Details

sample95.0ms

Algorithm

intervals

Results

52.0ms

643×

body

valid

simplify7.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5053
7	3274
6	782
5	232
4	111
3	65
2	40
1	25
0	12

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log`
8×	`add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`add-log-exp`
3×	`pow-unpow` `unpow-prod-down` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-pow` `flip3-+` `associate-r` `pow-exp` `*-commutative` `flip-+` `unswap-sqr` `sqr-pow`

Counts

3 → 50

Calls

3 calls:

30.0ms	(* 4.0 (* b b))
90.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
16.0ms	(pow (+ (* a a) (* b b)) 2.0)

series441.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* 4.0 (* b b))
154.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
250.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify7.0s

Counts

59 → 59

Iterations

Iter	Nodes
done	5021
3	4016
2	911
1	288
0	104

prune669.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize130.0ms

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)
15.3b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
15.3b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite251.0ms

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` `insert-posit16` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `flip-+` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

19.0ms	(pow (+ (* a a) (* b b)) 2.0)
13.0ms	(pow (+ (* a a) (* b b)) 2.0)
117.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
97.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series816.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(pow (+ (* a a) (* b b)) 2.0)
200.0ms	(pow (+ (* a a) (* b b)) 2.0)
175.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
215.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify4.1s

Counts

80 → 80

Iterations

Iter	Nodes
done	5010
3	2207
2	616
1	221
0	96

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize290.0ms

Local error

Found 4 expressions with local error:

15.3b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
16.0b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
16.0b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
16.0b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite313.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

121.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
65.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
67.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
59.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series1.4s

Counts

4 → 12

Calls

4 calls:

176.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
467.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
396.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
394.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify4.0s

Counts

70 → 70

Iterations

Iter	Nodes
done	5009
3	2026
2	576
1	207
0	95

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize387.0ms

Local error

Found 4 expressions with local error:

15.3b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
15.3b	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
16.0b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
16.0b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite397.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `sqrt-prod`
4×	`cbrt-div` `flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 60

Calls

4 calls:

148.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
127.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
76.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
41.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series1.3s

Counts

4 → 12

Calls

4 calls:

178.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
182.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
444.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
471.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify3.8s

Counts

72 → 72

Iterations

Iter	Nodes
done	5009
3	2026
2	576
1	207
0	95

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes862.0ms

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	17
1	17
0	14

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.9s

20753×

body

valid