Details

sample48.0ms

Algorithm

intervals

Results

11.0ms	182×	body	80	valid
9.0ms	32×	body	2560	valid
6.0ms	28×	body	1280	valid
5.0ms	256×	pre	80	true
2.0ms	10×	body	640	valid
1.0ms	4×	body	320	valid

simplify26.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize11.0ms

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	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.1b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

25.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 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)))))
12.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
53.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
72.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify903.0ms

Counts

93 → 93

Iterations

Useful iterations: 3 (283.0ms)

Iter	Nodes	Cost
0	137	1776
1	282	1594
2	709	1499
3	2107	1489
done	5000	1489

prune263.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.3b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

3.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
36.0ms	(* 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)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
55.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
73.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
53.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.6s

Counts

100 → 100

Iterations

Useful iterations: 3 (604.0ms)

Iter	Nodes	Cost
0	161	1872
1	391	1515
2	1055	1372
3	3350	1358
done	5001	1358

prune255.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.3b

localize13.0ms

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)))))
9.8b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite103.0ms

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:

55.0ms	(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
22.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (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)))))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
52.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify747.0ms

Counts

137 → 137

Iterations

Useful iterations: done (743.0ms)

Iter	Nodes	Cost
0	141	3702
1	289	2238
2	891	2066
done	5000	1948

prune317.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 15.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
7.6b	(+ 1.0 (* (/ (* (cbrt x) (cbrt x)) (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (/ (cbrt x) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
15.7b	(cbrt (+ (* (* 4.0 p) p) (* x x)))
15.7b	(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

0.0ms	(cbrt x)
2.0ms	(+ 1.0 (* (/ (* (cbrt x) (cbrt x)) (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (/ (cbrt x) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

series580.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(cbrt x)
166.0ms	(+ 1.0 (* (/ (* (cbrt x) (cbrt x)) (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (/ (cbrt x) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))
123.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))
124.0ms	(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify418.0ms

Counts

60 → 60

Iterations

Useful iterations: done (416.0ms)

Iter	Nodes	Cost
0	142	1383
1	356	1276
2	1196	1104
done	5000	1092

prune275.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 15.3b

regimes140.0ms

Accuracy

0% (1.3b remaining)

Error of 14.6b against oracle of 13.3b and baseline of 14.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	30
1	21	30
done	21	30

end0.0ms

sample838.0ms

Algorithm

intervals

Results

209.0ms	5975×	body	80	valid
182.0ms	823×	body	2560	valid
120.0ms	649×	body	1280	valid
108.0ms	8000×	pre	80	true
45.0ms	324×	body	640	valid
16.0ms	156×	body	320	valid
5.0ms	73×	body	160	valid