Details

sample377.0ms

Algorithm

intervals

Results

187.0ms	1846×	body	80	nan
27.0ms	258×	body	80	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1804
4	471
3	157
2	61
1	27
0	15

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log z) t)
0.2b	(fma (log t) (- a 0.5) (+ (log (+ y x)) (- (log z) t)))
0.3b	(+ (log (+ y x)) (- (log z) t))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 94

Calls

3 calls:

7.0ms	(- (log z) t)
0.0ms	(fma (log t) (- a 0.5) (+ (log (+ y x)) (- (log z) t)))
23.0ms	(+ (log (+ y x)) (- (log z) t))

series449.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(- (log z) t)
133.0ms	(fma (log t) (- a 0.5) (+ (log (+ y x)) (- (log z) t)))
224.0ms	(+ (log (+ y x)) (- (log z) t))

simplify1.1s

Counts

103 → 103

Iterations

Iter	Nodes
done	5001
2	1450
1	440
0	185

prune828.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize71.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `fma-udef`

Counts

4 → 46

Calls

4 calls:

0.0ms	(fma (log t) (- a 0.5) (+ (fma 2 (log (cbrt z)) (log (+ x y))) (- (log (cbrt z)) t)))
0.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))
1.0ms	(cbrt z)
1.0ms	(cbrt z)

series1.0s

Counts

4 → 12

Calls

4 calls:

230.0ms	(fma (log t) (- a 0.5) (+ (fma 2 (log (cbrt z)) (log (+ x y))) (- (log (cbrt z)) t)))
172.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))
277.0ms	(cbrt z)
332.0ms	(cbrt z)

simplify2.1s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
3	2770
2	622
1	227
0	106

prune525.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (- (log (cbrt z)) t))
0.5b	(fma 2 (log (cbrt z)) (log (+ x y)))
0.6b	(cbrt z)
0.6b	(cbrt z)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
23×	`associate-+r+`
17×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`prod-diff`
9×	`cbrt-prod`
8×	`pow1` `add-log-exp`
7×	`log-pow`
6×	`log-prod` `associate--l+`
5×	`pow1/3`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`fma-def` `distribute-lft-out`
2×	`sum-log` `fma-udef` `distribute-lft-out--`
1×	`+-commutative` `associate-+l+` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `flip-+`

Counts

4 → 81

Calls

4 calls:

19.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (- (log (cbrt z)) t))
0.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))
1.0ms	(cbrt z)
1.0ms	(cbrt z)

series1.1s

Counts

4 → 12

Calls

4 calls:

527.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (- (log (cbrt z)) t))
157.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))
237.0ms	(cbrt z)
209.0ms	(cbrt z)

simplify1.4s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1093
1	319
0	146

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (log t) (- a 0.5))
0.1b	(+ (* (log t) (- a 0.5)) (- (fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y)))) t))
0.4b	(fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y))))
0.6b	(fma 2/3 (log z) (log (+ x y)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

45×	`prod-diff`
40×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`add-cube-cbrt`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
12×	`associate-+r+`
9×	`add-log-exp`
7×	`pow1`
6×	`add-cbrt-cube` `associate-*r/` `add-exp-log`
5×	`sub-neg` `flip3--` `associate-r` `flip--`
4×	`expm1-log1p-u` `associate-l` `frac-add` `log1p-expm1-u`
3×	`fma-udef`
2×	`sum-log`
1×	`+-commutative` `associate-+r-` `fma-def` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `associate--l+` `log-pow` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 121

Calls

4 calls:

32.0ms	(* (log t) (- a 0.5))
28.0ms	(+ (* (log t) (- a 0.5)) (- (fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y)))) t))
0.0ms	(fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y))))
0.0ms	(fma 2/3 (log z) (log (+ x y)))

series516.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (log t) (- a 0.5))
132.0ms	(+ (* (log t) (- a 0.5)) (- (fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y)))) t))
154.0ms	(fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y))))
125.0ms	(fma 2/3 (log z) (log (+ x y)))

simplify1.8s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	3492
1	764
0	280

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes1.8s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	21
1	21
0	18

end0.0ms

sample11.9s

Algorithm

intervals

Results

6.5s	55612×	body	80	nan
1.2s	8043×	body	80	valid