Details

sample119.0ms

Algorithm

intervals

Results

99.0ms

620×

body

valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
5	4337
4	1523
3	552
2	166
1	54
0	18

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
0.1b	(* (* a a) (- 1 a))
0.3b	(* (* b b) (+ 3 a))
0.3b	(pow (+ (* a a) (* b b)) 2)

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`associate-r`
8×	`add-cube-cbrt`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/` `insert-posit16`
3×	`pow-unpow` `unpow-prod-down`
2×	`associate-+r+` `sub-neg` `flip3-+` `associate-l` `*-commutative` `flip-+` `difference-of-squares` `unswap-sqr`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-pow` `flip3--` `pow-exp` `flip--` `distribute-lft-out` `distribute-lft-out--` `unpow2` `sqr-pow`

Counts

4 → 87

Calls

4 calls:

62.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
30.0ms	(* (* a a) (- 1 a))
30.0ms	(* (* b b) (+ 3 a))
8.0ms	(pow (+ (* a a) (* b b)) 2)

series297.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
70.0ms	(* (* a a) (- 1 a))
58.0ms	(* (* b b) (+ 3 a))
55.0ms	(pow (+ (* a a) (* b b)) 2)

simplify4.8s

Counts

99 → 99

Iterations

Iter	Nodes
3	8271
2	1759
1	523
0	173

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2)
0.3b	(pow (+ (* a a) (* b b)) 2)
8.6b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
8.6b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`pow-unpow` `unpow-prod-down` `add-exp-log` `sqrt-prod`
4×	`add-cbrt-cube` `sqrt-div` `insert-posit16` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `flip-+` `unpow2` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

15.0ms	(pow (+ (* a a) (* b b)) 2)
16.0ms	(pow (+ (* a a) (* b b)) 2)
85.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
83.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

series549.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(pow (+ (* a a) (* b b)) 2)
62.0ms	(pow (+ (* a a) (* b b)) 2)
238.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
197.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

simplify1.3s

Counts

82 → 82

Iterations

Iter	Nodes
3	3536
2	799
1	256
0	103

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* a a) (- 1 a))
0.2b	(* (* a a) (* a a))
0.3b	(* (* b b) (+ 3 a))
0.8b	(* (* b b) (+ (* 2 (* a a)) (* b b)))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

130×	`pow1`
36×	`pow-prod-up`
32×	`pow-prod-down`
31×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
18×	`pow-plus`
17×	`prod-exp` `cbrt-unprod`
14×	`associate-r`
13×	`pow2` `add-sqr-sqrt`
12×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`associate-*r/`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`sub-neg` `flip3-+` `flip-+` `difference-of-squares`
1×	`flip3--` `swap-sqr` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 142

Calls

4 calls:

30.0ms	(* (* a a) (- 1 a))
40.0ms	(* (* a a) (* a a))
32.0ms	(* (* b b) (+ 3 a))
53.0ms	(* (* b b) (+ (* 2 (* a a)) (* b b)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (* a a) (- 1 a))
57.0ms	(* (* a a) (* a a))
53.0ms	(* (* b b) (+ 3 a))
68.0ms	(* (* b b) (+ (* 2 (* a a)) (* b b)))

simplify4.9s

Counts

154 → 154

Iterations

Iter	Nodes
3	7381
2	1903
1	550
0	175

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (pow a 4) (* (* b b) (+ (* 2 (* a a)) (* b b)))) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
0.1b	(* (* a a) (- 1 a))
0.3b	(* (* b b) (+ 3 a))
0.8b	(* (* b b) (+ (* 2 (* a a)) (* b b)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

34×	`associate-*r/`
20×	`frac-add`
19×	`pow1` `add-cbrt-cube` `add-exp-log`
15×	`flip3-+` `flip-+`
13×	`add-sqr-sqrt` `associate-r`
12×	`*-un-lft-identity`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
7×	`add-cube-cbrt`
5×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `flip--`
4×	`insert-posit16`
3×	`sum-log` `associate-l` `*-commutative` `unswap-sqr`
2×	`associate-+r+` `sub-neg` `difference-of-squares`
1×	`+-commutative` `associate-+l+` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 106

Calls

4 calls:

51.0ms	(+ (+ (pow a 4) (* (* b b) (+ (* 2 (* a a)) (* b b)))) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
26.0ms	(* (* a a) (- 1 a))
25.0ms	(* (* b b) (+ 3 a))
57.0ms	(* (* b b) (+ (* 2 (* a a)) (* b b)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(+ (+ (pow a 4) (* (* b b) (+ (* 2 (* a a)) (* b b)))) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a)))))
67.0ms	(* (* a a) (- 1 a))
44.0ms	(* (* b b) (+ 3 a))
76.0ms	(* (* b b) (+ (* 2 (* a a)) (* b b)))

simplify2.2s

Counts

118 → 118

Iterations

Iter	Nodes
2	5077
1	982
0	280

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes354.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	35
1	35
0	22

end0.0ms

sample4.2s

Algorithm

intervals

Results

3.8s

20611×

body

valid