Details

sample69.0ms

Algorithm

intervals

Results

13.0ms	286×	body	80	nan
10.0ms	45×	body	1280	valid
10.0ms	57×	body	640	valid
6.0ms	122×	body	80	valid
3.0ms	20×	body	320	valid
1.0ms	12×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize80.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

15.0ms	(sqrt (+ x 1.0))
85.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series190.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(sqrt (+ x 1.0))
135.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.1s

Counts

41 → 41

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	84	488
1	188	440
2	638	410
3	2563	402
done	5000	400

prune213.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
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 → 71

Calls

3 calls:

15.0ms	(sqrt (+ x 1.0))
71.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
85.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series419.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(sqrt (+ x 1.0))
107.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
262.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.2s

Counts

80 → 80

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	152	1125
1	361	1018
2	1505	937
done	5001	929

prune480.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite726.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 250

Calls

4 calls:

89.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
92.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
87.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
423.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

630.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
236.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
245.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
284.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify2.6s

Counts

262 → 262

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	311	6170
1	703	4400
2	3220	4128
done	5002	4073

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.2b	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

203×	`*-un-lft-identity`
168×	`sqrt-prod`
141×	`times-frac`
131×	`add-sqr-sqrt`
77×	`add-cube-cbrt`
68×	`distribute-lft-out`
60×	`associate-l`
37×	`associate-r`
34×	`add-exp-log`
22×	`add-cbrt-cube`
18×	`unswap-sqr`
16×	`sqrt-div`
15×	`pow1` `associate-/r*`
11×	`div-exp`
10×	`associate-/r/`
9×	`prod-exp`
6×	`cbrt-undiv` `frac-times` `associate-r/` `pow-prod-down` `associate-/l`
5×	`sqrt-pow1` `flip3-+` `cbrt-unprod` `flip-+` `div-inv`
4×	`associate-*l/` `add-log-exp`
3×	`rec-exp` `pow-flip` `pow1/2` `1-exp`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`sqrt-unprod` `swap-sqr` `inv-pow`

Counts

4 → 262

Calls

4 calls:

94.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
88.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
409.0ms	(* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
1.0s	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

452.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
245.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
245.0ms	(* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
293.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (* (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))))

simplify942.0ms

Counts

274 → 274

Iterations

Useful iterations: done (923.0ms)

Iter	Nodes	Cost
0	407	7103
1	1113	6491
done	5000	5808

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes133.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	33
1	21	33
done	21	33

end0.0ms

sample2.2s

Algorithm

intervals

Results

566.0ms	1773×	body	1280	valid
404.0ms	7916×	body	80	nan
339.0ms	4046×	body	80	valid
218.0ms	1235×	body	640	valid
148.0ms	617×	body	320	valid
29.0ms	329×	body	160	valid