Details

sample16.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
2.0ms	97×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

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))))

rewrite101.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`flip3-+` `flip-+` `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` `div-inv`

Counts

3 → 61

Calls

3 calls:

28.0ms	(+ 1.0 (sqrt (+ x 1.0)))
14.0ms	(sqrt (+ x 1.0))
57.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series335.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(+ 1.0 (sqrt (+ x 1.0)))
60.0ms	(sqrt (+ x 1.0))
201.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.3s

Counts

70 → 70

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	140	917
1	316	848
2	899	783
3	3661	775
done	5000	773

prune246.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

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×	`flip3-+` `flip-+` `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 → 86

Calls

4 calls:

33.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
19.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
5.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))

series691.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
296.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
138.0ms	(cbrt (+ x 1.0))
120.0ms	(cbrt (+ x 1.0))

simplify1.4s

Counts

98 → 98

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	272	2241
1	681	2077
2	2373	1964
done	5000	1889

prune378.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
0.2b	(cbrt (+ x 1.0))
0.2b	(cbrt (sqrt (+ x 1.0)))
0.2b	(cbrt (sqrt (+ x 1.0)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

66×	`cbrt-prod`
43×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
36×	`sqrt-prod`
21×	`add-cube-cbrt`
18×	`cbrt-div`
16×	`sqrt-div`
14×	`swap-sqr`
11×	`pow1`
10×	`associate-r` `associate-l`
9×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out` `unswap-sqr`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 117

Calls

4 calls:

43.0ms	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
4.0ms	(cbrt (+ x 1.0))
10.0ms	(cbrt (sqrt (+ x 1.0)))
5.0ms	(cbrt (sqrt (+ x 1.0)))

series814.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
97.0ms	(cbrt (+ x 1.0))
92.0ms	(cbrt (sqrt (+ x 1.0)))
524.0ms	(cbrt (sqrt (+ x 1.0)))

simplify2.1s

Counts

129 → 129

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	182	2091
1	367	1910
2	925	1826
3	2306	1640
done	5000	1507

prune409.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite188.0ms

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

Counts

4 → 132

Calls

4 calls:

15.0ms	(sqrt (+ x 1.0))
53.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
15.0ms	(+ 1.0 (sqrt (+ x 1.0)))
94.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series621.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ x 1.0))
363.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
49.0ms	(+ 1.0 (sqrt (+ x 1.0)))
174.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.4s

Counts

144 → 144

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	216	2303
1	520	2031
2	1708	1857
done	5000	1834

prune379.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes31.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	22
1	15	22
done	15	22

end0.0ms

sample651.0ms

Algorithm

intervals

Results

374.0ms	7999×	body	80	valid
77.0ms	2697×	body	80	nan
0.0ms	1×	body	1280	valid