Details

sample40.0ms

Algorithm

intervals

Results

9.0ms	66×	body	1280	valid
8.0ms	138×	body	80	valid
7.0ms	245×	body	80	nan
2.0ms	21×	body	640	valid
2.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite32.0ms

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-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `distribute-lft-out`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 37

Calls

2 calls:

5.0ms	(sqrt (+ x 1.0))
27.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series138.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(sqrt (+ x 1.0))
101.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.7s

Counts

43 → 43

Iterations

Iter	Nodes
done	5000
3	1569
2	532
1	195
0	88

prune212.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 27.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.4b	(+ x (- 1.0 x))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

109×	`*-un-lft-identity`
45×	`distribute-lft-out`
32×	`sqrt-prod`
30×	`times-frac`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
11×	`add-log-exp`
8×	`distribute-lft-out--`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1` `flip3-+` `flip-+` `associate-/l*`
4×	`insert-posit16`
3×	`sum-log`
2×	`+-commutative` `associate-+r+` `associate-+r-` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 109

Calls

4 calls:

9.0ms	(sqrt (+ x 1.0))
24.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
73.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms	(+ x (- 1.0 x))

series282.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (+ x 1.0))
78.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
170.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.0ms	(+ x (- 1.0 x))

simplify1.2s

Counts

121 → 121

Iterations

Iter	Nodes
done	5001
2	1480
1	446
0	183

prune493.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 3 expressions with local error:

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

rewrite62.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `insert-posit16` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

3 → 74

Calls

3 calls:

4.0ms	(sqrt (+ x 1.0))
25.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
31.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series374.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(sqrt (+ x 1.0))
107.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
223.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.1s

Counts

83 → 83

Iterations

Iter	Nodes
done	5012
3	3786
2	1149
1	374
0	159

prune300.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ 1.0 (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.3b	(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
74×	`*-un-lft-identity`
32×	`distribute-lft-out`
30×	`add-sqr-sqrt`
28×	`sqrt-div`
21×	`pow1`
16×	`add-cube-cbrt`
15×	`swap-sqr`
14×	`flip3-+` `flip-+`
11×	`add-cbrt-cube` `add-exp-log`
10×	`sqrt-pow1` `pow1/2`
9×	`associate-r` `associate-l`
8×	`frac-times` `associate-/r/`
5×	`pow-prod-up`
4×	`associate-l/` `associate-r/` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`times-frac` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cbrt-undiv` `rem-sqrt-square` `div-exp` `prod-exp` `cbrt-unprod`
1×	`pow2` `clear-num` `associate-/r` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `-commutative` `div-inv`

Counts

4 → 139

Calls

4 calls:

37.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
32.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
51.0ms	(/ 1.0 (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
127.0ms	(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series797.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
214.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
202.0ms	(/ 1.0 (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
114.0ms	(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify2.1s

Counts

151 → 151

Iterations

Iter	Nodes
done	5002
2	1609
1	559
0	228

prune658.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes75.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
1	9
0	7

end0.0ms

sample2.0s

Algorithm

intervals

Results

685.0ms	1731×	body	1280	valid
502.0ms	7851×	body	80	nan
277.0ms	1233×	body	640	valid
177.0ms	4077×	body	80	valid
105.0ms	636×	body	320	valid
26.0ms	323×	body	160	valid