Details

sample66.0ms

Algorithm

intervals

Results

30.0ms

356×

body

valid

simplify9.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
12	4899
11	3849
10	2818
9	2072
8	1738
7	1515
6	1194
5	771
4	477
3	234
2	90
1	35
0	17

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (fma (* a 27.0) b (* x 2.0)) (* (* 9.0 y) (* t z)))
0.1b	(fma (* a 27.0) b (* x 2.0))
5.6b	(* (* 9.0 y) (* t z))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `prod-diff` `log1p-expm1-u`
2×	`fma-udef`
1×	`sub-neg` `flip3--` `diff-log` `associate-r` `associate-l` `associate--l+` `*-commutative` `flip--`

Counts

3 → 55

Calls

3 calls:

12.0ms	(- (fma (* a 27.0) b (* x 2.0)) (* (* 9.0 y) (* t z)))
1.0ms	(fma (* a 27.0) b (* x 2.0))
61.0ms	(* (* 9.0 y) (* t z))

series430.0ms

Counts

3 → 9

Calls

3 calls:

298.0ms	(- (fma (* a 27.0) b (* x 2.0)) (* (* 9.0 y) (* t z)))
83.0ms	(fma (* a 27.0) b (* x 2.0))
49.0ms	(* (* 9.0 y) (* t z))

simplify6.0s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
3	4877
2	933
1	257
0	106

prune710.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fma (* a 27.0) b (* x 2.0)) (* (* (* 9.0 y) t) z))
0.1b	(fma (* a 27.0) b (* x 2.0))
0.5b	(* (* 9.0 y) t)
6.5b	(* (* (* 9.0 y) t) z)

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`associate-l` `*-commutative` `fma-udef`
1×	`sub-neg` `flip3--` `diff-log` `associate--l+` `flip--`

Counts

4 → 74

Calls

4 calls:

12.0ms	(- (fma (* a 27.0) b (* x 2.0)) (* (* (* 9.0 y) t) z))
1.0ms	(fma (* a 27.0) b (* x 2.0))
38.0ms	(* (* 9.0 y) t)
120.0ms	(* (* (* 9.0 y) t) z)

series465.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(- (fma (* a 27.0) b (* x 2.0)) (* (* (* 9.0 y) t) z))
80.0ms	(fma (* a 27.0) b (* x 2.0))
37.0ms	(* (* 9.0 y) t)
59.0ms	(* (* (* 9.0 y) t) z)

simplify2.5s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1119
1	303
0	126

prune967.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fma (* a 27.0) b (* x 2.0)) (* (* 9.0 (* y t)) z))
0.1b	(fma (* a 27.0) b (* x 2.0))
0.3b	(* 9.0 (* y t))
6.5b	(* (* 9.0 (* y t)) z)

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`*-commutative` `fma-udef`
1×	`sub-neg` `flip3--` `diff-log` `associate--l+` `flip--`

Counts

4 → 74

Calls

4 calls:

13.0ms	(- (fma (* a 27.0) b (* x 2.0)) (* (* 9.0 (* y t)) z))
1.0ms	(fma (* a 27.0) b (* x 2.0))
34.0ms	(* 9.0 (* y t))
100.0ms	(* (* 9.0 (* y t)) z)

series460.0ms

Counts

4 → 12

Calls

4 calls:

291.0ms	(- (fma (* a 27.0) b (* x 2.0)) (* (* 9.0 (* y t)) z))
73.0ms	(fma (* a 27.0) b (* x 2.0))
38.0ms	(* 9.0 (* y t))
58.0ms	(* (* 9.0 (* y t)) z)

simplify2.3s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1004
1	291
0	124

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 27.0 (* b a) (- (* 2.0 x) (* (* 9.0 z) (* t y))))
6.5b	(* (* 9.0 z) (* t y))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `log1p-expm1-u` `add-log-exp`
1×	`associate-r` `associate-l` `*-commutative` `fma-udef`

Counts

2 → 34

Calls

2 calls:

0.0ms	(fma 27.0 (* b a) (- (* 2.0 x) (* (* 9.0 z) (* t y))))
46.0ms	(* (* 9.0 z) (* t y))

series354.0ms

Counts

2 → 6

Calls

2 calls:

291.0ms	(fma 27.0 (* b a) (- (* 2.0 x) (* (* 9.0 z) (* t y))))
63.0ms	(* (* 9.0 z) (* t y))

simplify6.0s

Counts

40 → 40

Iterations

Iter	Nodes
done	5038
3	2856
2	622
1	180
0	76

prune392.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes1.3s

Accuracy

85.6% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 3.8b

bsearch301.0ms

Steps

Iters	Range		Point
9	5.692437874851714e-11	2.9589809551197953e-05	5.80575541487311e-08
7	-9.92142273098895e+28	-8.887026811072337e+26	-2.2864772462435855e+27

simplify28.0ms

Iterations

Iter	Nodes
done	40
1	40
0	29

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.4s

10923×

body

valid