Details

sample35.0ms

Algorithm

intervals

Results

6.0ms	192×	body	80	valid
6.0ms	28×	body	2560	valid
3.0ms	19×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	13×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	27	17
2	34	17
3	38	17
4	40	17
5	41	17
done	41	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

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)))))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

56.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.0ms	(+ (* (* 4.0 p) p) (* x x))
55.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series456.0ms

Counts

4 → 12

Calls

4 calls:

278.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
35.0ms	(+ (* (* 4.0 p) p) (* x x))
81.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.3s

Counts

63 → 63

Iterations

Useful iterations: 3 (428.0ms)

Iter	Nodes	Cost
0	100	1088
1	242	1002
2	735	913
3	2109	875
done	5000	875

prune223.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
3.4b	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

136.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
32.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
26.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
52.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify776.0ms

Counts

82 → 82

Iterations

Useful iterations: done (773.0ms)

Iter	Nodes	Cost
0	110	1486
1	291	1353
2	1115	1220
done	5001	1203

prune414.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
0.6b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.6b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite496.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

206.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
54.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
211.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
80.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
80.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.9s

Counts

70 → 70

Iterations

Useful iterations: 4 (914.0ms)

Iter	Nodes	Cost
0	94	1150
1	203	1063
2	535	951
3	1325	928
4	3086	926
done	5000	926

prune251.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(log (exp (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (+ (/ (* x x) (+ (* (* 4.0 p) p) (* x x))) (* 1.0 (- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.4b	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite848.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
36×	`log-pow`
35×	`exp-prod`
30×	`times-frac`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
15×	`distribute-lft-out`
12×	`unpow-prod-down` `cube-prod`
9×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`sqrt-prod` `associate-/r/`
4×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`log-prod` `associate-/r*` `sum-cubes`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `div-exp` `frac-add` `div-inv`
1×	`flip3--` `frac-2neg` `rem-log-exp` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `associate-/l*`

Counts

4 → 100

Calls

4 calls:

763.0ms	(log (exp (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (+ (/ (* x x) (+ (* (* 4.0 p) p) (* x x))) (* 1.0 (- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
32.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
26.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(log (exp (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (+ (/ (* x x) (+ (* (* 4.0 p) p) (* x x))) (* 1.0 (- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
56.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify775.0ms

Counts

112 → 112

Iterations

Useful iterations: done (771.0ms)

Iter	Nodes	Cost
0	202	3659
1	433	3363
2	1321	3133
done	5001	3108

prune453.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.7b

regimes183.0ms

Accuracy

0% (0.3b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 12.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	54
1	31	54
done	31	54

end0.0ms

sample823.0ms

Algorithm

intervals

Results

199.0ms	6097×	body	80	valid
175.0ms	793×	body	2560	valid
92.0ms	540×	body	1280	valid
92.0ms	8000×	pre	80	true
44.0ms	340×	body	640	valid
14.0ms	142×	body	320	valid
8.0ms	88×	body	160	valid