Details

sample31.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
3.0ms	100×	body	80	nan

simplify4.0ms

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: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`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×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u` `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` `hypot-def` `div-inv`

Counts

3 → 71

Calls

3 calls:

13.0ms	(sqrt (+ x 1.0))
27.0ms	(+ 1.0 (sqrt (+ x 1.0)))
42.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series292.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(sqrt (+ x 1.0))
49.0ms	(+ 1.0 (sqrt (+ x 1.0)))
209.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify854.0ms

Counts

80 → 80

Iterations

Iter	Nodes
done	5002
2	1541
1	333
0	143

prune401.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ 1.0 x)))
0.0b	(sqrt (sqrt (+ 1.0 x)))
0.1b	(/ x (+ 1.0 (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))))
0.2b	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

rewrite101.0ms

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-cbrt-cube` `add-exp-log` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `rem-sqrt-square` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-l/` `associate-r/` `associate-/r/`
1×	`pow2` `cbrt-undiv` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 169

Calls

4 calls:

10.0ms	(sqrt (sqrt (+ 1.0 x)))
7.0ms	(sqrt (sqrt (+ 1.0 x)))
7.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))))
65.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

series549.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(sqrt (sqrt (+ 1.0 x)))
134.0ms	(sqrt (sqrt (+ 1.0 x)))
235.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))))
43.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

simplify1.7s

Counts

181 → 181

Iterations

Iter	Nodes
done	5002
2	2760
1	568
0	245

prune697.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

360×	`times-frac`
288×	`*-un-lft-identity`
190×	`sqrt-prod`
189×	`add-sqr-sqrt`
186×	`add-cube-cbrt`
51×	`distribute-lft-out`
34×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/l*`
9×	`div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `flip-+`
2×	`clear-num` `frac-2neg` `sqrt-div` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/r/` `hypot-def`

Counts

4 → 305

Calls

4 calls:

6.0ms	(sqrt (+ x 1.0))
13.0ms	(+ 1.0 (sqrt (+ x 1.0)))
76.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
44.0ms	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

series827.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(sqrt (+ x 1.0))
73.0ms	(+ 1.0 (sqrt (+ x 1.0)))
515.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
184.0ms	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

simplify569.0ms

Counts

317 → 317

Iterations

Iter	Nodes
done	5000
1	1007
0	380

prune966.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt x) (cbrt (+ 1.0 (sqrt (+ 1.0 x)))))
0.9b	(cbrt (+ 1.0 (sqrt (+ 1.0 x))))
0.9b	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
0.9b	(cbrt (+ 1.0 (sqrt (+ x 1.0))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
42×	`times-frac`
40×	`cbrt-prod`
37×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`sqrt-prod`
10×	`distribute-lft-out`
8×	`cbrt-div`
7×	`associate-/r*`
6×	`add-exp-log` `associate-/l*`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `pow1` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 119

Calls

4 calls:

57.0ms	(/ (sqrt x) (cbrt (+ 1.0 (sqrt (+ 1.0 x)))))
22.0ms	(cbrt (+ 1.0 (sqrt (+ 1.0 x))))
12.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
14.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))

series2.5s

Counts

4 → 12

Calls

4 calls:

1.5s	(/ (sqrt x) (cbrt (+ 1.0 (sqrt (+ 1.0 x)))))
296.0ms	(cbrt (+ 1.0 (sqrt (+ 1.0 x))))
337.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))
308.0ms	(cbrt (+ 1.0 (sqrt (+ x 1.0))))

simplify1.1s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
2	2120
1	564
0	246

prune820.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes36.0ms

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	10
1	10
0	8

end0.0ms

sample834.0ms

Algorithm

intervals

Results

377.0ms	7998×	body	80	valid
165.0ms	2622×	body	80	nan
0.0ms	2×	body	1280	valid