Details

sample24.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	6	7
done	6	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize14.0ms

Local error

Found 1 expressions with local error:

15.3b

(/ x (+ (* x x) 1.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

28.0ms

(/ x (+ (* x x) 1.0))

series111.0ms

Counts

1 → 3

Calls

1 calls:

111.0ms

(/ x (+ (* x x) 1.0))

simplify1.1s

Counts

32 → 32

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	74	428
1	183	415
2	802	377
done	5001	375

prune177.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
0.0b	(/ x (sqrt (+ (* x x) 1.0)))
15.2b	(sqrt (+ (* x x) 1.0))
15.2b	(sqrt (+ (* x x) 1.0))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 262

Calls

4 calls:

81.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
39.0ms	(/ x (sqrt (+ (* x x) 1.0)))
20.0ms	(sqrt (+ (* x x) 1.0))
20.0ms	(sqrt (+ (* x x) 1.0))

series510.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
236.0ms	(/ x (sqrt (+ (* x x) 1.0)))
85.0ms	(sqrt (+ (* x x) 1.0))
83.0ms	(sqrt (+ (* x x) 1.0))

simplify3.5s

Counts

274 → 274

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	336	7324
1	835	6424
2	4182	5973
done	5000	5707

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 1 expressions with local error:

19.7b

(- (+ x (pow x 5)) (pow x 3))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-log-exp`
4×	`difference-of-squares`
2×	`diff-log` `distribute-lft-out--`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `unpow-prod-down` `flip3--` `cube-prod` `associate--l+` `sum-log` `add-cbrt-cube` `flip--` `distribute-lft-out` `sqr-pow`

Counts

1 → 20

Calls

1 calls:

159.0ms

(- (+ x (pow x 5)) (pow x 3))

series79.0ms

Counts

1 → 3

Calls

1 calls:

79.0ms

(- (+ x (pow x 5)) (pow x 3))

simplify4.8s

Counts

23 → 23

Iterations

Useful iterations: 3 (838.0ms)

Iter	Nodes	Cost
0	46	343
1	112	328
2	461	310
3	3812	304
done	5001	304

prune122.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 x) (/ 1.0 (pow x 3)))
0.1b	(/ 1.0 (pow x 5))
0.3b	(/ 1.0 (pow x 3))
18.7b	(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

rewrite765.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
84×	`times-frac`
70×	`*-un-lft-identity`
45×	`add-cube-cbrt`
27×	`unpow-prod-down`
19×	`associate-/r*`
15×	`cube-prod` `difference-of-squares`
14×	`add-exp-log`
11×	`add-log-exp` `sqr-pow`
8×	`add-cbrt-cube`
6×	`div-exp` `associate-/l*` `distribute-lft-out--`
4×	`pow1` `cube-mult` `unpow3` `div-inv` `distribute-lft-out`
3×	`frac-add`
2×	`cbrt-undiv` `pow-to-exp` `sub-neg` `associate-+l+` `flip3--` `frac-2neg` `diff-log` `pow-exp` `clear-num` `sum-log` `frac-sub` `flip--`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+`

Counts

4 → 163

Calls

4 calls:

89.0ms	(- (/ 1 x) (/ 1.0 (pow x 3)))
15.0ms	(/ 1.0 (pow x 5))
17.0ms	(/ 1.0 (pow x 3))
629.0ms	(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (/ 1 x) (/ 1.0 (pow x 3)))
95.0ms	(/ 1.0 (pow x 5))
78.0ms	(/ 1.0 (pow x 3))
92.0ms	(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

simplify2.3s

Counts

175 → 175

Iterations

Useful iterations: 2 (808.0ms)

Iter	Nodes	Cost
0	251	2490
1	556	2209
2	2664	2137
done	5002	2137

prune928.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes78.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.2b

bsearch106.0ms

Steps

Iters	Range		Point
10	2.8868360106527892e-08	453261925.93168354	742.6193916240435
6	-3.251690204975706e+154	-5.320162488446726e+153	-1.3440694370491086e+154

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	23	53
1	30	39
done	30	39

end0.0ms

sample686.0ms

Algorithm

intervals

Results

388.0ms

8000×

body

valid