Details

sample87.0ms

Algorithm

intervals

Results

61.0ms

612×

body

valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	3532
4	1319
3	449
2	159
1	53
0	19

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

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)))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite139.0ms

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×	`pow-unpow` `unpow-prod-down`
2×	`associate-+r+` `sub-neg` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-pow` `flip3--` `pow-exp` `flip--` `distribute-lft-out` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

56.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
26.0ms	(* (* a a) (+ 1.0 a))
41.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
15.0ms	(pow (+ (* a a) (* b b)) 2.0)

series447.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
70.0ms	(* (* a a) (+ 1.0 a))
74.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
143.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify2.0s

Counts

91 → 91

Iterations

Iter	Nodes
done	5001
2	1919
1	522
0	175

prune560.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize91.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
9.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
9.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite144.0ms

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` `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:

9.0ms	(pow (+ (* a a) (* b b)) 2.0)
15.0ms	(pow (+ (* a a) (* b b)) 2.0)
59.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
59.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series758.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(pow (+ (* a a) (* b b)) 2.0)
146.0ms	(pow (+ (* a a) (* b b)) 2.0)
227.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
226.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify3.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	4080
2	848
1	270
0	110

prune604.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize138.0ms

Local error

Found 4 expressions with local error:

9.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

75.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
7.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
8.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
8.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series755.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
183.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
174.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
185.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify2.6s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	3896
2	824
1	273
0	122

prune781.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize160.0ms

Local error

Found 4 expressions with local error:

11.8b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
11.8b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`cbrt-prod` `unpow-prod-down` `sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
6×	`rem-sqrt-square` `sqr-pow`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 68

Calls

4 calls:

18.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
22.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
13.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
14.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series872.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
201.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
226.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
241.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify2.3s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
4	1690
3	624
2	265
1	138
0	79

prune1.1s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes575.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	29
1	29
0	21

end0.0ms

sample3.7s

Algorithm

intervals

Results

3.1s

20694×

body

valid