Details

sample14.0ms

Algorithm

intervals

Results

5.0ms

256×

body

valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 15.7b

localize4.0ms

Local error

Found 1 expressions with local error:

15.7b

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

rewrite7.0ms

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:

6.0ms

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

series59.0ms

Counts

1 → 3

Calls

1 calls:

59.0ms

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

simplify1.6s

Counts

32 → 32

Iterations

Useful iterations: 3 (174.0ms)

Iter	Nodes	Cost
0	74	428
1	167	413
2	404	375
3	951	373
4	2588	373
done	5000	373

prune63.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ 1 (+ (* x x) 1.0))
15.6b	(* x (/ 1 (+ (* x x) 1.0)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`times-frac`
19×	`*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`add-exp-log` `associate-r`
9×	`add-cbrt-cube`
5×	`pow1`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

2 → 71

Calls

2 calls:

6.0ms	(/ 1 (+ (* x x) 1.0))
18.0ms	(* x (/ 1 (+ (* x x) 1.0)))

series98.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ 1 (+ (* x x) 1.0))
59.0ms	(* x (/ 1 (+ (* x x) 1.0)))

simplify1.7s

Counts

77 → 77

Iterations

Useful iterations: 3 (577.0ms)

Iter	Nodes	Cost
0	128	985
1	315	827
2	722	727
3	2196	725
done	5000	725

prune107.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ (* x x) 1.0))
0.2b	(/ 1 (+ (* x x) 1.0))
15.6b	(sqrt (/ 1 (+ (* x x) 1.0)))
15.6b	(sqrt (/ 1 (+ (* x x) 1.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
40×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
30×	`sqrt-prod`
12×	`add-exp-log`
10×	`pow1`
8×	`associate-/r/` `add-cbrt-cube`
6×	`rem-sqrt-square` `sqrt-pow1` `associate-/r` `associate-/l`
4×	`pow-flip` `flip3-+` `div-exp` `flip-+` `div-inv` `inv-pow` `add-log-exp`
2×	`cbrt-undiv` `rec-exp` `frac-2neg` `pow1/2` `sqrt-div` `1-exp` `clear-num`

Counts

4 → 126

Calls

4 calls:

6.0ms	(/ 1 (+ (* x x) 1.0))
6.0ms	(/ 1 (+ (* x x) 1.0))
6.0ms	(sqrt (/ 1 (+ (* x x) 1.0)))
7.0ms	(sqrt (/ 1 (+ (* x x) 1.0)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1 (+ (* x x) 1.0))
44.0ms	(/ 1 (+ (* x x) 1.0))
77.0ms	(sqrt (/ 1 (+ (* x x) 1.0)))
77.0ms	(sqrt (/ 1 (+ (* x x) 1.0)))

simplify1.4s

Counts

138 → 138

Iterations

Useful iterations: 3 (427.0ms)

Iter	Nodes	Cost
0	138	1850
1	285	1598
2	688	1464
3	2326	1446
done	5000	1446

prune234.0ms

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 5)) (/ 1.0 (pow x 3))))
0.1b	(/ 1.0 (pow x 5))
0.1b	(/ 1.0 (pow x 3))
16.5b	(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

rewrite239.0ms

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×	`pow1` `cube-mult` `unpow3`
3×	`frac-add`
2×	`cbrt-undiv` `pow-to-exp` `sub-neg` `associate-+r+` `flip3--` `frac-2neg` `diff-log` `pow-exp` `clear-num` `sum-log` `frac-sub` `flip--`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 171

Calls

4 calls:

167.0ms	(+ (/ 1 x) (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))))
3.0ms	(/ 1.0 (pow x 5))
4.0ms	(/ 1.0 (pow x 3))
58.0ms	(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (/ 1 x) (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))))
49.0ms	(/ 1.0 (pow x 5))
35.0ms	(/ 1.0 (pow x 3))
128.0ms	(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

simplify791.0ms

Counts

183 → 183

Iterations

Useful iterations: 2 (336.0ms)

Iter	Nodes	Cost
0	257	2827
1	568	2514
2	1571	2418
done	5001	2418

prune352.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes24.0ms

Accuracy

100% (0.0b remaining)

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

bsearch48.0ms

Steps

Iters	Range		Point
7	179.5191949529741	4368.076441928604	1964.7084475756017
8	-3540160029299381.0	-131863331651.28616	-6092285729639.722

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	22	47
1	30	33
done	30	33

end0.0ms

sample227.0ms

Algorithm

intervals

Results

141.0ms

8000×

body

valid