Details

sample56.0ms

Algorithm

intervals

Results

10.0ms	181×	body	80	valid
8.0ms	23×	body	2560	valid
6.0ms	21×	body	1280	valid
5.0ms	256×	pre	80	true
4.0ms	18×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid

simplify102.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize18.0ms

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))))
0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite174.0ms

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:

17.0ms	(+ (* (* 4.0 p) p) (* x x))
40.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
68.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
44.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* (* 4.0 p) p) (* x x))
75.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
119.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
90.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.1s

Counts

91 → 91

Iterations

Useful iterations: 3 (676.0ms)

Iter	Nodes	Cost
0	128	1657
1	277	1506
2	773	1400
3	2062	1385
done	5000	1385

prune498.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.1b

localize62.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

69.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
28.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
32.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
49.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
79.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
64.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
83.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify3.0s

Counts

69 → 69

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	67	1083
1	169	976
2	456	912
3	1142	869
4	2765	863
done	5000	863

prune536.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.1b

localize66.0ms

Local error

Found 4 expressions with local error:

10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.9b	(+ 1.0 (/ x (* (* (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))

rewrite409.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

44.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
49.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
29.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
286.0ms	(+ 1.0 (/ x (* (* (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))

series388.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
98.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
89.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
131.0ms	(+ 1.0 (/ x (* (* (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))

simplify2.2s

Counts

69 → 69

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	68	1558
1	173	1426
2	520	960
3	1625	869
done	5000	824

prune548.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 16.1b

localize26.0ms

Local error

Found 4 expressions with local error:

10.4b	(sqrt (* (* (cbrt (+ (* (* 4.0 p) p) (* x x))) (cbrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (+ (* (* 4.0 p) p) (* x x)))))
11.2b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
11.2b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
11.2b	(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

183.0ms	(sqrt (* (* (cbrt (+ (* (* 4.0 p) p) (* x x))) (cbrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (+ (* (* 4.0 p) p) (* x x)))))
14.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
26.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
15.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

series676.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt (* (* (cbrt (+ (* (* 4.0 p) p) (* x x))) (cbrt (+ (* (* 4.0 p) p) (* x x)))) (cbrt (+ (* (* 4.0 p) p) (* x x)))))
173.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
215.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
195.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.9s

Counts

101 → 101

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	177	3711
1	312	3363
2	570	2796
3	1192	2480
4	2851	2462
done	5000	2462

prune404.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.1b

regimes210.0ms

Accuracy

0% (0.5b remaining)

Error of 13.6b against oracle of 13.1b and baseline of 13.6b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	75
1	32	75
done	32	75

end0.0ms

sample2.3s

Algorithm

intervals

Results

790.0ms	746×	body	2560	valid
487.0ms	6016×	body	80	valid
327.0ms	8000×	pre	80	true
199.0ms	601×	body	1280	valid
117.0ms	341×	body	640	valid
30.0ms	155×	body	320	valid
26.0ms	56×	body	5120	valid
13.0ms	85×	body	160	valid