Details

sample118.0ms

Algorithm

intervals

Results

80.0ms

606×

body

valid

simplify4.4s

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

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	(* (* b b) (- 1.0 (* 3.0 a)))
0.1b	(* (* a a) (+ 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite166.0ms

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:

73.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
38.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
42.0ms	(* (* a a) (+ 1.0 a))
10.0ms	(pow (+ (* a a) (* b b)) 2.0)

series443.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
71.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
82.0ms	(* (* a a) (+ 1.0 a))
135.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify2.0s

Counts

91 → 91

Iterations

Iter	Nodes
done	5004
2	1996
1	519
0	175

prune634.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize121.0ms

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)))))))

rewrite174.0ms

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:

17.0ms	(pow (+ (* a a) (* b b)) 2.0)
13.0ms	(pow (+ (* a a) (* b b)) 2.0)
64.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
77.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series858.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(pow (+ (* a a) (* b b)) 2.0)
143.0ms	(pow (+ (* a a) (* b b)) 2.0)
264.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
295.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify2.9s

Counts

76 → 76

Iterations

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

prune703.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize195.0ms

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)))))))
20.5b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.5b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.5b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite131.0ms

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:

84.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
15.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
15.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
15.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series868.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
190.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
216.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
232.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify3.1s

Counts

72 → 72

Iterations

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

prune767.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.1b

localize218.0ms

Local error

Found 4 expressions with local error:

13.1b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
13.1b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
20.5b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
20.5b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite61.0ms

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:

15.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
24.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
12.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
8.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series842.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
211.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
221.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
220.0ms	(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

prune852.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

regimes794.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	27
1	27
0	19

end0.0ms

sample3.6s

Algorithm

intervals

Results

3.0s

20397×

body

valid