Details

sample87.0ms

Algorithm

intervals

Results

49.0ms

709×

body

valid

simplify5.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	17
1	25	17
2	40	17
3	66	17
4	118	17
5	255	17
6	849	17
7	3688	17
done	5000	17

prune4.0ms

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	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
0.0b	(+ (* a a) (* b b))
0.0b	(* 4.0 (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite811.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-log-exp`
10×	`pow1` `add-exp-log` `add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cbrt-cube`
7×	`add-cube-cbrt`
3×	`unpow-prod-down` `pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`diff-log` `sum-log`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `flip3-+` `associate-r` `pow-exp` `associate--l+` `*-commutative` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 63

Calls

4 calls:

760.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
17.0ms	(+ (* a a) (* b b))
20.0ms	(* 4.0 (* b b))
11.0ms	(pow (+ (* a a) (* b b)) 2.0)

series350.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
42.0ms	(+ (* a a) (* b b))
45.0ms	(* 4.0 (* b b))
150.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify2.4s

Counts

75 → 75

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	131	1045
1	326	990
2	965	914
3	3169	900
done	5001	900

prune270.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 4.0 (pow b 2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`associate-r`
6×	`add-exp-log`
4×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `unswap-sqr`
3×	`associate-l` `prod-exp` `add-cbrt-cube`
2×	`unpow2` `sqr-pow`
1×	`pow1` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

25.0ms

(* 4.0 (pow b 2))

series46.0ms

Counts

1 → 3

Calls

1 calls:

45.0ms

(* 4.0 (pow b 2))

simplify4.0s

Counts

30 → 30

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	51	232
1	107	209
2	233	176
3	678	176
4	3313	173
done	5001	173

prune130.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2))))
0.0b	(* 4.0 (* b b))
0.0b	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
1.2b	(* (pow a 2) (pow b 2))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

28.0ms	(+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2))))
35.0ms	(* 4.0 (* b b))
111.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
32.0ms	(* (pow a 2) (pow b 2))

series253.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2))))
31.0ms	(* 4.0 (* b b))
90.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
59.0ms	(* (pow a 2) (pow b 2))

simplify1.3s

Counts

106 → 106

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	154	1499
1	386	1335
2	1379	1083
done	5001	1055

prune374.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
1.2b	(* (pow a 2) (pow b 2))

rewrite51.0ms

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` `add-log-exp`
2×	`pow1`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 62

Calls

2 calls:

14.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
34.0ms	(* (pow a 2) (pow b 2))

series104.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
43.0ms	(* (pow a 2) (pow b 2))

simplify5.2s

Counts

68 → 68

Iterations

Useful iterations: done (5.2s)

Iter	Nodes	Cost
0	102	882
1	249	776
2	784	610
3	4464	600
done	5000	587

prune243.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes101.0ms

Accuracy

94.8% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 11.0b

bsearch149.0ms

Steps

Iters	Range		Point
9	0.9525777503998405	166099.72969241772	1.837689356044482
8	-2.284674362912159	-0.004460202384511771	-0.98226702836631

simplify16.0ms

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	23	53
1	32	37
done	32	37

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.0s

20533×

body

valid