Details

sample47.0ms

Algorithm

intervals

Results

26.0ms

699×

body

valid

simplify3.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

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)

rewrite91.0ms

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:

63.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
16.0ms	(* 4.0 (* b b))
10.0ms	(pow (+ (* a a) (* b b)) 2.0)

series206.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
31.0ms	(* 4.0 (* b b))
108.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify1.5s

Counts

69 → 69

Iterations

Useful iterations: 3 (537.0ms)

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

prune183.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 4.0 (* b b))
0.2b	(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (* b b)))

rewrite17.0ms

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:

16.0ms	(* 4.0 (* b b))
0.0ms	(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (* b b)))

series161.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(* 4.0 (* b b))
135.0ms	(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (* b b)))

simplify2.6s

Counts

37 → 37

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	73	620
1	164	481
2	462	409
3	1434	388
4	4251	366
done	5000	366

prune98.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.0ms

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:

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

series100.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(fma (* a a) 2 (* b b))
62.0ms	(fma (* b b) (fma (* a a) 2 (* b b)) (pow a 4))

simplify1.7s

Counts

26 → 26

Iterations

Useful iterations: 2 (34.0ms)

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

prune81.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* (pow a 2) (pow b 2)) 2.0 (pow b 4))
0.0b	(+ (fma (* (pow a 2) (pow b 2)) 2.0 (pow b 4)) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
1.4b	(* (pow a 2) (pow b 2))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`add-exp-log`
17×	`unswap-sqr`
14×	`unpow-prod-down`
12×	`prod-exp`
11×	`associate-l` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity` `unpow2` `sqr-pow`
9×	`pow1` `associate-r`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-def`
2×	`*-commutative` `fma-udef`
1×	`+-commutative` `associate-+l+` `flip3-+` `sum-log` `flip-+`

Counts

4 → 101

Calls

4 calls:

0.0ms	(fma (* (pow a 2) (pow b 2)) 2.0 (pow b 4))
7.0ms	(+ (fma (* (pow a 2) (pow b 2)) 2.0 (pow b 4)) (* 4.0 (* b b)))
16.0ms	(* 4.0 (* b b))
21.0ms	(* (pow a 2) (pow b 2))

series215.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(fma (* (pow a 2) (pow b 2)) 2.0 (pow b 4))
69.0ms	(+ (fma (* (pow a 2) (pow b 2)) 2.0 (pow b 4)) (* 4.0 (* b b)))
30.0ms	(* 4.0 (* b b))
35.0ms	(* (pow a 2) (pow b 2))

simplify3.4s

Counts

113 → 113

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	150	1431
1	335	1291
2	1036	1062
3	4852	1001
done	5000	1001

prune259.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes61.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	16	30
done	16	30

end0.0ms

sample1.3s

Algorithm

intervals

Results

781.0ms

20523×

body

valid