Details

sample56.0ms

Algorithm

intervals

Results

32.0ms

689×

body

valid

simplify1.8s

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	111	17
5	257	17
6	851	17
7	3883	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

localize10.0ms

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)

rewrite24.0ms

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)

series53.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* a a) (* b b))
19.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
3.0ms	(* 4.0 (* b b))
24.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify939.0ms

Counts

70 → 70

Iterations

Useful iterations: 3 (348.0ms)

Iter	Nodes	Cost
0	133	957
1	365	875
2	1218	791
3	3624	784
done	5000	784

prune128.0ms

Filtered

52 candidates to 70 candidates (-34.6%)

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)))

rewrite37.0ms

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:

22.0ms	(pow (sqrt (+ (* a a) (* b b))) 2.0)
37.0ms	(* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0))
7.0ms	(sqrt (+ (* a a) (* b b)))
7.0ms	(sqrt (+ (* a a) (* b b)))

simplify407.0ms

Counts

135 → 135

Iterations

Useful iterations: done (403.0ms)

Iter	Nodes	Cost
0	147	3122
1	331	2389
2	1106	2207
done	5000	2200

prune190.0ms

Filtered

82 candidates to 135 candidates (-64.6%)

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

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (sqrt (+ (* a a) (* b b))) (* 2 2.0)) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
0.0b	(pow (sqrt (+ (* a a) (* b b))) (* 2 2.0))
7.8b	(sqrt (+ (* a a) (* b b)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
10×	`add-exp-log` `add-sqr-sqrt`
9×	`add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `sqrt-prod` `add-log-exp`
3×	`pow-pow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `pow-unpow` `associate-r` `pow-exp` `sum-log` `*-commutative` `sqrt-pow2` `unswap-sqr` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

12.0ms	(+ (pow (sqrt (+ (* a a) (* b b))) (* 2 2.0)) (* 4.0 (* b b)))
7.0ms	(* 4.0 (* b b))
6.0ms	(pow (sqrt (+ (* a a) (* b b))) (* 2 2.0))
4.0ms	(sqrt (+ (* a a) (* b b)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (pow (sqrt (+ (* a a) (* b b))) (* 2 2.0)) (* 4.0 (* b b)))
3.0ms	(* 4.0 (* b b))
23.0ms	(pow (sqrt (+ (* a a) (* b b))) (* 2 2.0))
7.0ms	(sqrt (+ (* a a) (* b b)))

simplify851.0ms

Counts

78 → 78

Iterations

Useful iterations: 3 (327.0ms)

Iter	Nodes	Cost
0	139	1188
1	366	1055
2	1109	943
3	3333	933
done	5000	933

prune120.0ms

Filtered

56 candidates to 78 candidates (-39.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	78	2	80

Merged error: 0b

Counts

80 → 2

localize15.0ms

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))

rewrite31.0ms

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

series106.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (sqrt (+ (* a a) (* b b))) 2.0)
39.0ms	(pow (pow (sqrt (+ (* a a) (* b b))) 2.0) 6)
6.0ms	(sqrt (+ (* a a) (* b b)))
38.0ms	(cbrt (pow (pow (sqrt (+ (* a a) (* b b))) 2.0) 6))

simplify917.0ms

Counts

98 → 98

Iterations

Useful iterations: 3 (275.0ms)

Iter	Nodes	Cost
0	160	1726
1	360	1601
2	1000	1469
3	3268	1412
done	5000	1412

prune163.0ms

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

regimes137.0ms

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	15	20
1	19	20
done	19	20

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.0s

20932×

body

valid

Details

sample56.0ms

simplify1.8s

prune3.0ms

localize10.0ms

rewrite24.0ms

series53.0ms

simplify939.0ms

prune128.0ms

localize13.0ms

rewrite37.0ms

series72.0ms

simplify407.0ms

prune190.0ms

localize13.0ms

rewrite31.0ms

series45.0ms

simplify851.0ms

prune120.0ms

localize15.0ms

rewrite31.0ms

series106.0ms

simplify917.0ms

prune163.0ms

regimes137.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.7s

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