Details

sample57.0ms

Algorithm

intervals

Results

34.0ms

689×

body

valid

simplify3.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	17
1	25	17
2	39	17
3	63	17
4	109	17
5	245	17
6	813	17
7	3731	17
done	5000	17

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.2b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a a) (* b b))
0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

4.0ms	(+ (* a a) (* b b))
7.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
6.0ms	(* 4.0 (* b b))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series47.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* a a) (* b b))
15.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
4.0ms	(* 4.0 (* b b))
23.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify2.4s

Counts

70 → 70

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	133	957
1	360	859
2	1131	791
3	4357	784
done	5000	784

prune121.0ms

Filtered

49 candidates to 70 candidates (-42.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	4	71

Merged error: 0.0b

Counts

71 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (+ (* a a) (* b b))) 2.0)
0.4b	(* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0))
7.8b	(sqrt (+ (* a a) (* b b)))
7.8b	(sqrt (+ (* a a) (* b b)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
50×	`unpow-prod-down`
31×	`sqrt-prod`
21×	`add-cube-cbrt` `*-un-lft-identity`
17×	`add-exp-log`
16×	`unswap-sqr`
13×	`sqr-pow`
12×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`prod-exp`
8×	`pow1`
7×	`pow-to-exp` `pow-exp`
6×	`add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`pow-unpow` `pow-pow` `sqrt-pow1` `pow1/2`
2×	`rem-sqrt-square` `flip3-+` `flip-+`
1×	`pow2` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod`

Counts

4 → 123

Calls

4 calls:

6.0ms	(pow (sqrt (+ (* a a) (* b b))) 2.0)
15.0ms	(* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0))
4.0ms	(sqrt (+ (* a a) (* b b)))
4.0ms	(sqrt (+ (* a a) (* b b)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (sqrt (+ (* a a) (* b b))) 2.0)
39.0ms	(* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0))
6.0ms	(sqrt (+ (* a a) (* b b)))
6.0ms	(sqrt (+ (* a a) (* b b)))

simplify2.1s

Counts

135 → 135

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	147	3122
1	320	2379
2	967	2207
3	3569	2157
done	5001	2157

prune183.0ms

Filtered

81 candidates to 135 candidates (-66.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	137	2	139

Merged error: 0b

Counts

139 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (sqrt (+ (* a a) (* b b))) (+ 2.0 2.0)) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
0.0b	(pow (sqrt (+ (* a a) (* b b))) (+ 2.0 2.0))
7.8b	(sqrt (+ (* a a) (* b b)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`pow1` `pow-unpow`
10×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`unpow-prod-down` `sqrt-prod` `add-log-exp`
3×	`distribute-rgt-out` `pow-pow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`
1×	`unpow-prod-up` `+-commutative` `pow-to-exp` `rem-sqrt-square` `distribute-lft1-in` `count-2` `associate-r` `distribute-rgt1-in` `pow-exp` `sum-log` `*-commutative` `sqrt-pow2` `unswap-sqr` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

9.0ms	(+ (pow (sqrt (+ (* a a) (* b b))) (+ 2.0 2.0)) (* 4.0 (* b b)))
6.0ms	(* 4.0 (* b b))
8.0ms	(pow (sqrt (+ (* a a) (* b b))) (+ 2.0 2.0))
4.0ms	(sqrt (+ (* a a) (* b b)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (pow (sqrt (+ (* a a) (* b b))) (+ 2.0 2.0)) (* 4.0 (* b b)))
3.0ms	(* 4.0 (* b b))
23.0ms	(pow (sqrt (+ (* a a) (* b b))) (+ 2.0 2.0))
6.0ms	(sqrt (+ (* a a) (* b b)))

simplify2.1s

Counts

90 → 90

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	154	1340
1	407	1175
2	1154	1087
3	3960	1071
done	5000	1071

prune125.0ms

Filtered

60 candidates to 90 candidates (-50.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	90	2	92

Merged error: 0b

Counts

92 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (+ (* a a) (* b b))) 2.0)
0.2b	(pow (pow (sqrt (+ (* a a) (* b b))) 2.0) 6)
7.8b	(sqrt (+ (* a a) (* b b)))
29.7b	(cbrt (pow (pow (sqrt (+ (* a a) (* b b))) 2.0) 6))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

38×	`unpow-prod-down`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
14×	`cbrt-prod`
12×	`sqrt-prod`
7×	`pow1` `add-exp-log`
6×	`pow-unpow`
5×	`pow-exp` `sqr-pow`
4×	`pow-pow` `add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp`
2×	`sqrt-pow1` `pow1/2` `sqrt-div`
1×	`rem-sqrt-square` `flip3-+` `pow1/3` `sqrt-pow2` `flip-+`

Counts

4 → 86

Calls

4 calls:

6.0ms	(pow (sqrt (+ (* a a) (* b b))) 2.0)
7.0ms	(pow (pow (sqrt (+ (* a a) (* b b))) 2.0) 6)
4.0ms	(sqrt (+ (* a a) (* b b)))
10.0ms	(cbrt (pow (pow (sqrt (+ (* a a) (* b b))) 2.0) 6))

series102.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow (sqrt (+ (* a a) (* b b))) 2.0)
36.0ms	(pow (pow (sqrt (+ (* a a) (* b b))) 2.0) 6)
6.0ms	(sqrt (+ (* a a) (* b b)))
35.0ms	(cbrt (pow (pow (sqrt (+ (* a a) (* b b))) 2.0) 6))

simplify1.6s

Counts

98 → 98

Iterations

Useful iterations: 3 (734.0ms)

Iter	Nodes	Cost
0	160	1726
1	355	1590
2	855	1469
3	2903	1412
done	5000	1412

prune155.0ms

Filtered

65 candidates to 98 candidates (-50.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	98	2	100

Merged error: 0b

Counts

100 → 2

regimes132.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	20
1	17	20
done	17	20

end0.0ms

sample1.5s

Algorithm

intervals

Results

936.0ms

20932×

body

valid

Details

sample57.0ms

simplify3.8s

prune3.0ms

localize15.0ms

rewrite23.0ms

series47.0ms

simplify2.4s

prune121.0ms

localize13.0ms

rewrite34.0ms

series72.0ms

simplify2.1s

prune183.0ms

localize15.0ms

rewrite30.0ms

series44.0ms

simplify2.1s

prune125.0ms

localize14.0ms

rewrite30.0ms

series102.0ms

simplify1.6s

prune155.0ms

regimes132.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.5s

Profiling