Details

sample16.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
2.0ms	97×	body	80	nan

simplify2.0ms

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

localize6.0ms

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))))

rewrite95.0ms

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:

19.0ms	(+ 1.0 (sqrt (+ x 1.0)))
16.0ms	(sqrt (+ x 1.0))
57.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series359.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(+ 1.0 (sqrt (+ x 1.0)))
49.0ms	(sqrt (+ x 1.0))
236.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.4s

Counts

80 → 80

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	146	959
1	333	886
2	955	819
3	3894	808
done	5000	807

prune274.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

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))

rewrite66.0ms

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:

44.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
9.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))

series763.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
336.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
131.0ms	(cbrt (+ x 1.0))
141.0ms	(cbrt (+ x 1.0))

simplify1.9s

Counts

106 → 106

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	278	2317
1	707	2120
2	2507	1961
done	5001	1892

prune516.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize29.0ms

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)))

rewrite116.0ms

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×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `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 → 125

Calls

4 calls:

73.0ms	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
7.0ms	(cbrt (+ x 1.0))
9.0ms	(cbrt (sqrt (+ x 1.0)))
18.0ms	(cbrt (sqrt (+ x 1.0)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
108.0ms	(cbrt (+ x 1.0))
120.0ms	(cbrt (sqrt (+ x 1.0)))
139.0ms	(cbrt (sqrt (+ x 1.0)))

simplify2.8s

Counts

137 → 137

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	188	2149
1	384	1945
2	991	1861
3	2618	1665
done	5000	1522

prune619.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize21.0ms

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)))))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
59×	`add-sqr-sqrt`
52×	`times-frac`
40×	`add-cube-cbrt`
39×	`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×	`expm1-log1p-u` `flip3-+` `associate-/r*` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`fma-def`
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` `hypot-def`

Counts

4 → 144

Calls

4 calls:

9.0ms	(sqrt (+ x 1.0))
35.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
16.0ms	(+ 1.0 (sqrt (+ x 1.0)))
129.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series821.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (+ x 1.0))
507.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
52.0ms	(+ 1.0 (sqrt (+ x 1.0)))
210.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.7s

Counts

156 → 156

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	224	2373
1	545	2089
2	1780	1913
done	5000	1885

prune506.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes34.0ms

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

sample600.0ms

Algorithm

intervals

Results

332.0ms	7999×	body	80	valid
103.0ms	2697×	body	80	nan
0.0ms	1×	body	1280	valid