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

localize6.0ms

Local error

Found 1 expressions with local error:

16.7b

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

rewrite13.0ms

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:

12.0ms

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

series82.0ms

Counts

1 → 3

Calls

1 calls:

82.0ms

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

simplify1.5s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
2	783
1	183
0	74

prune116.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ 1.0 (* x x))))
0.0b	(* (/ 1 (sqrt (+ 1.0 (* x x)))) (/ x (sqrt (+ 1.0 (* x x)))))
16.6b	(sqrt (+ 1.0 (* x x)))
16.6b	(sqrt (+ 1.0 (* x x)))

rewrite116.0ms

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` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `pow-flip` `associate-/l*`
2×	`rem-sqrt-square`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `inv-pow`

Counts

4 → 164

Calls

4 calls:

18.0ms	(/ 1 (sqrt (+ 1.0 (* x x))))
78.0ms	(* (/ 1 (sqrt (+ 1.0 (* x x)))) (/ x (sqrt (+ 1.0 (* x x)))))
4.0ms	(sqrt (+ 1.0 (* x x)))
4.0ms	(sqrt (+ 1.0 (* x x)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ 1 (sqrt (+ 1.0 (* x x))))
108.0ms	(* (/ 1 (sqrt (+ 1.0 (* x x)))) (/ x (sqrt (+ 1.0 (* x x)))))
76.0ms	(sqrt (+ 1.0 (* x x)))
64.0ms	(sqrt (+ 1.0 (* x x)))

simplify2.4s

Counts

176 → 176

Iterations

Iter	Nodes
done	5000
2	4410
1	689
0	224

prune577.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite37.0ms

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:

11.0ms	(/ 1 (/ (+ 1.0 (* x x)) x))
22.0ms	(/ (+ 1.0 (* x x)) x)

series188.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(/ 1 (/ (+ 1.0 (* x x)) x))
103.0ms	(/ (+ 1.0 (* x x)) x)

simplify1.1s

Counts

111 → 111

Iterations

Iter	Nodes
done	5000
2	2306
1	463
0	172

prune345.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize17.0ms

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)))

rewrite715.0ms

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:

587.0ms	(+ (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))) (/ 1 x))
11.0ms	(/ 1.0 (pow x 5))
13.0ms	(/ 1.0 (pow x 3))
96.0ms	(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))) (/ 1 x))
56.0ms	(/ 1.0 (pow x 5))
40.0ms	(/ 1.0 (pow x 3))
229.0ms	(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

simplify1.2s

Counts

183 → 183

Iterations

Iter	Nodes
done	5002
2	2555
1	576
0	258

prune697.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes55.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch71.0ms

Steps

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

simplify6.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample515.0ms

Algorithm

intervals

Results

335.0ms

8000×

body

valid