Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	201×	body	80	valid
5.0ms	24×	body	2560	valid
4.0ms	256×	pre	80	true
2.0ms	14×	body	1280	valid
1.0ms	7×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	2×	body	160	valid

simplify26.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite57.0ms

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:

15.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
6.0ms	(+ (* (* 4.0 p) p) (* x x))
25.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
40.0ms	(+ (* (* 4.0 p) p) (* x x))
79.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.3s

Counts

91 → 91

Iterations

Useful iterations: 3 (461.0ms)

Iter	Nodes	Cost
0	128	1657
1	279	1506
2	786	1400
3	2661	1385
done	5000	1385

prune292.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.1b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
34.0ms	(* 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)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* (* 4.0 p) p) (* x x))
61.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
83.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.8s

Counts

98 → 98

Iterations

Useful iterations: 3 (664.0ms)

Iter	Nodes	Cost
0	152	1717
1	387	1427
2	991	1271
3	3241	1254
done	5001	1254

prune295.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite76.0ms

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:

25.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
25.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
82.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
66.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.9s

Counts

66 → 66

Iterations

Useful iterations: 4 (814.0ms)

Iter	Nodes	Cost
0	67	1106
1	169	1016
2	430	936
3	1109	890
4	2531	886
done	5000	886

prune279.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.7b	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.1b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`associate-/r*`
8×	`sqrt-div`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 94

Calls

4 calls:

14.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x 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)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
84.0ms	(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.6s

Counts

106 → 106

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	162	2389
1	345	2146
2	982	1980
3	3305	1768
done	5000	1755

prune318.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.3b

regimes125.0ms

Accuracy

0% (0.4b remaining)

Error of 13.1b against oracle of 12.7b and baseline of 13.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	19
1	24	19
done	24	19

end0.0ms

sample839.0ms

Algorithm

intervals

Results

222.0ms	6089×	body	80	valid
175.0ms	795×	body	2560	valid
107.0ms	8000×	pre	80	true
106.0ms	604×	body	1280	valid
40.0ms	292×	body	640	valid
15.0ms	143×	body	320	valid
5.0ms	77×	body	160	valid