Details

sample43.0ms

Algorithm

intervals

Results

13.0ms	67×	body	640	valid
6.0ms	124×	body	80	valid
6.0ms	20×	body	1280	valid
5.0ms	31×	body	320	valid
1.0ms	14×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
10	4810
9	1188
8	437
7	210
6	162
5	135
4	89
3	41
2	31
1	18
0	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.5b

localize17.0ms

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))
1.7b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite455.0ms

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-cbrt-cube` `add-exp-log` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `associate-+l+` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

11.0ms	(/ 1.0 (+ x 1.0))
18.0ms	(/ 1.0 (- x 1.0))
65.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
358.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1.0 (+ x 1.0))
47.0ms	(/ 1.0 (- x 1.0))
53.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
315.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.1s

Counts

126 → 126

Iterations

Iter	Nodes
done	5002
2	1953
1	515
0	212

prune515.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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)))
1.7b	(+ (+ (/ 1.0 (+ x 1.0)) (- (/ 2.0 x))) (/ 1.0 (- x 1.0)))

rewrite587.0ms

Algorithm

rewrite-expression-head

Rules

88×	`*-un-lft-identity`
43×	`times-frac`
31×	`add-sqr-sqrt`
24×	`distribute-lft-out`
23×	`add-cube-cbrt`
16×	`add-log-exp`
9×	`associate-/r*`
8×	`distribute-rgt-neg-in` `add-cbrt-cube` `add-exp-log`
7×	`sum-log`
6×	`associate-/l*` `distribute-lft-out--`
5×	`frac-add`
4×	`pow1` `flip3-+` `associate-/r/` `flip-+` `difference-of-squares`
3×	`associate-+l-`
2×	`neg-sub0` `cbrt-undiv` `+-commutative` `clear-num` `associate-+r-` `frac-2neg` `div-exp` `unsub-neg` `neg-log` `div-inv` `distribute-neg-frac`
1×	`associate-+l+` `flip3--` `flip--`

Counts

4 → 117

Calls

4 calls:

15.0ms	(/ 1.0 (+ x 1.0))
15.0ms	(/ 1.0 (- x 1.0))
74.0ms	(+ (/ 1.0 (+ x 1.0)) (- (/ 2.0 x)))
476.0ms	(+ (+ (/ 1.0 (+ x 1.0)) (- (/ 2.0 x))) (/ 1.0 (- x 1.0)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ 1.0 (+ x 1.0))
53.0ms	(/ 1.0 (- x 1.0))
56.0ms	(+ (/ 1.0 (+ x 1.0)) (- (/ 2.0 x)))
373.0ms	(+ (+ (/ 1.0 (+ x 1.0)) (- (/ 2.0 x))) (/ 1.0 (- x 1.0)))

simplify1.4s

Counts

129 → 129

Iterations

Iter	Nodes
done	5000
2	2323
1	530
0	208

prune612.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (- (/ 2.0 x)))
0.1b	(/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
6.8b	(+ (+ (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (- (/ 2.0 x))) (/ 1.0 (- x 1.0)))

rewrite3.1s

Algorithm

rewrite-expression-head

Rules

386×	`times-frac`
329×	`*-un-lft-identity`
224×	`sqrt-prod`
188×	`add-sqr-sqrt` `add-cube-cbrt`
68×	`distribute-lft-out`
30×	`associate-/l*`
20×	`sqrt-div` `associate-/r/`
16×	`add-log-exp`
14×	`associate-/r*`
13×	`flip3-+` `flip-+`
11×	`add-cbrt-cube` `add-exp-log`
10×	`div-inv`
7×	`sum-log`
5×	`distribute-rgt-neg-in` `frac-add`
4×	`pow1` `cbrt-undiv` `div-exp`
3×	`associate-+l-`
2×	`neg-sub0` `+-commutative` `clear-num` `associate-+r-` `frac-2neg` `unsub-neg` `neg-log` `distribute-neg-frac`
1×	`associate-+l+` `distribute-lft-out--` `associate-/l/`

Counts

4 → 329

Calls

4 calls:

387.0ms	(+ (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (- (/ 2.0 x)))
45.0ms	(/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
10.0ms	(/ 1.0 (sqrt (+ x 1.0)))
2.7s	(+ (+ (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (- (/ 2.0 x))) (/ 1.0 (- x 1.0)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (- (/ 2.0 x)))
49.0ms	(/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
106.0ms	(/ 1.0 (sqrt (+ x 1.0)))
290.0ms	(+ (+ (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (- (/ 2.0 x))) (/ 1.0 (- x 1.0)))

simplify2.2s

Counts

341 → 341

Iterations

Iter	Nodes
done	5001
2	4419
1	1018
0	404

prune1.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ 1.0 x))
1.2b	(- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))) (/ 2.0 x))
2.9b	(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))

rewrite683.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

10.0ms	(/ 1.0 (- x 1.0))
10.0ms	(/ 1.0 (+ 1.0 x))
573.0ms	(- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))) (/ 2.0 x))
85.0ms	(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 1.0 (- x 1.0))
39.0ms	(/ 1.0 (+ 1.0 x))
289.0ms	(- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))) (/ 2.0 x))
196.0ms	(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))

simplify1.3s

Counts

133 → 133

Iterations

Iter	Nodes
done	5001
2	2152
1	540
0	216

prune568.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 9.6b

bsearch170.0ms

Steps

Iters	Range		Point
10	2.777137017098532e-16	1126.7541422477805	119.61241846924294
9	-291337.82152789796	-0.7274215675205146	-105.69285877795477

simplify7.0ms

Iterations

Iter	Nodes
done	40
2	40
1	39
0	29

end0.0ms

sample1.9s

Algorithm

intervals

Results

905.0ms	1803×	body	640	valid
343.0ms	4238×	body	80	valid
264.0ms	951×	body	320	valid
151.0ms	568×	body	1280	valid
48.0ms	440×	body	160	valid