Details

sample171.0ms

Algorithm

intervals

Results

71.0ms	1640×	body	80	nan
13.0ms	256×	body	80	valid

simplify6.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	15	16
1	27	16
2	61	15
3	155	15
4	356	15
5	858	15
6	1598	15
7	2194	15
8	2618	15
9	2630	15
done	2630	15

prune10.0ms

Pruning

2 alts after pruning (2 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)
0.2b	(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
0.6b	(+ (log (+ x y)) (log z))

rewrite84.0ms

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:

67.0ms	(- (+ (log (+ x y)) (log z)) t)
0.0ms	(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
13.0ms	(+ (log (+ x y)) (log z))

series346.0ms

Counts

3 → 9

Calls

3 calls:

173.0ms	(- (+ (log (+ x y)) (log z)) t)
98.0ms	(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
75.0ms	(+ (log (+ x y)) (log z))

simplify1.7s

Counts

101 → 101

Iterations

Useful iterations: 3 (790.0ms)

Iter	Nodes	Cost
0	170	1568
1	388	1337
2	1000	1146
3	3921	1059
done	5000	1059

prune298.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (log (+ x y)) (log z)) t)
0.1b	(* (- a 0.5) (log t))
0.1b	(+ (* (- a 0.5) (log t)) (- (+ (log (+ x y)) (log z)) t))
0.6b	(+ (log (+ x y)) (log z))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

80×	`*-un-lft-identity`
44×	`pow1`
42×	`prod-diff`
40×	`add-sqr-sqrt`
38×	`log-pow`
37×	`distribute-lft-out`
34×	`add-cube-cbrt`
27×	`associate-+r+`
19×	`log-prod`
14×	`add-log-exp`
10×	`associate-+l+`
7×	`fma-neg`
6×	`add-exp-log` `distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-*l/` `sum-log` `add-cbrt-cube` `flip--` `distribute-lft-out--`
5×	`fma-def` `associate-l`
4×	`expm1-log1p-u` `associate-+l-` `log-div` `flip3-+` `diff-log` `associate-r` `frac-add` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `associate--l-` `sub-neg` `associate--l+` `difference-of-squares`
1×	`associate-+r-` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 164

Calls

4 calls:

65.0ms	(- (+ (log (+ x y)) (log z)) t)
23.0ms	(* (- a 0.5) (log t))
109.0ms	(+ (* (- a 0.5) (log t)) (- (+ (log (+ x y)) (log z)) t))
15.0ms	(+ (log (+ x y)) (log z))

series407.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(- (+ (log (+ x y)) (log z)) t)
57.0ms	(* (- a 0.5) (log t))
99.0ms	(+ (* (- a 0.5) (log t)) (- (+ (log (+ x y)) (log z)) t))
76.0ms	(+ (log (+ x y)) (log z))

simplify1.2s

Counts

176 → 176

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	275	3118
1	727	2688
2	2434	2395
done	5000	2295

prune502.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

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:

37.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
7.0ms	(cbrt (+ x y))
4.0ms	(cbrt (+ x y))
4.0ms	(cbrt (+ x y))

series582.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
137.0ms	(cbrt (+ x y))
132.0ms	(cbrt (+ x y))
138.0ms	(cbrt (+ x y))

simplify2.2s

Counts

115 → 115

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	120	1316
1	257	1186
2	623	1128
3	1512	1051
4	4536	1045
done	5000	1042

prune511.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a 0.5) (log (sqrt t)))
0.1b	(+ (* (- a 0.5) (log (sqrt t))) (fma (- a 0.5) (log (sqrt t)) (- (+ (log (+ x y)) (log z)) t)))
0.2b	(fma (- a 0.5) (log (sqrt t)) (- (+ (log (+ x y)) (log z)) t))
0.6b	(+ (log (+ x y)) (log z))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

31×	`log-prod`
25×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
16×	`associate-+l+`
13×	`pow1`
12×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
8×	`log-pow`
6×	`add-exp-log` `associate-r` `add-cbrt-cube` `add-log-exp`
5×	`fma-def` `associate-l` `distribute-lft-out`
4×	`expm1-log1p-u` `associate-+r+` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`+-commutative` `associate-+l-` `log-div` `associate-*l/` `sum-log` `fma-udef`
1×	`flip3--` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

27.0ms	(* (- a 0.5) (log (sqrt t)))
17.0ms	(+ (* (- a 0.5) (log (sqrt t))) (fma (- a 0.5) (log (sqrt t)) (- (+ (log (+ x y)) (log z)) t)))
0.0ms	(fma (- a 0.5) (log (sqrt t)) (- (+ (log (+ x y)) (log z)) t))
13.0ms	(+ (log (+ x y)) (log z))

series472.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (- a 0.5) (log (sqrt t)))
195.0ms	(+ (* (- a 0.5) (log (sqrt t))) (fma (- a 0.5) (log (sqrt t)) (- (+ (log (+ x y)) (log z)) t)))
148.0ms	(fma (- a 0.5) (log (sqrt t)) (- (+ (log (+ x y)) (log z)) t))
72.0ms	(+ (log (+ x y)) (log z))

simplify1.1s

Counts

118 → 118

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	240	1983
1	590	1835
2	1788	1654
done	5000	1576

prune454.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes523.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.4s	56116×	body	80	nan
418.0ms	8025×	body	80	valid