`associate-/r/`
3×	`pow1` `insert-posit16`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `flip-+` `div-inv` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 117

Calls

3 calls:

15.0ms	(/ x (+ x 1))
19.0ms	(/ (+ x 1) (- x 1))
62.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series179.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(/ x (+ x 1))
30.0ms	(/ (+ x 1) (- x 1))
118.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify2.3s

Counts

126 → 126

Iterations

Iter	Nodes
done	5008
3	3663
2	1074
1	399
0	180

prune490.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1))
0.0b	(/ 1 (- x 1))
0.1b	(* (+ x 1) (/ 1 (- x 1)))
7.8b	(- (/ x (+ x 1)) (* (+ x 1) (/ 1 (- x 1))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
69×	`*-un-lft-identity`
56×	`times-frac`
37×	`add-cube-cbrt`
27×	`associate-r`
19×	`add-exp-log`
14×	`difference-of-squares`
13×	`add-cbrt-cube`
11×	`associate-/r*`
7×	`pow1` `difference-of-sqr-1` `distribute-lft-out--`
6×	`associate-/r/` `frac-sub` `associate-/l*` `add-log-exp`
5×	`flip3-+` `div-exp` `flip-+` `distribute-lft-out`
4×	`frac-times` `associate-l` `associate-*l/` `prod-exp` `insert-posit16`
3×	`cbrt-undiv` `flip3--` `div-inv` `flip--` `unswap-sqr`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-*r/` `un-div-inv` `cbrt-unprod`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 159

Calls

4 calls:

16.0ms	(/ x (+ x 1))
13.0ms	(/ 1 (- x 1))
29.0ms	(* (+ x 1) (/ 1 (- x 1)))
73.0ms	(- (/ x (+ x 1)) (* (+ x 1) (/ 1 (- x 1))))

series185.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ x (+ x 1))
15.0ms	(/ 1 (- x 1))
30.0ms	(* (+ x 1) (/ 1 (- x 1)))
99.0ms	(- (/ x (+ x 1)) (* (+ x 1) (/ 1 (- x 1))))

simplify1.6s

Counts

171 → 171

Iterations

Iter	Nodes
done	5014
2	2340
1	607
0	238

prune603.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ 1 x) (* (- x 1) (- x 1)))
0.1b	(* x (* (- x 1) (- x 1)))
0.1b	(* (- (* x x) 1) (+ 1 x))
21.4b	(- (* x (* (- x 1) (- x 1))) (* (- (* x x) 1) (+ 1 x)))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

122×	`associate-*r/`
100×	`frac-times` `flip3--` `flip--`
64×	`frac-sub`
44×	`associate-*l/`
36×	`flip3-+` `flip-+`
26×	`distribute-rgt-in` `distribute-lft-in`
16×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`add-sqr-sqrt` `sub-neg` `-un-lft-identity` `associate-l*`
8×	`associate--l+` `add-cube-cbrt`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-r` `add-log-exp`
4×	`insert-posit16`
3×	`*-commutative` `unswap-sqr`
2×	`distribute-lft-out` `associate--r+` `difference-of-squares`
1×	`diff-log` `difference-of-sqr-1`

Counts

4 → 211

Calls

4 calls:

54.0ms	(* (+ 1 x) (* (- x 1) (- x 1)))
47.0ms	(* x (* (- x 1) (- x 1)))
48.0ms	(* (- (* x x) 1) (+ 1 x))
76.0ms	(- (* x (* (- x 1) (- x 1))) (* (- (* x x) 1) (+ 1 x)))

series143.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (+ 1 x) (* (- x 1) (- x 1)))
39.0ms	(* x (* (- x 1) (- x 1)))
29.0ms	(* (- (* x x) 1) (+ 1 x))
35.0ms	(- (* x (* (- x 1) (- x 1))) (* (- (* x x) 1) (+ 1 x)))

simplify1.8s

Counts

223 → 223

Iterations

Iter	Nodes
done	5000
1	1829
0	465

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- x 1) (- x 1))
0.1b	(* (+ 1 x) (* (- x 1) (- x 1)))
0.2b	(* (* x x) 3)
17.3b	(/ (+ (* x 2) (- 1 (* (* x x) 3))) (* (+ 1 x) (* (- x 1) (- x 1))))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

60×	`frac-times`
42×	`flip3--` `flip--`
36×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
30×	`associate-*r/`
26×	`associate-/r/`
25×	`add-cbrt-cube` `add-exp-log`
21×	`pow1`
19×	`flip3-+` `flip-+`
18×	`associate-*l/`
12×	`associate-l` `add-cube-cbrt`
11×	`swap-sqr` `associate-r`
10×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `cbrt-unprod` `difference-of-squares`
7×	`pow-prod-down`
6×	`sub-neg` `difference-of-sqr-1` `distribute-lft-out--`
4×	`insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `-commutative` `associate-/l` `unswap-sqr`
2×	`associate-/l/`
1×	`pow2` `clear-num` `associate-+r-` `associate-/r*` `frac-2neg` `pow-plus` `div-sub` `pow-sqr` `pow-prod-up` `div-inv` `distribute-lft-out`

Counts

4 → 182

Calls

4 calls:

34.0ms	(* (- x 1) (- x 1))
85.0ms	(* (+ 1 x) (* (- x 1) (- x 1)))
16.0ms	(* (* x x) 3)
106.0ms	(/ (+ (* x 2) (- 1 (* (* x x) 3))) (* (+ 1 x) (* (- x 1) (- x 1))))

series178.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (- x 1) (- x 1))
39.0ms	(* (+ 1 x) (* (- x 1) (- x 1)))
32.0ms	(* (* x x) 3)
85.0ms	(/ (+ (* x 2) (- 1 (* (* x x) 3))) (* (+ 1 x) (* (- x 1) (- x 1))))

simplify2.3s

Counts

194 → 194

Iterations

Iter	Nodes
done	5022
2	3721
1	863
0	269

prune663.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

regimes45.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 20.6b

bsearch136.0ms

Steps

Iters	Range		Point
9	68.55102067575892	801012902.7811656	176552.52851234598
7	-1777058.6317446793	-17438.246738609338	-350706.4836362626

simplify15.0ms

Iterations

Iter	Nodes
done	63
3	63
2	60
1	52
0	32

end0.0ms

sample1.9s

Algorithm

intervals

Results

893.0ms	1695×	body	1280	valid
337.0ms	1221×	body	640	valid
310.0ms	4115×	body	80	valid
205.0ms	641×	body	320	valid
61.0ms	328×	body	160	valid