Details

sample92.0ms

Algorithm

intervals

Results

62.0ms

709×

body

valid

simplify5.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	12	17
1	26	16
2	50	15
3	86	15
4	151	15
5	303	15
6	932	15
7	3961	15
done	5001	15

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
7×	`fma-def`
6×	`unpow-prod-down`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
2×	`sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `flip3-+` `associate-r` `pow-exp` `sum-log` `*-commutative` `flip-+` `unswap-sqr`

Counts

3 → 60

Calls

3 calls:

81.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
42.0ms	(* 4.0 (* b b))
16.0ms	(pow (+ (* a a) (* b b)) 2.0)

series276.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
26.0ms	(* 4.0 (* b b))
157.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify2.5s

Counts

69 → 69

Iterations

Useful iterations: 3 (930.0ms)

Iter	Nodes	Cost
0	107	829
1	254	707
2	740	649
3	2396	641
done	5000	641

prune310.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (* a a) 2 (* b b))
0.1b	(fma (* b b) (fma (* a a) 2 (* b b)) (pow a 4))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma (* a a) 2 (* b b))
1.0ms	(fma (* b b) (fma (* a a) 2 (* b b)) (pow a 4))

series154.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(fma (* a a) 2 (* b b))
87.0ms	(fma (* b b) (fma (* a a) 2 (* b b)) (pow a 4))

simplify2.9s

Counts

26 → 26

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	40	395
1	73	392
2	185	340
3	648	340
4	3404	340
done	5000	340

prune142.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 2 (* (pow a 2) (pow b 2)) (pow b 4))
1.8b	(* (pow a 2) (pow b 2))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`add-exp-log` `unpow-prod-down`
10×	`unpow2` `sqr-pow`
9×	`prod-exp`
8×	`associate-r` `associate-l`
6×	`pow-to-exp` `add-cube-cbrt` `*-un-lft-identity` `pow-exp`
4×	`add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 63

Calls

2 calls:

1.0ms	(fma 2 (* (pow a 2) (pow b 2)) (pow b 4))
36.0ms	(* (pow a 2) (pow b 2))

series173.0ms

Counts

2 → 6

Calls

2 calls:

131.0ms	(fma 2 (* (pow a 2) (pow b 2)) (pow b 4))
43.0ms	(* (pow a 2) (pow b 2))

simplify3.1s

Counts

69 → 69

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	93	810
1	190	730
2	516	568
3	2234	560
done	5000	543

prune273.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* b b))
0.1b	(pow (pow (fma a a (pow b 2)) 2.0) 3)
0.3b	(pow (fma a a (pow b 2)) 2.0)
27.2b	(cbrt (pow (pow (fma a a (pow b 2)) 2.0) 3))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

29×	`unpow-prod-down`
20×	`cbrt-prod`
18×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`cube-prod`
12×	`add-exp-log`
10×	`pow1` `add-cbrt-cube`
7×	`sqr-pow`
6×	`pow-unpow`
5×	`pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cube-mult` `pow-pow` `unpow3`
1×	`pow1/3` `associate-r` `*-commutative` `rem-cbrt-cube` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

36.0ms	(* 4.0 (* b b))
11.0ms	(pow (pow (fma a a (pow b 2)) 2.0) 3)
5.0ms	(pow (fma a a (pow b 2)) 2.0)
9.0ms	(cbrt (pow (pow (fma a a (pow b 2)) 2.0) 3))

series620.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 4.0 (* b b))
171.0ms	(pow (pow (fma a a (pow b 2)) 2.0) 3)
159.0ms	(pow (fma a a (pow b 2)) 2.0)
254.0ms	(cbrt (pow (pow (fma a a (pow b 2)) 2.0) 3))

simplify5.1s

Counts

118 → 118

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	156	1729
1	349	1395
2	919	1326
3	4921	1309
done	5000	1309

prune409.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes77.0ms

Accuracy

51% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 1.1b

bsearch2.0ms

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	30	67
1	37	50
done	37	50

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.3s

20340×

body

valid