Details

sample105.0ms

Algorithm

intervals

Results

67.0ms

656×

body

valid

simplify4.9s

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

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)

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

13.0ms	(+ (* a a) (* b b))
79.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
23.0ms	(* 4.0 (* b b))
18.0ms	(pow (+ (* a a) (* b b)) 2.0)

series316.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* a a) (* b b))
89.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
28.0ms	(* 4.0 (* b b))
150.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify2.4s

Counts

70 → 70

Iterations

Useful iterations: 2 (335.0ms)

Iter	Nodes	Cost
0	117	931
1	311	838
2	943	778
3	2993	778
done	5001	778

prune262.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b	(* 2 (* (pow a 2) (pow b 2)))
2.3b	(* (pow a 2) (pow b 2))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

25.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
70.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
46.0ms	(* 2 (* (pow a 2) (pow b 2)))
18.0ms	(* (pow a 2) (pow b 2))

series261.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
76.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
63.0ms	(* 2 (* (pow a 2) (pow b 2)))
63.0ms	(* (pow a 2) (pow b 2))

simplify1.2s

Counts

113 → 113

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	146	1649
1	373	1431
2	1239	1245
done	5000	1231

prune415.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
0.0b	(* 2.0 (* (pow a 2) (pow b 2)))
0.0b	(* 4.0 (* b b))
2.3b	(* (pow a 2) (pow b 2))

rewrite574.0ms

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:

105.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
52.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
394.0ms	(* 4.0 (* b b))
19.0ms	(* (pow a 2) (pow b 2))

series198.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
39.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
48.0ms	(* 4.0 (* b b))
41.0ms	(* (pow a 2) (pow b 2))

simplify1.4s

Counts

120 → 120

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	160	1554
1	385	1400
2	1327	1118
done	5000	1094

prune349.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

2.3b	(* (pow a 2) (pow b 2))
24.1b	(cbrt (* 4.0 (* b b)))
24.1b	(cbrt (* 4.0 (* b b)))
24.1b	(cbrt (* 4.0 (* b b)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

19.0ms	(* (pow a 2) (pow b 2))
12.0ms	(cbrt (* 4.0 (* b b)))
11.0ms	(cbrt (* 4.0 (* b b)))
12.0ms	(cbrt (* 4.0 (* b b)))

series1.1s

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (pow a 2) (pow b 2))
328.0ms	(cbrt (* 4.0 (* b b)))
381.0ms	(cbrt (* 4.0 (* b b)))
356.0ms	(cbrt (* 4.0 (* b b)))

simplify2.3s

Counts

90 → 90

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	93	890
1	189	804
2	504	626
3	2015	609
done	5000	592

prune305.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes112.0ms

Accuracy

22% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.9b

bsearch3.0ms

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	31	86
1	43	68
done	43	68

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.4s

20728×

body

valid