Details

sample18.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
2.0ms	95×	body	80	nan

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(+ 1.0 (sqrt (+ 1.0 x)))
0.2b	(/ x (+ 1.0 (sqrt (+ 1.0 x))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

3 → 61

Calls

3 calls:

11.0ms	(sqrt (+ 1.0 x))
15.0ms	(+ 1.0 (sqrt (+ 1.0 x)))
28.0ms	(/ x (+ 1.0 (sqrt (+ 1.0 x))))

series273.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(sqrt (+ 1.0 x))
55.0ms	(+ 1.0 (sqrt (+ 1.0 x)))
186.0ms	(/ x (+ 1.0 (sqrt (+ 1.0 x))))

simplify586.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	1502
1	317
0	137

prune283.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
26×	`times-frac`
23×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`distribute-lft-out`
8×	`pow1`
6×	`add-log-exp`
4×	`associate-/r*` `flip3-+` `div-exp` `prod-exp` `associate-/r/` `sqrt-prod` `flip-+`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-div` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 106

Calls

4 calls:

6.0ms	(sqrt (+ 1.0 x))
12.0ms	(+ 1.0 (sqrt (+ 1.0 x)))
32.0ms	(/ 1 (+ 1.0 (sqrt (+ 1.0 x))))
69.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ 1.0 x)))))

series373.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(sqrt (+ 1.0 x))
50.0ms	(+ 1.0 (sqrt (+ 1.0 x)))
121.0ms	(/ 1 (+ 1.0 (sqrt (+ 1.0 x))))
158.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ 1.0 x)))))

simplify879.0ms

Counts

118 → 118

Iterations

Iter	Nodes
done	5002
2	2462
1	467
0	183

prune380.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sqrt (+ 1.0 x)) 3)
0.2b	(* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x)))
3.7b	(- (* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x))) (* 1.0 (sqrt (+ 1.0 x))))
6.8b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ 1.0 x)) 3)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
62×	`sqrt-div`
43×	`add-sqr-sqrt`
34×	`sqrt-prod`
32×	`flip3-+` `flip-+`
31×	`add-cube-cbrt`
28×	`associate-*r/` `distribute-lft-out`
27×	`times-frac`
23×	`unpow-prod-down` `cube-prod`
21×	`pow1`
16×	`frac-sub`
12×	`frac-times`
11×	`swap-sqr`
9×	`associate-/r*` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log`
8×	`associate-*l/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`sum-cubes` `sub-div` `unswap-sqr`
3×	`pow-unpow` `pow-pow` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cube-div` `associate-/r/`
1×	`pow2` `cube-mult` `pow-to-exp` `cbrt-undiv` `clear-num` `sub-neg` `rem-square-sqrt` `frac-2neg` `pow-plus` `flip3--` `distribute-rgt-out--` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `sqrt-pow2` `flip--` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 184

Calls

4 calls:

8.0ms	(pow (sqrt (+ 1.0 x)) 3)
36.0ms	(* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x)))
26.0ms	(- (* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x))) (* 1.0 (sqrt (+ 1.0 x))))
74.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ 1.0 x)) 3)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(pow (sqrt (+ 1.0 x)) 3)
27.0ms	(* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x)))
96.0ms	(- (* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x))) (* 1.0 (sqrt (+ 1.0 x))))
263.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ 1.0 x)) 3)))

simplify493.0ms

Counts

196 → 196

Iterations

Iter	Nodes
done	5000
1	891
0	312

prune887.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ x (+ (pow 1.0 3) (* (sqrt (+ 1.0 x)) (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x))) (* 1.0 (sqrt (+ 1.0 x))))))
0.2b	(* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x)))
3.7b	(- (* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x))) (* 1.0 (sqrt (+ 1.0 x))))
6.8b	(/ x (+ (pow 1.0 3) (* (sqrt (+ 1.0 x)) (+ x 1.0))))

rewrite456.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-div`
45×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
34×	`flip3-+` `flip-+`
30×	`associate-*r/`
28×	`add-cube-cbrt`
26×	`sqrt-prod`
22×	`associate-l`
21×	`pow1`
19×	`times-frac`
16×	`frac-sub`
14×	`frac-times`
13×	`add-cbrt-cube` `add-exp-log`
11×	`swap-sqr`
10×	`associate-r`
9×	`associate-*l/`
8×	`sqrt-pow1` `pow1/2`
6×	`distribute-lft-out` `add-log-exp` `unswap-sqr`
5×	`pow-prod-up`
4×	`pow-prod-down` `associate-/r/` `sub-div`
3×	`associate-/r` `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 → 164

Calls

4 calls:

318.0ms	(* (/ x (+ (pow 1.0 3) (* (sqrt (+ 1.0 x)) (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x))) (* 1.0 (sqrt (+ 1.0 x))))))
55.0ms	(* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x)))
26.0ms	(- (* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x))) (* 1.0 (sqrt (+ 1.0 x))))
45.0ms	(/ x (+ (pow 1.0 3) (* (sqrt (+ 1.0 x)) (+ x 1.0))))

series792.0ms

Counts

4 → 12

Calls

4 calls:

423.0ms	(* (/ x (+ (pow 1.0 3) (* (sqrt (+ 1.0 x)) (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x))) (* 1.0 (sqrt (+ 1.0 x))))))
20.0ms	(* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x)))
63.0ms	(- (* (sqrt (+ 1.0 x)) (sqrt (+ 1.0 x))) (* 1.0 (sqrt (+ 1.0 x))))
286.0ms	(/ x (+ (pow 1.0 3) (* (sqrt (+ 1.0 x)) (+ x 1.0))))

simplify530.0ms

Counts

176 → 176

Iterations

Iter	Nodes
done	5001
1	1161
0	367

prune942.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	13
1	13
0	8

end0.0ms

sample587.0ms

Algorithm

intervals

Results

345.0ms	7998×	body	80	valid
69.0ms	2729×	body	80	nan
0.0ms	2×	body	1280	valid