Details

sample54.0ms

Algorithm

intervals

Results

36.0ms

622×

body

valid

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	31
1	53	31
2	140	31
3	344	31
4	841	31
5	1855	31
6	3754	31
done	5001	31

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
1.3b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite57.0ms

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:

23.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
13.0ms	(* (* a a) (+ 1.0 a))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
14.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
47.0ms	(* (* a a) (+ 1.0 a))
98.0ms	(pow (+ (* a a) (* b b)) 2.0)
51.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify978.0ms

Counts

91 → 91

Iterations

Useful iterations: 2 (339.0ms)

Iter	Nodes	Cost
0	175	1540
1	490	1431
2	2002	1287
done	5001	1287

prune250.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (* b b) (- 1.0 (* 3.0 a)))
8.9b	(cbrt (+ (* a a) (* b b)))
8.9b	(cbrt (+ (* a a) (* b b)))
8.9b	(cbrt (+ (* a a) (* b b)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

12.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
2.0ms	(cbrt (+ (* a a) (* b b)))
2.0ms	(cbrt (+ (* a a) (* b b)))
2.0ms	(cbrt (+ (* a a) (* b b)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
92.0ms	(cbrt (+ (* a a) (* b b)))
92.0ms	(cbrt (+ (* a a) (* b b)))
97.0ms	(cbrt (+ (* a a) (* b b)))

simplify2.7s

Counts

76 → 76

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	102	1069
1	272	1018
2	1044	884
3	4670	875
done	5000	875

prune330.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

8.2b	(sqrt (+ (* a a) (* b b)))
8.2b	(sqrt (+ (* a a) (* b b)))
8.9b	(cbrt (+ (* a a) (* b b)))
8.9b	(cbrt (+ (* a a) (* b b)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

3.0ms	(sqrt (+ (* a a) (* b b)))
3.0ms	(sqrt (+ (* a a) (* b b)))
2.0ms	(cbrt (+ (* a a) (* b b)))
3.0ms	(cbrt (+ (* a a) (* b b)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ (* a a) (* b b)))
38.0ms	(sqrt (+ (* a a) (* b b)))
93.0ms	(cbrt (+ (* a a) (* b b)))
92.0ms	(cbrt (+ (* a a) (* b b)))

simplify1.6s

Counts

68 → 68

Iterations

Useful iterations: 3 (185.0ms)

Iter	Nodes	Cost
0	65	890
1	144	824
2	357	716
3	1029	710
4	3241	710
done	5000	710

prune384.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b	(* 2 (* (pow a 2) (pow b 2)))
2.8b	(* (pow a 2) (pow b 2))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 90

Calls

3 calls:

17.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
10.0ms	(* 2 (* (pow a 2) (pow b 2)))
9.0ms	(* (pow a 2) (pow b 2))

series129.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
37.0ms	(* 2 (* (pow a 2) (pow b 2)))
36.0ms	(* (pow a 2) (pow b 2))

simplify793.0ms

Counts

99 → 99

Iterations

Useful iterations: done (790.0ms)

Iter	Nodes	Cost
0	132	1357
1	330	1202
2	1319	1010
done	5000	1006

prune191.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes156.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	63
1	35	63
done	35	63

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

20276×

body

valid