Details

sample71.0ms

Algorithm

intervals

Results

14.0ms	183×	body	80	valid
13.0ms	27×	body	2560	valid
10.0ms	26×	body	1280	valid
7.0ms	256×	pre	80	true
3.0ms	11×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	30	17
2	41	17
done	41	17

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize33.0ms

Local error

Found 2 expressions with local error:

0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

62.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
26.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series154.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
66.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify3.9s

Counts

33 → 33

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	67	553
1	292	508
2	1431	451
done	5000	449

prune121.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.1b

localize16.0ms

Local error

Found 3 expressions with local error:

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)))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite304.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 44

Calls

3 calls:

217.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
55.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
31.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series233.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
86.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
66.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.4s

Counts

53 → 53

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	90	918
1	326	821
2	1518	736
done	5001	734

prune219.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 15.1b

localize15.0ms

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)))))
8.6b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite261.0ms

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:

129.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
72.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
30.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
25.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
88.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
67.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.2s

Counts

137 → 137

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	141	3702
done	5001	2292

prune462.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 15.1b

localize20.0ms

Local error

Found 4 expressions with local error:

8.6b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
8.6b	(log (exp (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite409.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

71.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
280.0ms	(log (exp (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
25.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
31.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
88.0ms	(log (exp (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
68.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
66.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.5s

Counts

71 → 71

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	91	1703
1	367	1055
2	2854	954
done	5001	950

prune598.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 15.1b

regimes283.0ms

Accuracy

0% (0.2b remaining)

Error of 13.0b against oracle of 12.8b and baseline of 13.0b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample1.8s

Algorithm

intervals

Results

675.0ms	6044×	body	80	valid
342.0ms	740×	body	2560	valid
190.0ms	8000×	pre	80	true
186.0ms	627×	body	1280	valid
54.0ms	286×	body	640	valid
44.0ms	91×	body	160	valid
22.0ms	59×	body	5120	valid
21.0ms	153×	body	320	valid