Details

sample13.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	82×	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 3 expressions with local error:

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

rewrite33.0ms

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:

11.0ms	(+ 1.0 (sqrt (+ x 1.0)))
4.0ms	(sqrt (+ x 1.0))
16.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series230.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(+ 1.0 (sqrt (+ x 1.0)))
38.0ms	(sqrt (+ x 1.0))
148.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify556.0ms

Counts

70 → 70

Iterations

Useful iterations: done (554.0ms)

Iter	Nodes	Cost
0	140	917
1	316	848
2	1041	783
done	5000	775

prune138.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

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)
2.7b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.6b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite110.0ms

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:

21.0ms	(* (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))))
58.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
67.0ms	(pow (sqrt (+ x 1.0)) 3)
71.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
208.0ms	(/ 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

prune443.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

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:

8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
4.0ms	(sqrt (+ x 1.0))
17.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
48.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series548.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ 1.0 (sqrt (+ x 1.0)))
31.0ms	(sqrt (+ x 1.0))
319.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
148.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify614.0ms

Counts

144 → 144

Iterations

Useful iterations: done (610.0ms)

Iter	Nodes	Cost
0	216	2303
1	529	2031
2	1858	1857
done	5000	1848

prune260.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

185×	`sqrt-prod`
116×	`*-un-lft-identity`
104×	`times-frac`
98×	`add-sqr-sqrt`
68×	`add-cube-cbrt`
66×	`associate-r`
24×	`distribute-lft-out`
18×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
10×	`pow-prod-down`
8×	`associate-/r/` `unswap-sqr`
7×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-l`
6×	`rem-sqrt-square`
4×	`flip3-+` `associate-*r/` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
3×	`sqrt-unprod`
2×	`*-commutative`
1×	`frac-times` `associate-*l/`

Counts

4 → 202

Calls

4 calls:

20.0ms	(sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))
22.0ms	(sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))
50.0ms	(* (sqrt x) (sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))))
283.0ms	(* (* (sqrt x) (sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))) (sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))))

series900.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))
252.0ms	(sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))
260.0ms	(* (sqrt x) (sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))))
140.0ms	(* (* (sqrt x) (sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))) (sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))))

simplify948.0ms

Counts

214 → 214

Iterations

Useful iterations: done (941.0ms)

Iter	Nodes	Cost
0	321	4787
1	790	4174
2	2829	3813
done	5001	3811

prune494.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes33.0ms

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	6	8
1	8	8
done	8	8

end0.0ms

sample311.0ms

Algorithm

intervals

Results

158.0ms	7997×	body	80	valid
39.0ms	2656×	body	80	nan
0.0ms	3×	body	1280	valid