Details

sample56.0ms

Algorithm

intervals

Results

12.0ms	196×	body	80	valid
11.0ms	14×	body	640	valid
6.0ms	20×	body	2560	valid
5.0ms	256×	pre	80	true
4.0ms	15×	body	1280	valid
1.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	1×	body	160	valid

simplify49.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize26.0ms

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)))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite181.0ms

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))
40.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
66.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
45.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (* (* 4.0 p) p) (* x x))
78.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
89.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
66.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.7s

Counts

91 → 91

Iterations

Useful iterations: 3 (590.0ms)

Iter	Nodes	Cost
0	128	1657
1	277	1506
2	773	1400
3	2062	1385
done	5000	1385

prune474.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.1b

localize16.0ms

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)))))
3.9b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite146.0ms

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:

20.0ms	(+ (* (* 4.0 p) p) (* x x))
89.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
25.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* (* 4.0 p) p) (* x x))
59.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
88.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
71.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.2s

Counts

98 → 98

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	152	1717
1	377	1427
2	974	1271
3	2641	1254
done	5001	1254

prune384.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.7b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite430.0ms

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:

43.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
280.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
72.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
32.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
117.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
100.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.9s

Counts

97 → 97

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	139	1814
1	270	1631
2	628	1520
3	1395	1505
4	3319	1501
done	5000	1501

prune424.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
3.6b	(/ (* x x) (+ (* 4.0 (pow p 2)) (pow x 2)))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite279.0ms

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:

157.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
29.0ms	(/ (* x x) (+ (* 4.0 (pow p 2)) (pow x 2)))
40.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
49.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
60.0ms	(/ (* x x) (+ (* 4.0 (pow p 2)) (pow x 2)))
83.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify993.0ms

Counts

82 → 82

Iterations

Useful iterations: done (990.0ms)

Iter	Nodes	Cost
0	124	1486
1	329	1341
2	1211	1194
done	5000	1187

prune462.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.1b

regimes217.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	54
1	38	54
done	38	54

end0.0ms

sample1.8s

Algorithm

intervals

Results

439.0ms	8000×	pre	80	true
433.0ms	6047×	body	80	valid
320.0ms	723×	body	2560	valid
205.0ms	590×	body	1280	valid
63.0ms	333×	body	640	valid
55.0ms	77×	body	5120	valid
25.0ms	160×	body	320	valid
6.0ms	70×	body	160	valid