Details

sample13.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	76×	body	80	nan

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
done	8	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 45

Calls

2 calls:

8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
17.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series185.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(+ 1.0 (sqrt (+ x 1.0)))
141.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify513.0ms

Counts

51 → 51

Iterations

Useful iterations: done (511.0ms)

Iter	Nodes	Cost
0	117	739
1	277	693
2	954	636
done	5000	630

prune99.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (pow (+ 1.0 (sqrt (+ x 1.0))) 1))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`unpow-prod-down`
8×	`associate-/r*`
7×	`add-exp-log`
5×	`distribute-lft-out`
4×	`add-cbrt-cube` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-/l*`
2×	`pow1`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `flip3-+` `pow-exp` `clear-num` `sum-log` `flip-+` `div-inv`

Counts

2 → 61

Calls

2 calls:

8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
34.0ms	(/ x (pow (+ 1.0 (sqrt (+ x 1.0))) 1))

series183.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(+ 1.0 (sqrt (+ x 1.0)))
139.0ms	(/ x (pow (+ 1.0 (sqrt (+ x 1.0))) 1))

simplify504.0ms

Counts

67 → 67

Iterations

Useful iterations: done (502.0ms)

Iter	Nodes	Cost
0	151	1180
1	335	964
2	1234	856
done	5000	852

prune106.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(pow (sqrt (+ x 1.0)) 3)
3.2b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.3b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite106.0ms

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×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-/r*` `add-cbrt-cube`
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×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `pow-plus` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 184

Calls

4 calls:

20.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
5.0ms	(pow (sqrt (+ x 1.0)) 3)
13.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
57.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
69.0ms	(pow (sqrt (+ x 1.0)) 3)
61.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
190.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify1.3s

Counts

196 → 196

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	313	4015
1	736	2931
2	3191	2700
done	5000	2696

prune430.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

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)))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
53×	`add-sqr-sqrt`
52×	`times-frac`
37×	`add-cube-cbrt`
35×	`sqrt-prod`
30×	`associate-r`
14×	`distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l` `associate-/l*` `unswap-sqr`
5×	`pow1` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

3 → 116

Calls

3 calls:

8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
20.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
45.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series485.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ 1.0 (sqrt (+ x 1.0)))
304.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
133.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify587.0ms

Counts

125 → 125

Iterations

Useful iterations: done (583.0ms)

Iter	Nodes	Cost
0	193	2125
1	491	1876
2	1772	1710
done	5000	1703

prune220.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes14.0ms

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: 1 (1.0ms)

Iter	Nodes	Cost
0	8	10
1	12	8
done	12	8

end0.0ms

sample298.0ms

Algorithm

intervals

Results

150.0ms	7998×	body	80	valid
38.0ms	2640×	body	80	nan
0.0ms	2×	body	1280	valid