Details

sample74.0ms

Algorithm

intervals

Results

51.0ms

689×

body

valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	31
1	53	31
2	140	31
3	344	31
4	839	31
5	1818	31
6	3716	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)))

rewrite35.0ms

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))))))
8.0ms	(* (* a a) (+ 1.0 a))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
12.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series62.0ms

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

simplify1.2s

Counts

91 → 91

Iterations

Useful iterations: 2 (569.0ms)

Iter	Nodes	Cost
0	191	1566
1	533	1452
2	2104	1300
done	5000	1300

prune170.0ms

Filtered

60 candidates to 91 candidates (-51.7%)

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)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0))
10.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
6.0ms	(sqrt (+ (* a a) (* b b)))
6.0ms	(sqrt (+ (* a a) (* b b)))

simplify913.0ms

Counts

137 → 137

Iterations

Useful iterations: 2 (266.0ms)

Iter	Nodes	Cost
0	177	3122
1	424	2395
2	1557	2183
done	5000	2183

prune214.0ms

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

localize19.0ms

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:

10.0ms	(+ (pow (sqrt (+ (* a a) (* b b))) (+ 2.0 2.0)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
9.0ms	(* (* a a) (+ 1.0 a))
8.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms	(sqrt (+ (* a a) (* b b)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (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))
10.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
6.0ms	(sqrt (+ (* a a) (* b b)))

simplify1.1s

Counts

89 → 89

Iterations

Useful iterations: 2 (352.0ms)

Iter	Nodes	Cost
0	173	1552
1	492	1414
2	2097	1258
done	5000	1258

prune145.0ms

Filtered

60 candidates to 89 candidates (-48.3%)

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

localize25.0ms

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))

series118.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (+ (* a a) (* b b)))
36.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
37.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
39.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))

simplify2.2s

Counts

81 → 81

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	101	1473
1	223	1380
2	514	1270
3	1372	1238
4	4122	1232
done	5001	1232

prune263.0ms

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

sample2.0s

Algorithm

intervals

Results

1.4s

20932×

body

valid

Details

sample74.0ms

simplify3.6s

prune3.0ms

localize17.0ms

rewrite35.0ms

series62.0ms

simplify1.2s

prune170.0ms

localize20.0ms

rewrite37.0ms

series58.0ms

simplify913.0ms

prune214.0ms

localize19.0ms

rewrite33.0ms

series45.0ms

simplify1.1s

prune145.0ms

localize25.0ms

rewrite24.0ms

series118.0ms

simplify2.2s

prune263.0ms

regimes120.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.0s

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