Details

sample42.0ms

Algorithm

intervals

Results

24.0ms

631×

body

valid

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

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)

rewrite309.0ms

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:

275.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
7.0ms	(+ (* a a) (* b b))
16.0ms	(* 4.0 (* b b))
10.0ms	(pow (+ (* a a) (* b b)) 2.0)

series234.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
28.0ms	(+ (* a a) (* b b))
28.0ms	(* 4.0 (* b b))
104.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify1.4s

Counts

75 → 75

Iterations

Useful iterations: 3 (626.0ms)

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

prune159.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (pow a 4) (* 4.0 (pow b 2))) 1.0)
0.0b	(* 4.0 (pow b 2))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log` `*-un-lft-identity` `add-log-exp`
5×	`add-cube-cbrt`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `diff-log` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

61.0ms	(- (+ (pow a 4) (* 4.0 (pow b 2))) 1.0)
11.0ms	(* 4.0 (pow b 2))

series78.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (+ (pow a 4) (* 4.0 (pow b 2))) 1.0)
27.0ms	(* 4.0 (pow b 2))

simplify944.0ms

Counts

49 → 49

Iterations

Useful iterations: done (942.0ms)

Iter	Nodes	Cost
0	87	540
1	186	512
2	483	457
3	1798	449
done	5000	446

prune98.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (* (pow a 2) (pow b 2)))
0.0b	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
2.7b	(* (pow a 2) (pow b 2))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log`
31×	`prod-exp`
27×	`add-sqr-sqrt`
17×	`unswap-sqr`
16×	`add-cbrt-cube`
14×	`unpow-prod-down` `associate-l`
12×	`pow-to-exp` `pow-exp`
11×	`pow1`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r*` `unpow2` `sqr-pow`
9×	`add-log-exp`
7×	`cbrt-unprod`
5×	`pow-prod-down`
3×	`sum-log` `*-commutative`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+`

Counts

4 → 108

Calls

4 calls:

23.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
52.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
16.0ms	(* 4.0 (* b b))
16.0ms	(* (pow a 2) (pow b 2))

series155.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
62.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
25.0ms	(* 4.0 (* b b))
32.0ms	(* (pow a 2) (pow b 2))

simplify812.0ms

Counts

120 → 120

Iterations

Useful iterations: done (809.0ms)

Iter	Nodes	Cost
0	160	1554
1	385	1400
2	1326	1118
done	5000	1094

prune222.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* b b))
0.0b	(exp (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.5b	(log (exp (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

17.0ms	(* 4.0 (* b b))
504.0ms	(exp (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))
10.0ms	(pow (+ (* a a) (* b b)) 2.0)
542.0ms	(log (exp (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 4.0 (* b b))
79.0ms	(exp (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))
107.0ms	(pow (+ (* a a) (* b b)) 2.0)
74.0ms	(log (exp (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)))

simplify1.1s

Counts

88 → 88

Iterations

Useful iterations: 3 (407.0ms)

Iter	Nodes	Cost
0	140	1394
1	281	1309
2	712	1184
3	2219	1180
done	5001	1180

prune223.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes156.0ms

Accuracy

87.3% (1.4b remaining)

Error of 1.6b against oracle of 0.2b and baseline of 11.4b

bsearch91.0ms

Steps

Iters	Range		Point
9	211.08706756948936	26948912.295173395	213.20671289812063
7	-9.588134368690297e-05	-1.0861520957633684e-06	-9.434783373745747e-05

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	61
1	37	41
done	37	41

end0.0ms

sample1.2s

Algorithm

intervals

Results

714.0ms

20101×

body

valid