Details

sample116.0ms

Algorithm

intervals

Results

37.0ms	254×	body	160	nan
35.0ms	550×	body	80	nan
21.0ms	256×	body	80	valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
9	3422
8	1055
7	442
6	232
5	95
4	58
3	33
2	17
1	14
0	7

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (+ x (sqrt (- (* x x) 1))))
0.0b	(+ x (sqrt (- (* x x) 1)))
34.3b	(sqrt (- (* x x) 1))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
6×	`sqrt-prod`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`log-prod` `add-exp-log`
3×	`add-cbrt-cube` `insert-posit16`
2×	`log-div` `flip3-+` `sqrt-div` `flip-+` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3--` `pow1/2` `difference-of-sqr-1` `rem-log-exp` `log-pow` `flip--`

Counts

3 → 48

Calls

3 calls:

11.0ms	(log (+ x (sqrt (- (* x x) 1))))
15.0ms	(+ x (sqrt (- (* x x) 1)))
9.0ms	(sqrt (- (* x x) 1))

series270.0ms

Counts

3 → 9

Calls

3 calls:

146.0ms	(log (+ x (sqrt (- (* x x) 1))))
75.0ms	(+ x (sqrt (- (* x x) 1)))
48.0ms	(sqrt (- (* x x) 1))

simplify3.5s

Counts

57 → 57

Iterations

Iter	Nodes
4	5713
3	1912
2	697
1	298
0	135

prune435.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
0.0b	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.5b	(* (sqrt (+ x 1)) (sqrt (- x 1)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`sqrt-prod`
13×	`*-un-lft-identity`
12×	`sqrt-div`
10×	`associate-r`
8×	`pow1` `add-cube-cbrt`
7×	`associate-l`
6×	`add-exp-log`
5×	`flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`frac-times` `unswap-sqr`
3×	`log-prod` `flip3--` `pow-prod-down` `insert-posit16` `flip--`
2×	`log-div` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `difference-of-squares`
1×	`+-commutative` `sum-log` `sqrt-unprod` `difference-of-sqr-1` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

3 → 71

Calls

3 calls:

9.0ms	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
9.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
48.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

series365.0ms

Counts

3 → 9

Calls

3 calls:

195.0ms	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
87.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
82.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify1.1s

Counts

80 → 80

Iterations

Iter	Nodes
3	2640
2	917
1	386
0	175

prune780.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))))
0.4b	(* (sqrt (log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))) (sqrt (log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))))
0.5b	(* (sqrt (+ x 1)) (sqrt (- x 1)))
0.5b	(* (sqrt (+ x 1)) (sqrt (- x 1)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-prod`
58×	`add-sqr-sqrt`
35×	`pow1`
33×	`*-un-lft-identity`
27×	`associate-r`
24×	`sqrt-div`
21×	`associate-l` `add-cube-cbrt`
13×	`sqrt-pow1` `pow1/2`
12×	`unswap-sqr`
11×	`swap-sqr`
10×	`add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down`
8×	`frac-times`
7×	`log-pow`
6×	`flip3-+` `flip3--` `flip-+` `flip--`
5×	`pow-prod-up`
4×	`associate-l/` `associate-r/` `insert-posit16` `add-log-exp` `difference-of-squares`
3×	`sqrt-unprod` `prod-exp` `pow-sqr` `*-commutative` `cbrt-unprod`
2×	`difference-of-sqr-1` `distribute-lft-out` `distribute-lft-out--`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus`

Counts

4 → 158

Calls

4 calls:

1.0ms	(sqrt (log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))))
10.0ms	(* (sqrt (log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))) (sqrt (log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))))
28.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
24.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

series621.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(sqrt (log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))))
189.0ms	(* (sqrt (log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))) (sqrt (log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))))
121.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
88.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify1.7s

Counts

170 → 170

Iterations

Iter	Nodes
3	3790
2	1301
1	528
0	233

prune2.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	12
1	12
0	9

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.6s	7648×	body	160	nan
1.2s	8000×	body	80	valid
1.2s	16362×	body	80	nan