Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
3.0ms	85×	body	80	nan

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 1 expressions with local error:

0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
12×	`times-frac`
10×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`associate-/r*` `distribute-lft-out`
3×	`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 → 33

Calls

1 calls:

44.0ms

(/ x (+ 1.0 (sqrt (+ x 1.0))))

series223.0ms

Counts

1 → 3

Calls

1 calls:

223.0ms

(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify865.0ms

Counts

36 → 36

Iterations

Iter	Nodes
done	5002
2	1136
1	227
0	95

prune144.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ x (+ (* (* 1.0 1.0) 1.0) (* (+ 1.0 x) (sqrt (+ 1.0 x))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
3.9b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.7b	(/ x (+ (* (* 1.0 1.0) 1.0) (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

rewrite453.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-div`
54×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
34×	`flip3-+` `flip-+`
30×	`associate-*r/` `add-cube-cbrt`
26×	`sqrt-prod`
25×	`times-frac` `associate-l`
21×	`pow1`
16×	`frac-sub`
14×	`frac-times` `pow3`
13×	`add-cbrt-cube` `add-exp-log`
11×	`swap-sqr`
10×	`associate-r`
9×	`associate-*l/`
8×	`sqrt-pow1` `pow1/2`
7×	`sum-cubes`
6×	`distribute-lft-out` `add-log-exp` `unswap-sqr`
5×	`pow-prod-up`
4×	`associate-/r*` `pow-prod-down` `associate-/r/` `sub-div`
3×	`prod-exp` `pow-sqr` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `*-commutative` `div-inv`
1×	`pow2` `distribute-rgt-in` `clear-num` `sub-neg` `rem-square-sqrt` `frac-2neg` `distribute-lft-in` `pow-plus` `flip3--` `distribute-rgt-out--` `sqrt-unprod` `diff-log` `flip--`

Counts

4 → 171

Calls

4 calls:

312.0ms	(* (/ x (+ (* (* 1.0 1.0) 1.0) (* (+ 1.0 x) (sqrt (+ 1.0 x))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
48.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
25.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
53.0ms	(/ x (+ (* (* 1.0 1.0) 1.0) (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

series839.0ms

Counts

4 → 12

Calls

4 calls:

502.0ms	(* (/ x (+ (* (* 1.0 1.0) 1.0) (* (+ 1.0 x) (sqrt (+ 1.0 x))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
19.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
74.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
244.0ms	(/ x (+ (* (* 1.0 1.0) 1.0) (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

simplify1.5s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
1	1213
0	384

prune1.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
0.1b	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

360×	`times-frac`
280×	`*-un-lft-identity`
186×	`sqrt-prod`
182×	`add-sqr-sqrt` `add-cube-cbrt`
49×	`distribute-lft-out`
34×	`associate-/r*`
10×	`associate-/l*`
9×	`add-cbrt-cube` `add-exp-log` `div-inv`
4×	`cbrt-undiv` `div-exp`
2×	`pow1` `clear-num` `frac-2neg` `add-log-exp` `associate-/l/`
1×	`flip3-+` `associate-/r/` `flip-+`

Counts

2 → 265

Calls

2 calls:

70.0ms	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
54.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))

series434.0ms

Counts

2 → 6

Calls

2 calls:

245.0ms	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
188.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))

simplify1.4s

Counts

271 → 271

Iterations

Iter	Nodes
done	5001
1	903
0	336

prune994.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes26.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 7.4b

bsearch84.0ms

Steps

Iters	Range		Point
9	1.3550353371818475e+23	1.9162286267887673e+31	4.4800399799935e+28

simplify14.0ms

Iterations

Iter	Nodes
done	37
3	37
2	35
1	31
0	23

end0.0ms

sample752.0ms

Algorithm

intervals

Results

403.0ms	7999×	body	80	valid
131.0ms	2645×	body	80	nan
0.0ms	1×	body	1280	valid