Details

sample74.0ms

Algorithm

intervals

Results

20.0ms	256×	pre	80	true
13.0ms	199×	body	80	valid
8.0ms	19×	body	2560	valid
6.0ms	18×	body	1280	valid
3.0ms	8×	body	640	valid
2.0ms	3×	body	5120	valid
1.0ms	5×	body	320	valid
1.0ms	4×	body	160	valid

simplify52.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	40
4	40
3	38
2	34
1	27
0	14

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.5b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

64.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
84.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
30.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series680.0ms

Counts

3 → 9

Calls

3 calls:

456.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
136.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
88.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.6s

Counts

49 → 49

Iterations

Iter	Nodes
done	5002
4	3270
3	1405
2	545
1	208
0	88

prune373.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.6b

localize82.0ms

Local error

Found 4 expressions with local error:

5.8b	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
5.8b	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
15.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `associate-/r*` `times-frac` `sqrt-prod`
4×	`cbrt-undiv` `flip3-+` `sqrt-div` `div-exp` `associate-/r/` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

33.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
29.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
29.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
71.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
77.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
70.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.5s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1058
1	232
0	79

prune560.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.5b

localize68.0ms

Local error

Found 4 expressions with local error:

5.7b	(* (* x x) (/ 1 (+ (* (* 4.0 p) p) (* x x))))
5.8b	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
15.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
21×	`add-sqr-sqrt` `add-cbrt-cube`
16×	`*-un-lft-identity`
15×	`associate-r` `add-cube-cbrt`
14×	`times-frac`
13×	`prod-exp`
11×	`pow1`
7×	`cbrt-unprod`
6×	`div-exp` `sqrt-prod`
4×	`cbrt-undiv` `flip3-+` `sqrt-div` `associate-/r/` `flip-+` `add-log-exp`
3×	`associate-/r*` `pow-prod-down` `unswap-sqr`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `div-inv`
1×	`clear-num` `frac-2neg` `associate-l` `associate-r/` `un-div-inv` `-commutative` `associate-/l*`

Counts

4 → 96

Calls

4 calls:

99.0ms	(* (* x x) (/ 1 (+ (* (* 4.0 p) p) (* x x))))
41.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
20.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
29.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (* x x) (/ 1 (+ (* (* 4.0 p) p) (* x x))))
83.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
80.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.8s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
2	1706
1	445
0	143

prune850.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.5b

localize95.0ms

Local error

Found 4 expressions with local error:

5.7b	(* (* x x) (/ 1 (+ (* (* 4.0 p) p) (* x x))))
15.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.3b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.8b	(log (+ (* (* 4.0 p) p) (* x x)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log`
20×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
15×	`-un-lft-identity` `associate-r*`
14×	`add-cube-cbrt`
12×	`pow1` `prod-exp`
11×	`times-frac`
6×	`sqrt-prod` `cbrt-unprod`
4×	`flip3-+` `sqrt-div` `div-exp` `flip-+` `add-log-exp`
3×	`log-prod` `pow-prod-down` `unswap-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `log-div` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/r/`
1×	`rem-log-exp` `associate-l` `associate-r/` `log-pow` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 87

Calls

4 calls:

83.0ms	(* (* x x) (/ 1 (+ (* (* 4.0 p) p) (* x x))))
29.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
28.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
20.0ms	(log (+ (* (* 4.0 p) p) (* x x)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (* x x) (/ 1 (+ (* (* 4.0 p) p) (* x x))))
79.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
77.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
70.0ms	(log (+ (* (* 4.0 p) p) (* x x)))

simplify2.4s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
3	3757
2	1127
1	380
0	140

prune878.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.5b

regimes429.0ms

Accuracy

0% (0.6b remaining)

Error of 13.4b against oracle of 12.8b and baseline of 13.4b

bsearch0.0ms

simplify18.0ms

Iterations

Iter	Nodes
done	40
1	40
0	28

end0.0ms

sample2.0s

Algorithm

intervals

Results

663.0ms	745×	body	2560	valid
499.0ms	6051×	body	80	valid
220.0ms	606×	body	1280	valid
177.0ms	8000×	pre	80	true
80.0ms	332×	body	640	valid
66.0ms	68×	body	5120	valid
24.0ms	138×	body	320	valid
7.0ms	60×	body	160	valid