Details

sample66.0ms

Algorithm

intervals

Results

42.0ms

658×

body

valid

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	3678
5	427
4	120
3	66
2	40
1	25
0	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b	(+ (* a a) (* b b))
0.0b	(* 4.0 (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log`
9×	`add-cbrt-cube`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
3×	`pow-unpow` `unpow-prod-down` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `sum-log` `flip3-+` `flip-+`
1×	`pow-to-exp` `pow-pow` `associate-r` `pow-exp` `*-commutative` `unswap-sqr` `sqr-pow`

Counts

4 → 58

Calls

4 calls:

67.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
11.0ms	(+ (* a a) (* b b))
27.0ms	(* 4.0 (* b b))
11.0ms	(pow (+ (* a a) (* b b)) 2.0)

series287.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
42.0ms	(+ (* a a) (* b b))
34.0ms	(* 4.0 (* b b))
128.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify1.3s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
2	2107
1	382
0	117

prune359.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

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)
15.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
15.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite156.0ms

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)
16.0ms	(pow (+ (* a a) (* b b)) 2.0)
70.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
59.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series584.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(pow (+ (* a a) (* b b)) 2.0)
176.0ms	(pow (+ (* a a) (* b b)) 2.0)
114.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
109.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify3.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	4721
2	822
1	226
0	94

prune450.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

9.7b	(sqrt (+ (* a a) (* b b)))
9.7b	(sqrt (+ (* a a) (* b b)))
15.2b	(sqrt (+ (* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0)) (* 4.0 (* b b))))
15.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

7.0ms	(sqrt (+ (* a a) (* b b)))
6.0ms	(sqrt (+ (* a a) (* b b)))
37.0ms	(sqrt (+ (* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0)) (* 4.0 (* b b))))
51.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series316.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (+ (* a a) (* b b)))
55.0ms	(sqrt (+ (* a a) (* b b)))
102.0ms	(sqrt (+ (* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0)) (* 4.0 (* b b))))
106.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify805.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	1177
1	281
0	114

prune625.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

9.7b	(sqrt (+ (* a a) (* b b)))
9.7b	(sqrt (+ (* a a) (* b b)))
15.2b	(sqrt (+ (* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (* (sqrt (sqrt (+ (* a a) (* b b)))) (sqrt (sqrt (+ (* a a) (* b b))))) 2.0)) (* 4.0 (* b b))))
15.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite394.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

6.0ms	(sqrt (+ (* a a) (* b b)))
6.0ms	(sqrt (+ (* a a) (* b b)))
335.0ms	(sqrt (+ (* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (* (sqrt (sqrt (+ (* a a) (* b b)))) (sqrt (sqrt (+ (* a a) (* b b))))) 2.0)) (* 4.0 (* b b))))
46.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ (* a a) (* b b)))
43.0ms	(sqrt (+ (* a a) (* b b)))
120.0ms	(sqrt (+ (* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (* (sqrt (sqrt (+ (* a a) (* b b)))) (sqrt (sqrt (+ (* a a) (* b b))))) 2.0)) (* 4.0 (* b b))))
119.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify894.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1307
1	292
0	116

prune719.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes429.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	24
1	24
0	19

end0.0ms

sample2.5s

Algorithm

intervals

Results

2.0s

20454×

body

valid