Details

sample100.0ms

Algorithm

intervals

Results

57.0ms

684×

body

valid

simplify4.4s

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	120	17
5	426	17
6	3507	17
done	5001	17

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

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))
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite175.0ms

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:

106.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
18.0ms	(+ (* a a) (* b b))
30.0ms	(* 4.0 (* b b))
18.0ms	(pow (+ (* a a) (* b b)) 2.0)

series416.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
55.0ms	(+ (* a a) (* b b))
57.0ms	(* 4.0 (* b b))
175.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify2.2s

Counts

70 → 70

Iterations

Useful iterations: 2 (583.0ms)

Iter	Nodes	Cost
0	117	931
1	382	848
2	2133	778
done	5000	778

prune507.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b	(* 2 (* (pow a 2) (pow b 2)))
2.2b	(* (pow a 2) (pow b 2))

rewrite205.0ms

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:

70.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
35.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
54.0ms	(* 2 (* (pow a 2) (pow b 2)))
37.0ms	(* (pow a 2) (pow b 2))

series332.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
101.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
71.0ms	(* 2 (* (pow a 2) (pow b 2)))
62.0ms	(* (pow a 2) (pow b 2))

simplify3.0s

Counts

113 → 113

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	146	1649
1	386	1443
2	2409	1247
done	5000	1233

prune687.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* a a) (* b b))
0.0b	(* 4.0 (* b b))
0.4b	(pow (/ (- (pow a 4) (pow b 4)) (- (* a a) (* b b))) 2.0)
18.0b	(/ (- (pow a 4) (pow b 4)) (- (* a a) (* b b)))

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

154×	`add-sqr-sqrt`
134×	`unpow-prod-down`
112×	`times-frac`
111×	`difference-of-squares`
81×	`*-un-lft-identity`
55×	`sqr-pow`
45×	`add-cube-cbrt`
18×	`distribute-lft-out--`
14×	`add-exp-log` `associate-/l*`
11×	`add-cbrt-cube`
10×	`pow1`
6×	`add-log-exp`
4×	`flip3--` `associate-/r*` `associate-/r/` `flip--`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`div-exp` `pow-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r` `clear-num` `*-commutative` `unswap-sqr`

Counts

4 → 200

Calls

4 calls:

19.0ms	(- (* a a) (* b b))
36.0ms	(* 4.0 (* b b))
100.0ms	(pow (/ (- (pow a 4) (pow b 4)) (- (* a a) (* b b))) 2.0)
117.0ms	(/ (- (pow a 4) (pow b 4)) (- (* a a) (* b b)))

series518.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* a a) (* b b))
49.0ms	(* 4.0 (* b b))
265.0ms	(pow (/ (- (pow a 4) (pow b 4)) (- (* a a) (* b b))) 2.0)
142.0ms	(/ (- (pow a 4) (pow b 4)) (- (* a a) (* b b)))

simplify1.1s

Counts

212 → 212

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	377	5514
1	1346	5142
done	5001	5038

prune1.9s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize48.0ms

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))
2.2b	(* (pow a 2) (pow b 2))

rewrite230.0ms

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:

47.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
106.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
36.0ms	(* 4.0 (* b b))
34.0ms	(* (pow a 2) (pow b 2))

series273.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
109.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
44.0ms	(* 4.0 (* b b))
55.0ms	(* (pow a 2) (pow b 2))

simplify2.8s

Counts

120 → 120

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	160	1554
1	433	1422
2	2787	1118
done	5001	1106

prune575.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes426.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	17
1	15	17
done	15	17

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.8s

20353×

body

valid