Details

sample13.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify2.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	6
1	6
0	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize8.0ms

Local error

Found 1 expressions with local error:

16.7b

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 29

Calls

1 calls:

22.0ms

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

series106.0ms

Counts

1 → 3

Calls

1 calls:

106.0ms

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

simplify1.1s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
2	783
1	183
0	74

prune171.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ x (sqrt (+ 1.0 (* x x)))) (sqrt (+ (* x x) 1.0)))
16.6b	(sqrt (+ 1.0 (* x x)))
16.6b	(sqrt (+ (* x x) 1.0))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
148×	`add-sqr-sqrt`
146×	`*-un-lft-identity` `add-cube-cbrt`
144×	`sqrt-prod`
24×	`associate-/l*`
20×	`sqrt-div`
16×	`associate-/r/`
10×	`flip3-+` `flip-+`
8×	`add-cbrt-cube` `add-exp-log` `div-inv`
6×	`associate-/r*`
5×	`pow1`
3×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`clear-num` `frac-2neg` `associate-/l/`

Counts

3 → 221

Calls

3 calls:

55.0ms	(/ (/ x (sqrt (+ 1.0 (* x x)))) (sqrt (+ (* x x) 1.0)))
8.0ms	(sqrt (+ 1.0 (* x x)))
15.0ms	(sqrt (+ (* x x) 1.0))

series224.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(/ (/ x (sqrt (+ 1.0 (* x x)))) (sqrt (+ (* x x) 1.0)))
68.0ms	(sqrt (+ 1.0 (* x x)))
61.0ms	(sqrt (+ (* x x) 1.0))

simplify1.4s

Counts

230 → 230

Iterations

Iter	Nodes
done	5001
2	3263
1	814
0	342

prune852.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ 1 (/ (+ 1.0 (* x x)) x))
16.6b	(/ (+ 1.0 (* x x)) x)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
52×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv`
3×	`pow1`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `add-log-exp` `associate-/l/`
1×	`flip3-+` `associate-/r/` `flip-+` `pow-flip` `inv-pow`

Counts

2 → 105

Calls

2 calls:

18.0ms	(/ 1 (/ (+ 1.0 (* x x)) x))
34.0ms	(/ (+ 1.0 (* x x)) x)

series178.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(/ 1 (/ (+ 1.0 (* x x)) x))
101.0ms	(/ (+ 1.0 (* x x)) x)

simplify1.3s

Counts

111 → 111

Iterations

Iter	Nodes
done	5000
2	2306
1	463
0	172

prune314.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))) (/ 1 x))
0.0b	(/ 1.0 (pow x 5))
0.1b	(/ 1.0 (pow x 3))
15.8b	(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

rewrite619.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
97×	`times-frac`
69×	`*-un-lft-identity`
47×	`add-cube-cbrt`
33×	`unpow-prod-down`
20×	`difference-of-squares`
19×	`associate-/r*`
17×	`sqr-pow`
16×	`cube-prod`
14×	`add-exp-log`
11×	`add-log-exp`
8×	`add-cbrt-cube` `distribute-lft-out--`
6×	`div-exp` `div-inv` `associate-/l*`
5×	`distribute-lft-out`
4×	`cube-mult` `pow1` `unpow3`
3×	`frac-add`
2×	`pow-to-exp` `cbrt-undiv` `associate-+l+` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `pow-exp` `frac-sub` `flip--`
1×	`+-commutative` `flip3-+` `associate-+l-` `flip-+`

Counts

4 → 171

Calls

4 calls:

513.0ms	(+ (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))) (/ 1 x))
9.0ms	(/ 1.0 (pow x 5))
7.0ms	(/ 1.0 (pow x 3))
83.0ms	(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))) (/ 1 x))
67.0ms	(/ 1.0 (pow x 5))
55.0ms	(/ 1.0 (pow x 3))
196.0ms	(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

simplify1.3s

Counts

183 → 183

Iterations

Iter	Nodes
done	5002
2	2555
1	576
0	258

prune853.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes74.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.6b

bsearch95.0ms

Steps

Iters	Range		Point
8	5.1212688054922095	257785.57693934403	446.6796391904089
8	-346749.28651926527	-205.8624528279525	-503.9443077846877

simplify3.0ms

Iterations

Iter	Nodes
done	31
1	31
0	25

end0.0ms

sample536.0ms

Algorithm

intervals

Results

355.0ms

8000×

body

valid