Details

sample34.0ms

Algorithm

intervals

Results

7.0ms	194×	body	80	valid
6.0ms	27×	body	2560	valid
4.0ms	256×	pre	80	true
3.0ms	16×	body	1280	valid
2.0ms	11×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify23.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	27	17
2	33	17
3	37	17
4	39	17
5	40	17
done	40	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `flip-+`
3×	`associate-/l*`
2×	`+-commutative` `sum-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 79

Calls

4 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
12.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
25.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (* (* 4.0 p) p) (* x x))
56.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
76.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.6s

Counts

91 → 91

Iterations

Useful iterations: 3 (422.0ms)

Iter	Nodes	Cost
0	128	1657
1	283	1514
2	972	1400
3	4152	1385
done	5000	1385

prune278.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
6×	`pow1` `add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`log-pow`
4×	`log-prod` `exp-prod` `sqrt-div`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`associate-/r/` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `exp-sum` `clear-num` `sum-log` `div-inv`

Counts

4 → 85

Calls

4 calls:

14.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
100.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
25.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
75.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify941.0ms

Counts

97 → 97

Iterations

Useful iterations: 3 (270.0ms)

Iter	Nodes	Cost
0	139	1814
1	282	1639
2	780	1520
3	2194	1505
done	5000	1505

prune333.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
22×	`times-frac`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
14×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
5×	`unswap-sqr`
4×	`flip3-+` `sqrt-div` `prod-exp` `flip-+`
3×	`associate-l`
2×	`+-commutative` `div-exp` `sum-log` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 86

Calls

4 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
33.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* (* 4.0 p) p) (* x x))
52.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
76.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.0s

Counts

98 → 98

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	152	1717
1	393	1465
2	1625	1271
done	5001	1269

prune277.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.3b	(/ (* x x) (+ (* 4.0 (pow p 2)) (pow x 2)))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt`
7×	`sqrt-prod`
6×	`pow1` `add-log-exp`
5×	`times-frac`
4×	`sqrt-div`
3×	`flip3-+` `associate-/r*` `flip-+` `difference-of-squares`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-/r/`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `div-inv` `associate-/l*` `distribute-lft-out--`

Counts

4 → 69

Calls

4 calls:

26.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms	(/ (* x x) (+ (* 4.0 (pow p 2)) (pow x 2)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
51.0ms	(/ (* x x) (+ (* 4.0 (pow p 2)) (pow x 2)))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify499.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	125	1406
1	325	1299
2	1246	1151
done	5001	1151

prune414.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.5b

regimes305.0ms

Accuracy

0% (0.3b remaining)

Error of 13.4b against oracle of 13.1b and baseline of 13.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	19
1	21	19
done	21	19

end0.0ms

sample827.0ms

Algorithm

intervals

Results

205.0ms	5999×	body	80	valid
181.0ms	801×	body	2560	valid
116.0ms	642×	body	1280	valid
107.0ms	8000×	pre	80	true
43.0ms	317×	body	640	valid
16.0ms	156×	body	320	valid
6.0ms	85×	body	160	valid