Details

sample54.0ms

Algorithm

intervals

Results

13.0ms	35×	body	2560	valid
11.0ms	188×	body	80	valid
5.0ms	256×	pre	80	true
4.0ms	14×	body	1280	valid
2.0ms	10×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify85.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	27	17
2	34	17
3	38	17
4	40	17
5	41	17
done	41	17

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`add-exp-log` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 51

Calls

4 calls:

78.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
34.0ms	(+ (* (* 4.0 p) p) (* x x))
73.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
36.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series656.0ms

Counts

4 → 12

Calls

4 calls:

399.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
64.0ms	(+ (* (* 4.0 p) p) (* x x))
122.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
71.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify714.0ms

Counts

63 → 63

Iterations

Useful iterations: done (712.0ms)

Iter	Nodes	Cost
0	100	1088
1	258	1002
2	1089	921
done	5000	905

prune266.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.3b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite426.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 125

Calls

4 calls:

218.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
100.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
50.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
47.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
141.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
82.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
79.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.7s

Counts

137 → 137

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	141	3702
1	322	2251
2	1347	2066
done	5001	2029

prune597.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+`
2×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `distribute-lft-out`

Counts

4 → 54

Calls

4 calls:

55.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
64.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
43.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
50.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
101.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
63.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
71.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.8s

Counts

66 → 66

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	67	1106
1	169	1016
2	475	936
3	1358	890
4	3740	886
done	5001	886

prune410.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.6b

localize32.0ms

Local error

Found 4 expressions with local error:

7.4b	(+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.3b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
15.3b	(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `distribute-lft-out`

Counts

4 → 53

Calls

4 calls:

46.0ms	(+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
39.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
18.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
29.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

series729.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(+ 1.0 (/ x (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
98.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
174.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
190.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify887.0ms

Counts

65 → 65

Iterations

Useful iterations: done (884.0ms)

Iter	Nodes	Cost
0	138	1484
1	348	1391
2	1400	1279
done	5001	1223

prune578.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 13.6b

regimes455.0ms

Accuracy

0% (0.2b remaining)

Error of 13.6b against oracle of 13.3b and baseline of 13.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	34
1	21	34
done	21	34

end0.0ms

sample2.5s

Algorithm

intervals

Results

852.0ms	5977×	body	80	valid
395.0ms	793×	body	2560	valid
355.0ms	631×	body	1280	valid
320.0ms	8000×	pre	80	true
143.0ms	318×	body	640	valid
35.0ms	58×	body	5120	valid
32.0ms	154×	body	320	valid
10.0ms	69×	body	160	valid