Details

sample88.0ms

Algorithm

intervals

Results

57.0ms

656×

body

valid

simplify6.2s

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a a) (* b b))
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)

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

10.0ms	(+ (* a a) (* b b))
122.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
33.0ms	(* 4.0 (* b b))
21.0ms	(pow (+ (* a a) (* b b)) 2.0)

series379.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* a a) (* b b))
116.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
36.0ms	(* 4.0 (* b b))
175.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify2.6s

Counts

86 → 86

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	125	1011
1	329	844
2	1052	772
3	3512	764
done	5000	764

prune392.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 2 (* a a))
0.2b	(fma (* b b) (fma b b (* 2 (* a a))) (pow a 4))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 31

Calls

2 calls:

31.0ms	(* 2 (* a a))
1.0ms	(fma (* b b) (fma b b (* 2 (* a a))) (pow a 4))

series168.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(* 2 (* a a))
115.0ms	(fma (* b b) (fma b b (* 2 (* a a))) (pow a 4))

simplify3.1s

Counts

37 → 37

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	59	429
1	128	408
2	336	360
3	902	354
4	3277	354
done	5000	348

prune160.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* (* a a) (* b b)) 2.0 (pow b 4))
0.0b	(+ (fma (* (* a a) (* b b)) 2.0 (pow b 4)) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
2.3b	(* (* a a) (* b b))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

37×	`pow1`
21×	`add-exp-log` `add-cbrt-cube`
17×	`pow-prod-down`
11×	`prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`expm1-log1p-u` `pow-plus` `associate-l` `pow-prod-up` `log1p-expm1-u`
3×	`fma-def`
2×	`pow2` `associate-r` `pow-sqr` `*-commutative` `fma-udef` `unswap-sqr`
1×	`+-commutative` `associate-+l+` `flip3-+` `sum-log` `flip-+`

Counts

4 → 79

Calls

4 calls:

0.0ms	(fma (* (* a a) (* b b)) 2.0 (pow b 4))
9.0ms	(+ (fma (* (* a a) (* b b)) 2.0 (pow b 4)) (* 4.0 (* b b)))
18.0ms	(* 4.0 (* b b))
44.0ms	(* (* a a) (* b b))

series321.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(fma (* (* a a) (* b b)) 2.0 (pow b 4))
123.0ms	(+ (fma (* (* a a) (* b b)) 2.0 (pow b 4)) (* 4.0 (* b b)))
44.0ms	(* 4.0 (* b b))
52.0ms	(* (* a a) (* b b))

simplify3.1s

Counts

91 → 91

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	107	1136
1	257	1045
2	894	891
3	3860	823
done	5000	823

prune372.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cbrt 4.0) (cbrt 4.0)) (* (cbrt 4.0) (* b b)))
0.3b	(* (cbrt 4.0) (* b b))
1.0b	(* (cbrt 4.0) (cbrt 4.0))
2.3b	(* (* a a) (* b b))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

65×	`pow1`
44×	`add-exp-log`
34×	`pow-prod-down`
30×	`add-cbrt-cube`
27×	`prod-exp` `cbrt-unprod`
24×	`add-sqr-sqrt`
20×	`cbrt-prod`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
9×	`associate-r`
7×	`unswap-sqr`
6×	`pow1/3` `swap-sqr` `pow-prod-up`
5×	`pow-plus`
4×	`expm1-log1p-u` `pow-sqr` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`pow2`

Counts

4 → 128

Calls

4 calls:

115.0ms	(* (* (cbrt 4.0) (cbrt 4.0)) (* (cbrt 4.0) (* b b)))
40.0ms	(* (cbrt 4.0) (* b b))
22.0ms	(* (cbrt 4.0) (cbrt 4.0))
56.0ms	(* (* a a) (* b b))

series255.0ms

Counts

4 → 10

Calls

4 calls:

117.0ms	(* (* (cbrt 4.0) (cbrt 4.0)) (* (cbrt 4.0) (* b b)))
82.0ms	(* (cbrt 4.0) (* b b))
0.0ms	(* (cbrt 4.0) (cbrt 4.0))
56.0ms	(* (* a a) (* b b))

simplify5.4s

Counts

138 → 138

Iterations

Useful iterations: done (5.4s)

Iter	Nodes	Cost
0	132	1372
1	287	1296
2	1039	971
3	4211	835
done	5001	831

prune475.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes147.0ms

Accuracy

94.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.0b

bsearch1.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	50
1	31	50
done	31	50

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.3s

20728×

body

valid