Details

sample17.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
2.0ms	80×	body	80	nan

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
5×	`distribute-lft-out`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`fma-def` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 52

Calls

2 calls:

18.0ms	(+ 1.0 (sqrt (+ x 1.0)))
36.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series219.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(+ 1.0 (sqrt (+ x 1.0)))
151.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.2s

Counts

58 → 58

Iterations

Useful iterations: 3 (905.0ms)

Iter	Nodes	Cost
0	121	771
1	289	722
2	872	665
3	3751	657
done	5000	657

prune168.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

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)))
2.7b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
9.9b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite267.0ms

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:

11.0ms	(pow (sqrt (+ x 1.0)) 3)
64.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
38.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
144.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(pow (sqrt (+ x 1.0)) 3)
26.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
67.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
297.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify1.9s

Counts

206 → 206

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	326	4145
1	804	2987
2	2940	2729
done	5000	2724

prune707.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

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)))))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
52×	`times-frac`
38×	`add-cube-cbrt`
35×	`sqrt-prod`
30×	`associate-r`
14×	`distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l` `associate-/l*` `unswap-sqr`
5×	`pow1` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

3 → 125

Calls

3 calls:

29.0ms	(+ 1.0 (sqrt (+ x 1.0)))
43.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
121.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series644.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(+ 1.0 (sqrt (+ x 1.0)))
406.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
172.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.3s

Counts

134 → 134

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	199	2185
1	502	1925
2	1698	1759
done	5001	1732

prune358.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes49.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample744.0ms

Algorithm

intervals

Results

341.0ms	7998×	body	80	valid
144.0ms	2680×	body	80	nan
0.0ms	2×	body	1280	valid