Details

sample37.0ms

Algorithm

intervals

Results

7.0ms	185×	body	80	valid
6.0ms	24×	body	2560	valid
5.0ms	26×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	16×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify23.0ms

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: 15.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.0b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite80.0ms

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:

15.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
26.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
26.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
279.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
79.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.1s

Counts

93 → 93

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	137	1776
1	282	1602
2	668	1503
3	1633	1487
4	4040	1483
done	5001	1483

prune292.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.9b	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
1.0b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

26.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
29.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series750.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
291.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
80.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.8s

Counts

68 → 68

Iterations

Useful iterations: 4 (797.0ms)

Iter	Nodes	Cost
0	111	1297
1	236	1164
2	556	1076
3	1384	1040
4	3316	1038
done	5000	1038

prune280.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.2b

localize13.0ms

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)))))
4.2b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite56.0ms

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))))))))
37.0ms	(* 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)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
62.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
83.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.1s

Counts

100 → 100

Iterations

Useful iterations: 3 (553.0ms)

Iter	Nodes	Cost
0	161	1872
1	391	1553
2	938	1372
3	2371	1352
done	5000	1352

prune307.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.5b	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.6b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

39×	`sqrt-prod`
27×	`associate-r`
22×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
11×	`pow1`
10×	`sqrt-div`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`flip3-+` `flip-+`
3×	`associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`+-commutative` `frac-times` `associate-l` `associate-l/` `sum-log` `-commutative` `div-inv`

Counts

4 → 86

Calls

4 calls:

80.0ms	(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
2.0ms	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
79.0ms	(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.1s

Counts

98 → 98

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	157	2661
1	388	1898
2	1233	1680
3	3490	1577
done	5000	1577

prune312.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.2b

regimes142.0ms

Accuracy

0% (1.1b remaining)

Error of 14.0b against oracle of 12.9b and baseline of 14.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	47
1	31	47
done	31	47

end0.0ms

sample887.0ms

Algorithm

intervals

Results

230.0ms	6058×	body	80	valid
179.0ms	777×	body	2560	valid
122.0ms	635×	body	1280	valid
115.0ms	8000×	pre	80	true
48.0ms	318×	body	640	valid
16.0ms	149×	body	320	valid
5.0ms	63×	body	160	valid