Details

sample64.0ms

Algorithm

intervals

Results

50.0ms

638×

body

valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2029
6	2029
5	1889
4	575
3	160
2	62
1	29
0	12

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a a) (* b b))
0.0b	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
0.0b	(* 4 (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2)

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `pow1` `add-exp-log`
9×	`fma-def` `*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
8×	`add-log-exp`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `sum-log` `flip3-+` `flip-+` `unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `associate-r` `pow-exp` `*-commutative` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

8.0ms	(+ (* a a) (* b b))
57.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
14.0ms	(* 4 (* b b))
11.0ms	(pow (+ (* a a) (* b b)) 2)

series247.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* a a) (* b b))
108.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
51.0ms	(* 4 (* b b))
56.0ms	(pow (+ (* a a) (* b b)) 2)

simplify1.1s

Counts

92 → 92

Iterations

Iter	Nodes
done	2000
3	2000
2	1587
1	384
0	121

prune508.0ms

Pruning

5 alts after pruning (5 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)
0.3b	(pow (+ (* a a) (* b b)) 2)
12.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
12.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))

rewrite193.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `flip-+` `unpow2` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

16.0ms	(pow (+ (* a a) (* b b)) 2)
17.0ms	(pow (+ (* a a) (* b b)) 2)
85.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
73.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))

series350.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(pow (+ (* a a) (* b b)) 2)
50.0ms	(pow (+ (* a a) (* b b)) 2)
126.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
113.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))

simplify950.0ms

Counts

90 → 90

Iterations

Iter	Nodes
done	2001
3	2001
2	727
1	236
0	93

prune457.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize65.0ms

Local error

Found 4 expressions with local error:

12.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
12.8b	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
12.8b	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
12.8b	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 66

Calls

4 calls:

72.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
47.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
37.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
31.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))

series850.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
253.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
231.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
264.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))

simplify888.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	2007
3	2007
2	690
1	214
0	94

prune741.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize97.0ms

Local error

Found 4 expressions with local error:

12.2b	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
12.8b	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
12.8b	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
12.8b	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 66

Calls

4 calls:

67.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
28.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
33.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
41.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))

series770.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
214.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
213.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))
217.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))))

simplify817.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	2007
3	2007
2	690
1	214
0	94

prune578.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes328.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	14

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.6s

20446×

body

valid