Details

sample13.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	79×	body	80	nan

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4
done	8	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 3 expressions with local error:

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

rewrite54.0ms

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-exp-log` `add-cbrt-cube` `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` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 61

Calls

3 calls:

7.0ms	(sqrt (+ x 1.0))
17.0ms	(+ 1.0 (sqrt (+ x 1.0)))
28.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series195.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(sqrt (+ x 1.0))
41.0ms	(+ 1.0 (sqrt (+ x 1.0)))
126.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify34.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	317	483
1	1159	435
2	5001	427
done	5001	427

prune125.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize6.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

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×	`flip3-+` `div-exp` `prod-exp` `associate-/r*` `sqrt-prod` `associate-/r/` `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` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 106

Calls

4 calls:

7.0ms	(sqrt (+ x 1.0))
14.0ms	(+ 1.0 (sqrt (+ x 1.0)))
67.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
30.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ x 1.0))
39.0ms	(+ 1.0 (sqrt (+ x 1.0)))
128.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
93.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

simplify54.0ms

Counts

118 → 118

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	452	821
1	1973	707
2	5001	668
done	5001	668

prune171.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3)))
0.2b	(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
0.2b	(pow (sqrt (+ x 1.0)) 3)
8.3b	(cbrt (pow (sqrt (+ x 1.0)) 3))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
23×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`cbrt-prod`
16×	`sqrt-prod`
14×	`unpow-prod-down` `cube-prod`
12×	`times-frac`
9×	`distribute-lft-out`
7×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`cube-div` `flip3-+` `sqrt-div` `associate-/r*` `flip-+`
3×	`pow-unpow` `pow-pow` `associate-/l*`
2×	`cube-mult` `cbrt-div` `unpow3` `associate-/r/` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `div-exp` `pow-exp` `clear-num` `sum-log` `sqrt-pow2` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 112

Calls

4 calls:

31.0ms	(+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3)))
66.0ms	(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
9.0ms	(pow (sqrt (+ x 1.0)) 3)
9.0ms	(cbrt (pow (sqrt (+ x 1.0)) 3))

series264.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3)))
135.0ms	(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
58.0ms	(pow (sqrt (+ x 1.0)) 3)
32.0ms	(cbrt (pow (sqrt (+ x 1.0)) 3))

simplify53.0ms

Counts

124 → 124

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	462	878
1	1929	749
2	5002	731
done	5002	731

prune204.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
52×	`times-frac`
39×	`add-cube-cbrt` `sqrt-prod`
30×	`associate-r`
15×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-l` `associate-/l*` `add-log-exp` `unswap-sqr`
4×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 132

Calls

4 calls:

6.0ms	(sqrt (+ x 1.0))
15.0ms	(+ 1.0 (sqrt (+ x 1.0)))
30.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
76.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series475.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt (+ x 1.0))
38.0ms	(+ 1.0 (sqrt (+ x 1.0)))
285.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
124.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify68.0ms

Counts

144 → 144

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	529	1281
1	2243	1134
2	5001	1107
done	5001	1107

prune245.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	5
1	13	5
done	13	5

end0.0ms

sample341.0ms

Algorithm

intervals

Results

156.0ms	7998×	body	80	valid
39.0ms	2650×	body	80	nan
0.0ms	2×	body	1280	valid