Details

sample178.0ms

Algorithm

intervals

Results

127.0ms

684×

body

valid

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	31
1	53	31
2	161	31
3	486	31
4	1645	31
done	5001	31

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b	(* (* a a) (+ 1.0 a))
0.2b	(* (* b b) (- 1.0 (* 3.0 a)))
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
3×	`unpow-prod-down` `pow-unpow`
2×	`sub-neg` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

102.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
60.0ms	(* (* a a) (+ 1.0 a))
48.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
31.0ms	(pow (+ (* a a) (* b b)) 2.0)

series538.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
90.0ms	(* (* a a) (+ 1.0 a))
89.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
173.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify4.5s

Counts

91 → 91

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	175	1540
1	552	1441
2	3933	1287
done	5001	1287

prune635.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0))
0.1b	(* (* a a) (+ 1.0 a))
0.2b	(* (* b b) (- 1.0 (* 3.0 a)))
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`associate-*r/`
3×	`distribute-rgt-in` `unpow-prod-down` `pow-unpow` `distribute-lft-in`
2×	`sub-neg` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

102.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0))
56.0ms	(* (* a a) (+ 1.0 a))
63.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
20.0ms	(pow (+ (* a a) (* b b)) 2.0)

series484.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0))
85.0ms	(* (* a a) (+ 1.0 a))
83.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
176.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify5.0s

Counts

89 → 89

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	169	1320
1	533	1229
2	3833	1095
done	5000	1095

prune688.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (+ (* a a) (* b b)) 2.0)
0.4b	(pow (+ (* a a) (* b b)) 2.0)
12.0b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0)))
12.0b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0)))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`add-exp-log` `unpow-prod-down` `pow-unpow` `sqrt-prod`
4×	`sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `flip-+` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

23.0ms	(pow (+ (* a a) (* b b)) 2.0)
23.0ms	(pow (+ (* a a) (* b b)) 2.0)
127.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0)))
125.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0)))

series941.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(pow (+ (* a a) (* b b)) 2.0)
198.0ms	(pow (+ (* a a) (* b b)) 2.0)
279.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0)))
277.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0)))

simplify849.0ms

Counts

76 → 76

Iterations

Useful iterations: done (844.0ms)

Iter	Nodes	Cost
0	85	1564
1	213	1372
2	801	1336
done	5001	1332

prune839.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize116.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (+ (* a a) (* b b)) 2.0)
12.0b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0)))
12.0b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0)))
12.0b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0)))

rewrite407.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
8×	`pow1`
6×	`sqrt-div`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `rem-sqrt-square` `pow-unpow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`

Counts

4 → 62

Calls

4 calls:

21.0ms	(pow (+ (* a a) (* b b)) 2.0)
126.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0)))
131.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0)))
126.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

190.0ms	(pow (+ (* a a) (* b b)) 2.0)
280.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0)))
276.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0)))
278.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* (* (* a a) (+ 1.0 a)) 4.0)))

simplify818.0ms

Counts

74 → 74

Iterations

Useful iterations: done (813.0ms)

Iter	Nodes	Cost
0	85	1824
1	213	1584
2	801	1530
done	5001	1524

prune850.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes281.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	33
1	29	33
done	29	33

end0.0ms

sample4.6s

Algorithm

intervals

Results

3.7s

20353×

body

valid