Details

sample25.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	6
1	6
0	5

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) 1.0)
15.5b	(/ x (+ (* x x) 1.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 40

Calls

2 calls:

6.0ms	(+ (* x x) 1.0)
11.0ms	(/ x (+ (* x x) 1.0))

series133.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(+ (* x x) 1.0)
88.0ms	(/ x (+ (* x x) 1.0))

simplify1.0s

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	943
1	224
0	85

prune206.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
0.0b	(/ x (sqrt (+ (* x x) 1.0)))
15.4b	(sqrt (+ (* x x) 1.0))
15.4b	(sqrt (+ (* x x) 1.0))

rewrite96.0ms

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:

39.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
13.0ms	(/ x (sqrt (+ (* x x) 1.0)))
8.0ms	(sqrt (+ (* x x) 1.0))
11.0ms	(sqrt (+ (* x x) 1.0))

series409.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
168.0ms	(/ x (sqrt (+ (* x x) 1.0)))
59.0ms	(sqrt (+ (* x x) 1.0))
75.0ms	(sqrt (+ (* x x) 1.0))

simplify2.2s

Counts

274 → 274

Iterations

Iter	Nodes
done	5001
2	1987
1	797
0	336

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (* x x))
0.5b	(/ 1 (+ 1.0 (* x x)))
14.9b	(* x (/ 1 (+ 1.0 (* x x))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 82

Calls

3 calls:

4.0ms	(+ 1.0 (* x x))
8.0ms	(/ 1 (+ 1.0 (* x x)))
33.0ms	(* x (/ 1 (+ 1.0 (* x x))))

series203.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(+ 1.0 (* x x))
56.0ms	(/ 1 (+ 1.0 (* x x)))
82.0ms	(* x (/ 1 (+ 1.0 (* x x))))

simplify1.6s

Counts

91 → 91

Iterations

Iter	Nodes
done	5001
2	1569
1	368
0	137

prune338.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (* x x))
0.1b	(* (+ (* x x) 1.0) (- 1.0 (* x x)))
2.9b	(/ x (* (+ (* x x) 1.0) (- 1.0 (* x x))))
20.2b	(* (/ x (* (+ (* x x) 1.0) (- 1.0 (* x x)))) (- 1.0 (* x x)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-cbrt-cube` `add-exp-log`
18×	`add-sqr-sqrt` `associate-l`
16×	`associate-/r/`
14×	`frac-times`
12×	`flip3--` `flip--`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`flip3-+` `flip-+`
8×	`pow1` `associate-r` `associate-*r/`
7×	`associate-*l/`
6×	`times-frac` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`sub-neg`
4×	`distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `div-exp`
3×	`associate-/l*` `difference-of-squares`
2×	`pow-prod-down` `*-commutative` `div-inv` `unswap-sqr`
1×	`clear-num` `associate-/r*` `frac-2neg` `diff-log`

Counts

4 → 117

Calls

4 calls:

4.0ms	(- 1.0 (* x x))
43.0ms	(* (+ (* x x) 1.0) (- 1.0 (* x x)))
14.0ms	(/ x (* (+ (* x x) 1.0) (- 1.0 (* x x))))
71.0ms	(* (/ x (* (+ (* x x) 1.0) (- 1.0 (* x x)))) (- 1.0 (* x x)))

series622.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- 1.0 (* x x))
200.0ms	(* (+ (* x x) 1.0) (- 1.0 (* x x)))
283.0ms	(/ x (* (+ (* x x) 1.0) (- 1.0 (* x x))))
91.0ms	(* (/ x (* (+ (* x x) 1.0) (- 1.0 (* x x)))) (- 1.0 (* x x)))

simplify2.1s

Counts

129 → 129

Iterations

Iter	Nodes
done	5065
2	2904
1	594
0	194

prune572.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes44.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 23.7b

bsearch60.0ms

Steps

Iters	Range		Point
9	28.34319947931986	37605091470.942024	207140092.44270322
8	-2980.3304644899954	-0.1501579911863904	-1117.2756278429308

simplify9.0ms

Iterations

Iter	Nodes
done	32
1	32
0	23

end0.0ms

sample470.0ms

Algorithm

intervals

Results

324.0ms

8000×

body

valid