Details

sample24.0ms

Algorithm

intervals

Results

11.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize9.0ms

Local error

Found 1 expressions with local error:

15.9b

(/ 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))

series70.0ms

Counts

1 → 3

Calls

1 calls:

70.0ms

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

simplify2.8s

Counts

32 → 32

Iterations

Useful iterations: 2 (118.0ms)

Iter	Nodes	Cost
0	74	428
1	167	413
2	438	373
3	1017	373
4	2805	373
done	5000	373

prune102.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
0.0b	(/ 1 (sqrt (+ (* x x) 1.0)))
15.8b	(sqrt (+ (* x x) 1.0))
15.8b	(sqrt (+ (* x x) 1.0))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
30×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`pow1` `sqrt-div` `div-exp`
8×	`prod-exp`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`rec-exp` `pow-flip` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `associate-/l*`
2×	`rem-sqrt-square`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `inv-pow`

Counts

4 → 164

Calls

4 calls:

143.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
23.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
14.0ms	(sqrt (+ (* x x) 1.0))
15.0ms	(sqrt (+ (* x x) 1.0))

series347.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
120.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
74.0ms	(sqrt (+ (* x x) 1.0))
76.0ms	(sqrt (+ (* x x) 1.0))

simplify4.2s

Counts

176 → 176

Iterations

Useful iterations: 3 (2.6s)

Iter	Nodes	Cost
0	225	3329
1	602	2901
2	1728	2399
3	4974	2392
done	5000	2392

prune486.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 1 expressions with local error:

15.9b

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

rewrite16.0ms

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:

15.0ms

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

series80.0ms

Counts

1 → 3

Calls

1 calls:

80.0ms

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

simplify3.1s

Counts

32 → 32

Iterations

Useful iterations: 2 (139.0ms)

Iter	Nodes	Cost
0	74	428
1	167	413
2	438	373
3	1017	373
4	2805	373
done	5000	373

prune115.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 (pow x 5)) (/ 1 x))
0.3b	(/ 1.0 (pow x 5))
0.4b	(/ 1.0 (pow x 3))
19.2b	(- (+ (/ 1.0 (pow x 5)) (/ 1 x)) (/ 1.0 (pow x 3)))

rewrite617.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 151

Calls

4 calls:

84.0ms	(+ (/ 1.0 (pow x 5)) (/ 1 x))
15.0ms	(/ 1.0 (pow x 5))
17.0ms	(/ 1.0 (pow x 3))
490.0ms	(- (+ (/ 1.0 (pow x 5)) (/ 1 x)) (/ 1.0 (pow x 3)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(+ (/ 1.0 (pow x 5)) (/ 1 x))
71.0ms	(/ 1.0 (pow x 5))
47.0ms	(/ 1.0 (pow x 3))
79.0ms	(- (+ (/ 1.0 (pow x 5)) (/ 1 x)) (/ 1.0 (pow x 3)))

simplify1.2s

Counts

163 → 163

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	229	2274
1	472	2011
2	1505	1921
done	5000	1903

prune550.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes57.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.7b

bsearch80.0ms

Steps

Iters	Range		Point
9	3.244205803610274e-06	1902.9075791774285	470.1828671092737
8	-2.6354521979890637e+33	-5.620501265456609e+28	-1.2032692145665368e+31

simplify9.0ms

Iterations

Useful iterations: done (9.0ms)

Iter	Nodes	Cost
0	26	54
1	34	37
done	34	33

end0.0ms

sample466.0ms

Algorithm

intervals

Results

293.0ms

8000×

body

valid