Details

sample90.0ms

Algorithm

intervals

Results

70.0ms

621×

body

valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5009
4	3931
3	672
2	166
1	54
0	18

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize48.0ms

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))))) 1)
0.1b	(* (* a a) (- 1 a))
0.3b	(pow (+ (* a a) (* b b)) 2)
0.6b	(* (* b b) (+ 3 a))

rewrite332.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

241.0ms	(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1)
38.0ms	(* (* a a) (- 1 a))
10.0ms	(pow (+ (* a a) (* b b)) 2)
41.0ms	(* (* b b) (+ 3 a))

series307.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1)
76.0ms	(* (* a a) (- 1 a))
47.0ms	(pow (+ (* a a) (* b b)) 2)
38.0ms	(* (* b b) (+ 3 a))

simplify1.7s

Counts

104 → 104

Iterations

Iter	Nodes
done	5007
2	1910
1	540
0	179

prune503.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* a a) (* (* a a) a))
0.1b	(* (* a a) a)
0.3b	(pow (+ (* a a) (* b b)) 2)
0.6b	(* (* b b) (+ 3 a))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1`
15×	`add-exp-log`
14×	`add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`associate-r`
6×	`pow-plus` `pow-prod-down` `prod-exp` `pow-prod-up` `cbrt-unprod` `add-log-exp`
4×	`insert-posit16`
3×	`pow-unpow` `unpow-prod-down`
2×	`pow2` `associate-l` `associate-r/` `pow-sqr` `-commutative` `unswap-sqr`
1×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `flip3-+` `flip3--` `distribute-rgt-out--` `diff-log` `pow3` `pow-exp` `flip-+` `flip--` `distribute-lft-out` `unpow2` `sqr-pow`

Counts

4 → 87

Calls

4 calls:

7.0ms	(- (* a a) (* (* a a) a))
17.0ms	(* (* a a) a)
15.0ms	(pow (+ (* a a) (* b b)) 2)
26.0ms	(* (* b b) (+ 3 a))

series225.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- (* a a) (* (* a a) a))
48.0ms	(* (* a a) a)
43.0ms	(pow (+ (* a a) (* b b)) 2)
39.0ms	(* (* b b) (+ 3 a))

simplify1.3s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	1696
1	445
0	143

prune330.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* b b) (+ 3 a))
0.6b	(* (* b b) (+ 3 a))
9.1b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
9.1b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
14×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`associate-r` `add-cube-cbrt`
6×	`pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`flip3-+` `sqrt-div` `associate-*r/` `flip-+` `insert-posit16` `add-log-exp`
2×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

23.0ms	(* (* b b) (+ 3 a))
21.0ms	(* (* b b) (+ 3 a))
43.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
44.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

series465.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (* b b) (+ 3 a))
39.0ms	(* (* b b) (+ 3 a))
188.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
203.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

simplify1.4s

Counts

94 → 94

Iterations

Iter	Nodes
done	5005
2	1434
1	330
0	114

prune687.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize78.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* b b) (+ 3 a))
9.1b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
9.1b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
9.1b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `pow1`
10×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
8×	`add-cube-cbrt`
6×	`sqrt-div`
4×	`flip3-+` `associate-r` `flip-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative` `distribute-lft-out` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

30.0ms	(* (* b b) (+ 3 a))
39.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
40.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
44.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

series709.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (* b b) (+ 3 a))
257.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
205.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))
190.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))))

simplify1.5s

Counts

85 → 85

Iterations

Iter	Nodes
done	5005
2	1434
1	330
0	114

prune776.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes389.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	34
1	34
0	23

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.6s

20480×

body

valid