Details

sample24.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	6
1	6
0	5

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize13.0ms

Local error

Found 1 expressions with local error:

15.0b

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

rewrite25.0ms

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:

23.0ms

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

series115.0ms

Counts

1 → 3

Calls

1 calls:

115.0ms

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

simplify1.1s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
2	783
1	183
0	74

prune151.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ 1.0 (* x x))))
0.0b	(/ (/ x (sqrt (+ 1.0 (* x x)))) (sqrt (+ (* x x) 1.0)))
15.0b	(sqrt (+ 1.0 (* x x)))
15.0b	(sqrt (+ (* x x) 1.0))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 262

Calls

4 calls:

14.0ms	(/ x (sqrt (+ 1.0 (* x x))))
55.0ms	(/ (/ x (sqrt (+ 1.0 (* x x)))) (sqrt (+ (* x x) 1.0)))
5.0ms	(sqrt (+ 1.0 (* x x)))
8.0ms	(sqrt (+ (* x x) 1.0))

series383.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ x (sqrt (+ 1.0 (* x x))))
74.0ms	(/ (/ x (sqrt (+ 1.0 (* x x)))) (sqrt (+ (* x x) 1.0)))
56.0ms	(sqrt (+ 1.0 (* x x)))
68.0ms	(sqrt (+ (* x x) 1.0))

simplify1.5s

Counts

274 → 274

Iterations

Iter	Nodes
done	5002
2	3493
1	874
0	368

prune972.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))) (/ 1 x))
0.1b	(/ 1.0 (pow x 3))
0.3b	(/ 1.0 (pow x 5))
20.1b	(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

rewrite751.0ms

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:

610.0ms	(+ (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))) (/ 1 x))
13.0ms	(/ 1.0 (pow x 3))
13.0ms	(/ 1.0 (pow x 5))
104.0ms	(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(+ (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))) (/ 1 x))
70.0ms	(/ 1.0 (pow x 3))
70.0ms	(/ 1.0 (pow x 5))
205.0ms	(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

simplify1.1s

Counts

183 → 183

Iterations

Iter	Nodes
done	5001
2	2560
1	576
0	258

prune763.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes141.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.5b

bsearch56.0ms

Steps

Iters	Range		Point
7	13.800596953327334	2205.5689030668646	507.01009039307485
2	-3.2275392569223236e+62	-2.967245708633018e+62	-3.1950025633861604e+62

simplify3.0ms

Iterations

Iter	Nodes
done	28
1	28
0	21

end0.0ms

sample511.0ms

Algorithm

intervals

Results

332.0ms

8000×

body

valid