Details

sample78.0ms

Algorithm

intervals

Results

53.0ms

689×

body

valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	31
1	53	31
2	140	31
3	348	31
4	858	31
5	1862	31
6	3881	31
done	5000	31

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

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b	(* (* a a) (+ 1.0 a))
0.4b	(pow (+ (* a a) (* b b)) 2.0)
1.0b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
3×	`unpow-prod-down` `pow-unpow`
2×	`sub-neg` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

8.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
9.0ms	(* (* a a) (+ 1.0 a))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
8.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
6.0ms	(* (* a a) (+ 1.0 a))
27.0ms	(pow (+ (* a a) (* b b)) 2.0)
8.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify587.0ms

Counts

91 → 91

Iterations

Useful iterations: 2 (174.0ms)

Iter	Nodes	Cost
0	191	1566
1	544	1466
2	2231	1300
done	5000	1300

prune172.0ms

Filtered

61 candidates to 91 candidates (-49.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	84	7	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	7	92

Merged error: 0.0b

Counts

92 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0))
1.0b	(* (* b b) (- 1.0 (* 3.0 a)))
7.8b	(sqrt (+ (* a a) (* b b)))
7.8b	(sqrt (+ (* a a) (* b b)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`unpow-prod-down`
28×	`sqrt-prod`
21×	`add-exp-log`
19×	`add-cube-cbrt` `*-un-lft-identity`
17×	`unswap-sqr`
13×	`associate-r`
12×	`swap-sqr` `prod-exp` `sqr-pow`
11×	`pow1` `associate-l` `add-cbrt-cube`
6×	`pow-to-exp` `pow-exp`
4×	`sqrt-div` `pow-prod-down` `cbrt-unprod` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `-commutative` `flip-+`
1×	`pow2` `flip3--` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 125

Calls

4 calls:

16.0ms	(* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0))
8.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms	(sqrt (+ (* a a) (* b b)))
4.0ms	(sqrt (+ (* a a) (* b b)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0))
8.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
7.0ms	(sqrt (+ (* a a) (* b b)))
10.0ms	(sqrt (+ (* a a) (* b b)))

simplify481.0ms

Counts

137 → 137

Iterations

Useful iterations: 2 (140.0ms)

Iter	Nodes	Cost
0	177	3122
1	437	2403
2	1668	2183
done	5001	2183

prune206.0ms

Filtered

80 candidates to 137 candidates (-71.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	6	0	6
Picked	0	1	1
Done	0	0	0
Total	141	3	144

Merged error: 0b

Counts

144 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (sqrt (+ (* a a) (* b b))) (+ 2.0 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b	(* (* a a) (+ 1.0 a))
1.0b	(* (* b b) (- 1.0 (* 3.0 a)))
7.8b	(sqrt (+ (* a a) (* b b)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt` `associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`sub-neg` `associate-+r+` `sqrt-div` `associate-l` `*-commutative` `unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `sum-log` `flip--` `distribute-lft-out`

Counts

4 → 77

Calls

4 calls:

11.0ms	(+ (pow (sqrt (+ (* a a) (* b b))) (+ 2.0 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
8.0ms	(* (* a a) (+ 1.0 a))
8.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms	(sqrt (+ (* a a) (* b b)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (pow (sqrt (+ (* a a) (* b b))) (+ 2.0 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
6.0ms	(* (* a a) (+ 1.0 a))
8.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
6.0ms	(sqrt (+ (* a a) (* b b)))

simplify594.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (168.0ms)

Iter	Nodes	Cost
0	173	1552
1	505	1428
2	2156	1258
done	5000	1258

prune148.0ms

Filtered

61 candidates to 89 candidates (-45.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	89	3	92

Merged error: 0b

Counts

92 → 3

localize24.0ms

Local error

Found 4 expressions with local error:

7.8b	(sqrt (+ (* a a) (* b b)))
8.4b	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
8.4b	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
8.4b	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod`
18×	`unpow-prod-down`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-prod`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 69

Calls

4 calls:

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

series123.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* a a) (* b b)))
40.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
36.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
40.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))

simplify854.0ms

Counts

81 → 81

Iterations

Useful iterations: 4 (378.0ms)

Iter	Nodes	Cost
0	101	1473
1	224	1389
2	551	1270
3	1317	1238
4	3431	1232
done	5001	1232

prune258.0ms

Filtered

63 candidates to 81 candidates (-28.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	81	3	84

Merged error: 0b

Counts

84 → 3

regimes120.0ms

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	21	34
1	29	34
done	29	34

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.5s

20932×

body

valid

Details

sample78.0ms

simplify2.0s

prune3.0ms

localize17.0ms

rewrite32.0ms

series66.0ms

simplify587.0ms

prune172.0ms

localize20.0ms

rewrite37.0ms

series60.0ms

simplify481.0ms

prune206.0ms

localize22.0ms

rewrite33.0ms

series43.0ms

simplify594.0ms

prune148.0ms

localize24.0ms

rewrite24.0ms

series123.0ms

simplify854.0ms

prune258.0ms

regimes120.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.1s

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