Details

sample13.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	90×	body	80	nan

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
done	8	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

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-exp-log` `add-cbrt-cube` `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` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 71

Calls

3 calls:

8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
4.0ms	(sqrt (+ x 1.0))
16.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series220.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(+ 1.0 (sqrt (+ x 1.0)))
30.0ms	(sqrt (+ x 1.0))
146.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify541.0ms

Counts

80 → 80

Iterations

Useful iterations: done (539.0ms)

Iter	Nodes	Cost
0	146	959
1	333	886
2	1012	819
done	5000	809

prune160.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sqrt (+ x 1.0)) 3)
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
4.2b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.8b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
62×	`sqrt-div`
43×	`add-sqr-sqrt`
34×	`sqrt-prod`
32×	`flip3-+` `flip-+`
31×	`add-cube-cbrt`
28×	`associate-*r/` `distribute-lft-out`
27×	`times-frac`
23×	`unpow-prod-down` `cube-prod`
21×	`pow1`
16×	`frac-sub`
12×	`frac-times`
11×	`swap-sqr`
9×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-/r*` `add-cbrt-cube`
8×	`associate-*l/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `sum-cubes` `log1p-expm1-u` `sub-div` `unswap-sqr`
3×	`pow-unpow` `pow-pow` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cube-div` `associate-/r/`
1×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `prod-diff` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 194

Calls

4 calls:

5.0ms	(pow (sqrt (+ x 1.0)) 3)
22.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
13.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
58.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (sqrt (+ x 1.0)) 3)
20.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
62.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
199.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify1.3s

Counts

206 → 206

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	326	4145
1	781	2999
2	3046	2729
done	5000	2725

prune435.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ x (fma 1.0 1.0 (- (+ x 1.0) (* 1.0 (sqrt (+ x 1.0)))))) (+ 1.0 (sqrt (+ x 1.0))))
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
4.2b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
4.2b	(- (+ x 1.0) (* 1.0 (sqrt (+ x 1.0))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

109×	`*-un-lft-identity`
97×	`times-frac`
76×	`add-sqr-sqrt`
64×	`sqrt-div`
63×	`add-cube-cbrt`
35×	`flip3-+` `flip-+`
32×	`associate-*r/`
26×	`sqrt-prod`
22×	`distribute-lft-out`
20×	`frac-sub`
19×	`pow1`
13×	`associate-/l*`
12×	`frac-times`
11×	`add-exp-log` `swap-sqr` `add-cbrt-cube` `add-log-exp`
8×	`sqrt-pow1` `pow1/2` `associate-*l/`
7×	`associate-r` `associate-l`
6×	`div-inv`
5×	`fma-neg` `prod-diff` `pow-prod-up`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `sub-div` `unswap-sqr`
3×	`cbrt-undiv` `diff-log` `div-exp` `pow-prod-down` `pow-sqr`
2×	`sub-neg` `flip3--` `distribute-rgt-out--` `associate-/r/` `flip--`
1×	`pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `prod-exp` `associate--l+` `clear-num` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `associate-/l/`

Counts

4 → 218

Calls

4 calls:

21.0ms	(/ (/ x (fma 1.0 1.0 (- (+ x 1.0) (* 1.0 (sqrt (+ x 1.0)))))) (+ 1.0 (sqrt (+ x 1.0))))
20.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
16.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
23.0ms	(- (+ x 1.0) (* 1.0 (sqrt (+ x 1.0))))

series614.0ms

Counts

4 → 12

Calls

4 calls:

463.0ms	(/ (/ x (fma 1.0 1.0 (- (+ x 1.0) (* 1.0 (sqrt (+ x 1.0)))))) (+ 1.0 (sqrt (+ x 1.0))))
16.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
68.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
67.0ms	(- (+ x 1.0) (* 1.0 (sqrt (+ x 1.0))))

simplify1.3s

Counts

230 → 230

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	429	6838
1	1061	5814
2	3666	5408
done	5000	5406

prune601.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(* (/ x (- (* 1.0 1.0) (+ x 1.0))) (- 1.0 (sqrt (+ x 1.0))))
4.1b	(- (* 1.0 1.0) (+ x 1.0))
4.2b	(- 1.0 (sqrt (+ x 1.0)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
67×	`prod-diff`
55×	`add-cube-cbrt`
42×	`sqrt-prod`
23×	`distribute-rgt-in` `distribute-lft-in`
18×	`associate-l`
13×	`times-frac`
11×	`distribute-lft-out` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`difference-of-squares`
7×	`pow1`
6×	`associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `fma-neg` `log1p-expm1-u`
3×	`diff-log`
2×	`frac-times` `sqrt-div` `associate-*r/` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+` `hypot-def` `div-inv` `associate--r+`

Counts

4 → 174

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
74.0ms	(* (/ x (- (* 1.0 1.0) (+ x 1.0))) (- 1.0 (sqrt (+ x 1.0))))
10.0ms	(- (* 1.0 1.0) (+ x 1.0))
11.0ms	(- 1.0 (sqrt (+ x 1.0)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1.0))
75.0ms	(* (/ x (- (* 1.0 1.0) (+ x 1.0))) (- 1.0 (sqrt (+ x 1.0))))
12.0ms	(- (* 1.0 1.0) (+ x 1.0))
55.0ms	(- 1.0 (sqrt (+ x 1.0)))

simplify1.2s

Counts

186 → 186

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	270	5231
1	684	4226
2	2418	3485
done	5000	3479

prune282.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes42.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	43
1	20	43
done	20	43

end0.0ms

sample316.0ms

Algorithm

intervals

Results

160.0ms	7995×	body	80	valid
42.0ms	2793×	body	80	nan
0.0ms	5×	body	1280	valid