Details

sample22.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
2.0ms	81×	body	80	nan

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

localize9.0ms

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))))

rewrite125.0ms

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:

42.0ms	(+ 1.0 (sqrt (+ x 1.0)))
14.0ms	(sqrt (+ x 1.0))
65.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series348.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(+ 1.0 (sqrt (+ x 1.0)))
53.0ms	(sqrt (+ x 1.0))
217.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify911.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (298.0ms)

Iter	Nodes	Cost
0	140	917
1	326	848
2	1523	785
done	5001	785

prune189.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x 1.0)))
0.1b	(sqrt (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
0.2b	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-r/` `associate-l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 161

Calls

4 calls:

8.0ms	(sqrt (sqrt (+ x 1.0)))
9.0ms	(sqrt (sqrt (+ x 1.0)))
14.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
89.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series567.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(sqrt (sqrt (+ x 1.0)))
148.0ms	(sqrt (sqrt (+ x 1.0)))
194.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
52.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify1.7s

Counts

173 → 173

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	242	2891
1	561	1781
2	2711	1679
done	5001	1670

prune511.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sqrt (+ x 1.0)) 3)
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
4.8b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.0b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite301.0ms

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	(pow (sqrt (+ x 1.0)) 3)
69.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
40.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
151.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(pow (sqrt (+ x 1.0)) 3)
35.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
117.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
311.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify1.2s

Counts

196 → 196

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	313	4015
1	895	2975
done	5001	2738

prune649.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite284.0ms

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:

58.0ms	(+ (sqrt (+ x 1.0)) 1.0)
15.0ms	(sqrt (+ x 1.0))
73.0ms	(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
127.0ms	(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

series751.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+ (sqrt (+ x 1.0)) 1.0)
54.0ms	(sqrt (+ x 1.0))
447.0ms	(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
188.0ms	(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

simplify3.9s

Counts

144 → 144

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	216	2303
1	556	2113
2	3970	1871
done	5000	1845

prune393.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes40.0ms

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

sample772.0ms

Algorithm

intervals

Results

385.0ms	7997×	body	80	valid
114.0ms	2645×	body	80	nan
1.0ms	3×	body	1280	valid