Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize9.0ms

Local error

Found 1 expressions with local error:

13.2b

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

rewrite29.0ms

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:

27.0ms

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

series82.0ms

Counts

1 → 3

Calls

1 calls:

82.0ms

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

simplify2.6s

Counts

32 → 32

Iterations

Useful iterations: 2 (87.0ms)

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

prune110.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* x x) 1.0)))
0.0b	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
13.1b	(sqrt (+ (* x x) 1.0))
13.1b	(sqrt (+ (* x x) 1.0))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 158

Calls

4 calls:

17.0ms	(/ x (sqrt (+ (* x x) 1.0)))
134.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
12.0ms	(sqrt (+ (* x x) 1.0))
16.0ms	(sqrt (+ (* x x) 1.0))

series402.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ x (sqrt (+ (* x x) 1.0)))
74.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
77.0ms	(sqrt (+ (* x x) 1.0))
58.0ms	(sqrt (+ (* x x) 1.0))

simplify2.2s

Counts

170 → 170

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	228	3302
1	589	2939
2	1745	2433
done	5000	2426

prune479.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ 1 (/ (sqrt (+ (* x x) 1.0)) x)))
0.1b	(/ 1 (/ (sqrt (+ (* x x) 1.0)) x))
13.1b	(sqrt (+ (* x x) 1.0))
13.1b	(sqrt (+ (* x x) 1.0))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

354×	`times-frac`
277×	`add-sqr-sqrt`
185×	`*-un-lft-identity`
156×	`add-cube-cbrt`
102×	`sqrt-prod`
98×	`add-exp-log`
71×	`associate-r`
49×	`div-exp`
35×	`unswap-sqr`
30×	`add-cbrt-cube`
28×	`prod-exp`
24×	`associate-l`
22×	`associate-/r*`
17×	`rec-exp` `1-exp`
12×	`cbrt-undiv`
11×	`pow1`
10×	`div-inv`
6×	`sqrt-div` `cbrt-unprod`
4×	`associate-/r/` `add-log-exp`
3×	`pow-flip` `flip3-+` `pow-prod-down` `flip-+` `associate-/l*` `inv-pow`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `un-div-inv` `*-commutative`

Counts

4 → 321

Calls

4 calls:

128.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ 1 (/ (sqrt (+ (* x x) 1.0)) x)))
25.0ms	(/ 1 (/ (sqrt (+ (* x x) 1.0)) x))
10.0ms	(sqrt (+ (* x x) 1.0))
11.0ms	(sqrt (+ (* x x) 1.0))

series403.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ 1 (/ (sqrt (+ (* x x) 1.0)) x)))
174.0ms	(/ 1 (/ (sqrt (+ (* x x) 1.0)) x))
63.0ms	(sqrt (+ (* x x) 1.0))
59.0ms	(sqrt (+ (* x x) 1.0))

simplify2.2s

Counts

333 → 333

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	401	7816
1	1085	6418
2	2328	5351
done	5000	5206

prune629.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 x) (/ 1.0 (pow x 3)))
0.3b	(/ 1.0 (pow x 3))
0.5b	(/ 1.0 (pow x 5))
21.0b	(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

rewrite509.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

61.0ms	(- (/ 1 x) (/ 1.0 (pow x 3)))
9.0ms	(/ 1.0 (pow x 3))
8.0ms	(/ 1.0 (pow x 5))
421.0ms	(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (/ 1 x) (/ 1.0 (pow x 3)))
70.0ms	(/ 1.0 (pow x 3))
81.0ms	(/ 1.0 (pow x 5))
78.0ms	(+ (- (/ 1 x) (/ 1.0 (pow x 3))) (/ 1.0 (pow x 5)))

simplify1.5s

Counts

175 → 175

Iterations

Useful iterations: 2 (442.0ms)

Iter	Nodes	Cost
0	251	2490
1	510	2209
2	1454	2125
done	5001	2125

prune614.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes92.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.1b

bsearch103.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	529.597454464039
10	-6045414056204.408	-123.41774798665298	-853997951174.7607

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	21	45
1	28	31
done	28	31

end0.0ms

sample509.0ms

Algorithm

intervals

Results

326.0ms

8000×

body

valid