Details

sample72.0ms

Algorithm

intervals

Results

25.0ms	202×	body	80	valid
10.0ms	23×	body	2560	valid
6.0ms	256×	pre	80	true
4.0ms	13×	body	1280	valid
4.0ms	13×	body	640	valid
2.0ms	1×	body	5120	valid
1.0ms	4×	body	320	valid

simplify65.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 38

Calls

3 calls:

35.0ms	(+ (* (* 4.0 p) p) (* x x))
85.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
44.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series257.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(+ (* (* 4.0 p) p) (* x x))
110.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
89.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.2s

Counts

47 → 47

Iterations

Useful iterations: 3 (589.0ms)

Iter	Nodes	Cost
0	79	761
1	203	711
2	635	637
3	1870	612
done	5000	612

prune265.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
17.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

106.0ms	(cbrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
50.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
46.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series840.0ms

Counts

4 → 12

Calls

4 calls:

560.0ms	(cbrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
77.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
105.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
97.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.6s

Counts

71 → 71

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	86	1203
1	199	1093
2	483	1025
3	1181	978
4	2752	970
done	5000	968

prune466.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.5b

localize31.0ms

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)))))
7.3b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
17.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite401.0ms

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:

189.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
109.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
48.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
41.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
128.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
103.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
110.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.7s

Counts

137 → 137

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	141	3702
1	288	2238
2	835	2066
3	2879	1948
done	5001	1887

prune385.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.5b

localize42.0ms

Local error

Found 4 expressions with local error:

7.8b	(+ 1.0 (/ x (* (* (sqrt (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
17.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
18.1b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
18.1b	(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite257.0ms

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:

172.0ms	(+ 1.0 (/ x (* (* (sqrt (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
38.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
29.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
16.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

series674.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(+ 1.0 (/ x (* (* (sqrt (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
79.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
196.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
159.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.0s

Counts

65 → 65

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	142	1752
1	325	1648
2	936	1478
3	3318	1433
done	5000	1400

prune487.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.5b

regimes371.0ms

Accuracy

0% (1.5b remaining)

Error of 14.8b against oracle of 13.3b and baseline of 14.8b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	47
1	32	47
done	32	47

end0.0ms

sample2.0s

Algorithm

intervals

Results

442.0ms	8000×	pre	80	true
425.0ms	793×	body	2560	valid
412.0ms	5980×	body	80	valid
319.0ms	636×	body	1280	valid
70.0ms	299×	body	640	valid
58.0ms	151×	body	320	valid
26.0ms	58×	body	5120	valid
10.0ms	83×	body	160	valid