Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 13.6b

localize10.0ms

Local error

Found 1 expressions with local error:

13.6b

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

rewrite16.0ms

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:

15.0ms

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

series95.0ms

Counts

1 → 3

Calls

1 calls:

95.0ms

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

simplify672.0ms

Counts

32 → 32

Iterations

Useful iterations: done (670.0ms)

Iter	Nodes	Cost
0	74	428
1	183	415
2	802	377
done	5001	375

prune97.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* x x) 1.0)))
0.0b	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
13.6b	(sqrt (+ (* x x) 1.0))
13.6b	(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`
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` `pow-flip` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `associate-/l*`
2×	`rem-sqrt-square`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `inv-pow`

Counts

4 → 164

Calls

4 calls:

21.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
108.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
18.0ms	(sqrt (+ (* x x) 1.0))
28.0ms	(sqrt (+ (* x x) 1.0))

series275.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
83.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
48.0ms	(sqrt (+ (* x x) 1.0))
60.0ms	(sqrt (+ (* x x) 1.0))

simplify2.8s

Counts

176 → 176

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	225	3329
1	689	3027
2	4377	2647
done	5001	2643

prune390.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.6b	(/ 1 (+ (* x x) 1.0))
12.9b	(* x (/ 1 (+ (* x x) 1.0)))

rewrite90.0ms

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:

26.0ms	(/ 1 (+ (* x x) 1.0))
60.0ms	(* x (/ 1 (+ (* x x) 1.0)))

series143.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ 1 (+ (* x x) 1.0))
91.0ms	(* x (/ 1 (+ (* x x) 1.0)))

simplify1.8s

Counts

77 → 77

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	128	985
1	352	882
2	2025	733
done	5001	727

prune191.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x x) 1.0)
0.1b	(* x (pow x 3))
3.2b	(/ x (- (* x (pow x 3)) (* 1.0 1.0)))
19.1b	(* (/ x (- (* x (pow x 3)) (* 1.0 1.0))) (- (* x x) 1.0))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-l`
16×	`add-exp-log` `associate-r`
13×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp` `unswap-sqr`
5×	`flip3--` `prod-exp` `flip--`
4×	`unpow-prod-down` `cube-prod` `associate-/r/`
3×	`sub-neg` `associate-/r` `cbrt-unprod` `associate-/l`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-r/` `div-exp` `-commutative` `div-inv` `difference-of-squares` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `frac-2neg` `diff-log` `unpow3` `pow-prod-down` `associate-*l/` `pow-exp` `clear-num` `pow-prod-up`

Counts

4 → 117

Calls

4 calls:

10.0ms	(- (* x x) 1.0)
19.0ms	(* x (pow x 3))
28.0ms	(/ x (- (* x (pow x 3)) (* 1.0 1.0)))
110.0ms	(* (/ x (- (* x (pow x 3)) (* 1.0 1.0))) (- (* x x) 1.0))

series426.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* x x) 1.0)
60.0ms	(* x (pow x 3))
172.0ms	(/ x (- (* x (pow x 3)) (* 1.0 1.0)))
142.0ms	(* (/ x (- (* x (pow x 3)) (* 1.0 1.0))) (- (* x x) 1.0))

simplify3.9s

Counts

129 → 129

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	202	2068
1	599	1974
2	4015	1560
done	5000	1556

prune435.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes35.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.7b

bsearch82.0ms

Steps

Iters	Range		Point
8	1.4124627081995123	1575.9184687212278	986.0371090468709
4	-2.529568732130994e+18	-1.3980170606481126e+18	-2.4658381815044797e+18

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	25	55
1	33	41
done	33	41

end0.0ms

sample539.0ms

Algorithm

intervals

Results

338.0ms

8000×

body

valid