Details

sample157.0ms

Algorithm

intervals

Results

77.0ms	1620×	body	80	nan
15.0ms	256×	body	80	valid

simplify5.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	15	16
1	27	16
2	60	15
3	130	15
4	332	15
5	893	15
6	1661	15
7	2904	15
8	3221	15
9	3228	15
done	3228	15

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (log (+ x y)) (log z)) t)
0.3b	(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
0.6b	(+ (log (+ x y)) (log z))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
28×	`pow1`
25×	`log-pow` `distribute-lft-out`
21×	`prod-diff`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
7×	`log-prod` `fma-neg`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`associate-+l-` `log-div` `associate-+l+` `fma-def`
3×	`add-exp-log` `expm1-log1p-u` `associate-+r+` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`associate--l-` `diff-log` `sum-log`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--` `fma-udef` `difference-of-squares`

Counts

3 → 92

Calls

3 calls:

32.0ms	(- (+ (log (+ x y)) (log z)) t)
0.0ms	(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
6.0ms	(+ (log (+ x y)) (log z))

series327.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(- (+ (log (+ x y)) (log z)) t)
89.0ms	(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
72.0ms	(+ (log (+ x y)) (log z))

simplify458.0ms

Counts

101 → 101

Iterations

Useful iterations: done (455.0ms)

Iter	Nodes	Cost
0	170	1568
1	394	1337
2	1215	1125
done	5000	1113

prune305.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
0.6b	(* (cbrt (+ x y)) (cbrt (+ x y)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

4.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
19.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))

series551.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(cbrt (+ x y))
126.0ms	(cbrt (+ x y))
129.0ms	(cbrt (+ x y))
161.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))

simplify2.2s

Counts

115 → 115

Iterations

Useful iterations: 3 (544.0ms)

Iter	Nodes	Cost
0	120	1316
1	261	1198
2	961	1128
3	3682	1051
done	5000	1051

prune533.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
0.6b	(* (cbrt (+ x y)) (cbrt (+ x y)))
5.1b	(pow (+ x y) 1/3)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
32×	`cbrt-prod`
24×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `cbrt-div`
12×	`pow1`
9×	`swap-sqr` `distribute-lft-out`
8×	`flip3-+` `pow1/3` `flip-+`
7×	`add-exp-log` `associate-r` `associate-l`
4×	`expm1-log1p-u` `frac-times` `unpow-prod-down` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-unpow`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-to-exp` `pow-pow` `pow-plus` `unpow1/3` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 108

Calls

4 calls:

2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
18.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
4.0ms	(pow (+ x y) 1/3)

series568.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt (+ x y))
127.0ms	(cbrt (+ x y))
167.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
147.0ms	(pow (+ x y) 1/3)

simplify696.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (142.0ms)

Iter	Nodes	Cost
0	151	1355
1	330	1090
2	1354	978
done	5000	978

prune584.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (+ (log (+ x y)) (* 2 (log (cbrt z)))) (log (cbrt z)))
0.5b	(+ (log (+ x y)) (* 2 (log (cbrt z))))
0.6b	(cbrt z)
0.6b	(cbrt z)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

22×	`log-prod`
20×	`*-un-lft-identity`
18×	`associate-+r+`
15×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
7×	`fma-def` `add-log-exp`
6×	`pow1` `distribute-rgt-in` `associate-+l-` `distribute-lft-in`
5×	`associate-+l+`
4×	`add-exp-log` `expm1-log1p-u` `log-div` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`distribute-lft-out`
2×	`+-commutative` `pow1/3` `log-pow`

Counts

4 → 89

Calls

4 calls:

16.0ms	(+ (+ (log (+ x y)) (* 2 (log (cbrt z)))) (log (cbrt z)))
10.0ms	(+ (log (+ x y)) (* 2 (log (cbrt z))))
1.0ms	(cbrt z)
1.0ms	(cbrt z)

series649.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(+ (+ (log (+ x y)) (* 2 (log (cbrt z)))) (log (cbrt z)))
144.0ms	(+ (log (+ x y)) (* 2 (log (cbrt z))))
181.0ms	(cbrt z)
187.0ms	(cbrt z)

simplify2.5s

Counts

101 → 101

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	154	1132
1	362	996
2	1149	851
3	4772	767
done	5000	764

prune450.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

regimes645.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	21	27
done	21	27

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.5s	54937×	body	80	nan
451.0ms	8032×	body	80	valid