Details

sample14.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	80×	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	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite32.0ms

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:

4.0ms	(sqrt (+ x 1.0))
9.0ms	(+ 1.0 (sqrt (+ x 1.0)))
17.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series219.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(sqrt (+ x 1.0))
40.0ms	(+ 1.0 (sqrt (+ x 1.0)))
144.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify610.0ms

Counts

80 → 80

Iterations

Useful iterations: done (608.0ms)

Iter	Nodes	Cost
0	146	959
1	342	886
2	1253	819
done	5000	812

prune166.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.2b	(cbrt (+ x 1.0))
0.2b	(cbrt (+ x 1.0))
0.2b	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`cbrt-prod`
10×	`associate-r`
9×	`times-frac` `sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cbrt-div`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 94

Calls

4 calls:

14.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))
4.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))

series493.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
91.0ms	(cbrt (+ x 1.0))
87.0ms	(cbrt (+ x 1.0))
216.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))

simplify938.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (236.0ms)

Iter	Nodes	Cost
0	278	2317
1	716	2128
2	3038	1961
done	5001	1961

prune330.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(pow (sqrt (+ x 1.0)) 3)
5.0b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.0b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite111.0ms

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:

22.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
6.0ms	(pow (sqrt (+ x 1.0)) 3)
16.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
57.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
68.0ms	(pow (sqrt (+ x 1.0)) 3)
66.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
189.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify2.0s

Counts

206 → 206

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	326	4145
1	817	2999
2	3828	2729
done	5001	2725

prune462.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3)
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))
34.3b	(cbrt (pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

82×	`*-un-lft-identity`
60×	`times-frac`
48×	`add-sqr-sqrt` `add-cube-cbrt`
42×	`cbrt-prod`
36×	`unpow-prod-down` `cube-prod`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `associate-/l*`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `sum-log` `rem-cbrt-cube`

Counts

4 → 164

Calls

4 calls:

14.0ms	(+ 1.0 (sqrt (+ x 1.0)))
20.0ms	(pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3)
17.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
24.0ms	(cbrt (pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3))

series667.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ 1.0 (sqrt (+ x 1.0)))
268.0ms	(pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3)
146.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
209.0ms	(cbrt (pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3))

simplify1.1s

Counts

176 → 176

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	248	3277
1	682	2725
2	2931	2482
done	5000	2474

prune298.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes42.0ms

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

sample333.0ms

Algorithm

intervals

Results

164.0ms	7993×	body	80	valid
42.0ms	2733×	body	80	nan
1.0ms	7×	body	1280	valid