Details

sample51.0ms

Algorithm

intervals

Results

30.0ms

644×

body

valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	3678
5	427
4	120
3	66
2	40
1	25
0	12

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

57.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
12.0ms	(+ (* a a) (* b b))
15.0ms	(* 4.0 (* b b))
11.0ms	(pow (+ (* a a) (* b b)) 2.0)

series284.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
31.0ms	(+ (* a a) (* b b))
27.0ms	(* 4.0 (* b b))
156.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify1.1s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
2	2107
1	382
0	117

prune324.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (+ (pow a 4) (pow b 4)) (* (* 2 a) (* a (* b b)))) 1.0)
0.0b	(+ (+ (pow a 4) (pow b 4)) (* (* 2 a) (* a (* b b))))
0.4b	(* a (* b b))
1.3b	(* (* 2 a) (* a (* b b)))

rewrite736.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity`
6×	`sum-log`
5×	`add-cube-cbrt`
4×	`associate-l`
3×	`diff-log`
2×	`associate-r` `*-commutative`
1×	`+-commutative` `associate-+l+` `sub-neg` `flip3-+` `flip3--` `associate--l+` `flip-+` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

542.0ms	(- (+ (+ (pow a 4) (pow b 4)) (* (* 2 a) (* a (* b b)))) 1.0)
111.0ms	(+ (+ (pow a 4) (pow b 4)) (* (* 2 a) (* a (* b b))))
12.0ms	(* a (* b b))
65.0ms	(* (* 2 a) (* a (* b b)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (+ (+ (pow a 4) (pow b 4)) (* (* 2 a) (* a (* b b)))) 1.0)
68.0ms	(+ (+ (pow a 4) (pow b 4)) (* (* 2 a) (* a (* b b))))
42.0ms	(* a (* b b))
70.0ms	(* (* 2 a) (* a (* b b)))

simplify1.6s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	2577
1	367
0	128

prune365.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (pow b 2) (* (* 2 a) a))
2.4b	(* (pow b 2) (* (* 2 a) a))
13.9b	(sqrt (+ (* (pow b 2) (* (* 2 a) a)) (+ (pow a 4) (pow b 4))))
13.9b	(sqrt (+ (* (pow b 2) (* (* 2 a) a)) (+ (pow a 4) (pow b 4))))

rewrite503.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
36×	`prod-exp`
22×	`add-cbrt-cube`
16×	`associate-l`
12×	`add-sqr-sqrt` `cbrt-unprod`
10×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow-to-exp` `pow1` `unpow-prod-down` `pow-exp` `sqrt-prod`
4×	`sqrt-div` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r` `*-commutative` `flip-+` `unpow2` `sqr-pow`

Counts

4 → 88

Calls

4 calls:

46.0ms	(* (pow b 2) (* (* 2 a) a))
72.0ms	(* (pow b 2) (* (* 2 a) a))
169.0ms	(sqrt (+ (* (pow b 2) (* (* 2 a) a)) (+ (pow a 4) (pow b 4))))
213.0ms	(sqrt (+ (* (pow b 2) (* (* 2 a) a)) (+ (pow a 4) (pow b 4))))

series308.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (pow b 2) (* (* 2 a) a))
48.0ms	(* (pow b 2) (* (* 2 a) a))
105.0ms	(sqrt (+ (* (pow b 2) (* (* 2 a) a)) (+ (pow a 4) (pow b 4))))
93.0ms	(sqrt (+ (* (pow b 2) (* (* 2 a) a)) (+ (pow a 4) (pow b 4))))

simplify965.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	1542
1	276
0	99

prune612.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 2.0 (* b b)) (pow a 2)) (pow b 4))
0.0b	(* 2.0 (* b b))
0.0b	(* 4.0 (* b b))
2.4b	(* (* 2.0 (* b b)) (pow a 2))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
24×	`prod-exp`
23×	`add-cbrt-cube`
14×	`pow1`
12×	`cbrt-unprod`
10×	`add-sqr-sqrt` `associate-r`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l`
6×	`pow-prod-down` `add-log-exp`
3×	`pow-to-exp` `unpow-prod-down` `pow-exp` `*-commutative`
2×	`unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `unpow2` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

64.0ms	(+ (* (* 2.0 (* b b)) (pow a 2)) (pow b 4))
13.0ms	(* 2.0 (* b b))
20.0ms	(* 4.0 (* b b))
54.0ms	(* (* 2.0 (* b b)) (pow a 2))

series207.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ (* (* 2.0 (* b b)) (pow a 2)) (pow b 4))
50.0ms	(* 2.0 (* b b))
30.0ms	(* 4.0 (* b b))
49.0ms	(* (* 2.0 (* b b)) (pow a 2))

simplify2.3s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	2976
1	372
0	127

prune448.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes291.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.3s

20523×

body

valid