Details

sample24.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
1.0ms	47×	body	80	nan

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite91.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
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 → 64

Calls

3 calls:

18.0ms	(sqrt (+ x 1.0))
25.0ms	(+ 1.0 (sqrt (+ x 1.0)))
42.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series322.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(sqrt (+ x 1.0))
75.0ms	(+ 1.0 (sqrt (+ x 1.0)))
203.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.4s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
2	1073
1	319
0	140

prune630.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ x (+ (* (sqrt (+ 1.0 x)) (+ 1.0 x)) (* 1.0 (* 1.0 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
4.6b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.3b	(/ x (+ (* (sqrt (+ 1.0 x)) (+ 1.0 x)) (* 1.0 (* 1.0 1.0))))

rewrite704.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-div`
54×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
34×	`flip3-+` `flip-+`
30×	`associate-*r/` `add-cube-cbrt`
26×	`sqrt-prod`
25×	`times-frac` `associate-l`
21×	`pow1`
16×	`frac-sub`
14×	`frac-times` `cube-unmult`
13×	`add-cbrt-cube` `add-exp-log`
11×	`swap-sqr`
10×	`associate-r`
9×	`associate-*l/`
8×	`sqrt-pow1` `pow1/2`
7×	`sum-cubes`
6×	`distribute-lft-out` `add-log-exp` `unswap-sqr`
5×	`pow-prod-up`
4×	`associate-/r*` `pow-prod-down` `associate-/r/` `insert-posit16` `sub-div`
3×	`prod-exp` `pow-sqr` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `*-commutative` `div-inv`
1×	`pow2` `distribute-rgt-in` `clear-num` `sub-neg` `rem-square-sqrt` `frac-2neg` `distribute-lft-in` `pow-plus` `flip3--` `distribute-rgt-out--` `sqrt-unprod` `diff-log` `flip--`

Counts

4 → 175

Calls

4 calls:

505.0ms	(* (/ x (+ (* (sqrt (+ 1.0 x)) (+ 1.0 x)) (* 1.0 (* 1.0 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
58.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
40.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
81.0ms	(/ x (+ (* (sqrt (+ 1.0 x)) (+ 1.0 x)) (* 1.0 (* 1.0 1.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

666.0ms	(* (/ x (+ (* (sqrt (+ 1.0 x)) (+ 1.0 x)) (* 1.0 (* 1.0 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
35.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
122.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
379.0ms	(/ x (+ (* (sqrt (+ 1.0 x)) (+ 1.0 x)) (* 1.0 (* 1.0 1.0))))

simplify6.6s

Counts

187 → 187

Iterations

Iter	Nodes
done	5008
2	4610
1	1206
0	388

prune1.8s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite335.0ms

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-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-l` `associate-/l*` `add-log-exp` `unswap-sqr`
4×	`associate-/r*` `flip3-+` `associate-/r/` `flip-+` `insert-posit16`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 136

Calls

4 calls:

20.0ms	(sqrt (+ x 1.0))
42.0ms	(+ 1.0 (sqrt (+ x 1.0)))
88.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
173.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series824.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sqrt (+ x 1.0))
67.0ms	(+ 1.0 (sqrt (+ x 1.0)))
464.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
230.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify3.9s

Counts

148 → 148

Iterations

Iter	Nodes
done	5002
2	1904
1	551
0	217

prune1.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ x (+ 1.0 (sqrt (+ x 1.0)))))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))
0.4b	(* (sqrt (/ x (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (/ x (+ 1.0 (sqrt (+ x 1.0))))))

rewrite566.0ms

Algorithm

rewrite-expression-head

Rules

134×	`*-un-lft-identity`
116×	`sqrt-prod`
103×	`times-frac`
101×	`add-sqr-sqrt`
70×	`add-cube-cbrt`
29×	`swap-sqr` `distribute-lft-out`
21×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
10×	`add-cbrt-cube` `add-exp-log`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
8×	`associate-/r*`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 208

Calls

4 calls:

89.0ms	(sqrt (/ x (+ 1.0 (sqrt (+ x 1.0)))))
81.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
56.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
309.0ms	(* (sqrt (/ x (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (/ x (+ 1.0 (sqrt (+ x 1.0))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

380.0ms	(sqrt (/ x (+ 1.0 (sqrt (+ x 1.0)))))
244.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
218.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
243.0ms	(* (sqrt (/ x (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (/ x (+ 1.0 (sqrt (+ x 1.0))))))

simplify3.6s

Counts

220 → 220

Iterations

Iter	Nodes
done	5002
2	1758
1	526
0	242

prune1.7s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes166.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	8
1	8
0	6

end0.0ms

sample757.0ms

Algorithm

intervals

Results

372.0ms	7999×	body	80	valid
118.0ms	2672×	body	80	nan
0.0ms	1×	body	1280	valid