Details

sample70.0ms

Algorithm

intervals

Results

15.0ms	35×	body	2560	valid
11.0ms	175×	body	80	valid
8.0ms	25×	body	1280	valid
6.0ms	256×	pre	80	true
3.0ms	12×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify73.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite221.0ms

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:

27.0ms	(+ (* (* 4.0 p) p) (* x x))
49.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
99.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
42.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (* (* 4.0 p) p) (* x x))
83.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
109.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
89.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify983.0ms

Counts

91 → 91

Iterations

Useful iterations: done (978.0ms)

Iter	Nodes	Cost
0	128	1657
1	307	1506
2	1436	1422
done	5000	1406

prune630.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.8b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
40×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
26×	`sqrt-prod`
24×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`sqrt-div` `associate-/r*` `add-log-exp`
5×	`unswap-sqr`
4×	`flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip-+`
3×	`pow-flip` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 122

Calls

4 calls:

54.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
130.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
41.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
82.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
114.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
96.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.1s

Counts

134 → 134

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	158	2438
1	401	2090
2	1652	1869
done	5000	1863

prune644.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.7b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.7b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite531.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

52.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
88.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
348.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
38.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
117.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
126.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
100.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.3s

Counts

97 → 97

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	139	1814
1	298	1631
2	1036	1532
done	5000	1511

prune659.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.1b	(+ 1.0 (/ (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite456.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
30×	`add-sqr-sqrt` `*-un-lft-identity`
28×	`add-cube-cbrt`
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` `distribute-lft-out`

Counts

4 → 95

Calls

4 calls:

57.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
316.0ms	(+ 1.0 (/ (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
39.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
39.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series524.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
121.0ms	(+ 1.0 (/ (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
82.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
92.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.0s

Counts

107 → 107

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	163	2380
1	356	1911
2	1280	1812
done	5001	1792

prune707.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.7b

regimes548.0ms

Accuracy

0% (0.2b remaining)

Error of 13.4b against oracle of 13.2b and baseline of 13.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample2.7s

Algorithm

intervals

Results

960.0ms	802×	body	2560	valid
587.0ms	6020×	body	80	valid
334.0ms	622×	body	1280	valid
231.0ms	8000×	pre	80	true
90.0ms	287×	body	640	valid
73.0ms	142×	body	320	valid
27.0ms	46×	body	5120	valid
12.0ms	81×	body	160	valid