Details

sample12.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize5.0ms

Local error

Found 1 expressions with local error:

13.4b

(/ 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))

series105.0ms

Counts

1 → 3

Calls

1 calls:

105.0ms

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

simplify2.5s

Counts

32 → 32

Iterations

Useful iterations: 2 (116.0ms)

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

prune118.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* x x) 1.0)))
0.0b	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
13.3b	(sqrt (+ (* x x) 1.0))
13.3b	(sqrt (+ (* x x) 1.0))

rewrite153.0ms

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:

34.0ms	(/ x (sqrt (+ (* x x) 1.0)))
62.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
16.0ms	(sqrt (+ (* x x) 1.0))
11.0ms	(sqrt (+ (* x x) 1.0))

series421.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ x (sqrt (+ (* x x) 1.0)))
104.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
54.0ms	(sqrt (+ (* x x) 1.0))
76.0ms	(sqrt (+ (* x x) 1.0))

simplify3.1s

Counts

274 → 274

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	336	7324
1	766	6348
2	1626	5885
3	4560	5656
done	5001	5542

prune683.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 2 expressions with local error:

5.4b	(/ x (- (pow x 4) (* 1.0 1.0)))
19.4b	(* (/ x (- (pow x 4) (* 1.0 1.0))) (- (* x x) 1.0))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
37×	`times-frac`
24×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
22×	`difference-of-squares`
9×	`add-exp-log` `add-cbrt-cube`
7×	`unpow-prod-down` `sqr-pow`
6×	`associate-/r*`
4×	`pow1` `flip3--` `associate-r` `associate-/r/` `flip--`
3×	`associate-/l*`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-times` `sub-neg` `distribute-lft-in` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

2 → 93

Calls

2 calls:

42.0ms	(/ x (- (pow x 4) (* 1.0 1.0)))
107.0ms	(* (/ x (- (pow x 4) (* 1.0 1.0))) (- (* x x) 1.0))

series353.0ms

Counts

2 → 6

Calls

2 calls:

195.0ms	(/ x (- (pow x 4) (* 1.0 1.0)))
158.0ms	(* (/ x (- (pow x 4) (* 1.0 1.0))) (- (* x x) 1.0))

simplify1.6s

Counts

99 → 99

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	199	1803
1	492	1731
2	1562	1573
done	5000	1369

prune314.0ms

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 x) (/ 1.0 (pow x 5)))
0.0b	(/ 1.0 (pow x 5))
0.4b	(/ 1.0 (pow x 3))
18.5b	(- (+ (/ 1 x) (/ 1.0 (pow x 5))) (/ 1.0 (pow x 3)))

rewrite607.0ms

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:

70.0ms	(+ (/ 1 x) (/ 1.0 (pow x 5)))
13.0ms	(/ 1.0 (pow x 5))
9.0ms	(/ 1.0 (pow x 3))
503.0ms	(- (+ (/ 1 x) (/ 1.0 (pow x 5))) (/ 1.0 (pow x 3)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (/ 1 x) (/ 1.0 (pow x 5)))
61.0ms	(/ 1.0 (pow x 5))
65.0ms	(/ 1.0 (pow x 3))
82.0ms	(- (+ (/ 1 x) (/ 1.0 (pow x 5))) (/ 1.0 (pow x 3)))

simplify1.3s

Counts

163 → 163

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	229	2276
1	472	2013
2	1501	1931
done	5000	1915

prune500.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes49.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.8b

bsearch76.0ms

Steps

Iters	Range		Point
10	8.937283511995443e-05	28405617999702.24	434.3260566585274
8	-3122934099202797.0	-115102859795.89769	-4377789621347.088

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	26	53
1	33	39
done	33	39

end0.0ms

sample475.0ms

Algorithm

intervals

Results

337.0ms

8000×

body

valid