Details

sample39.0ms

Algorithm

intervals

Results

7.0ms	190×	body	80	valid
6.0ms	27×	body	2560	valid
4.0ms	2×	body	160	valid
4.0ms	22×	body	1280	valid
3.0ms	256×	pre	80	true
1.0ms	11×	body	640	valid
0.0ms	4×	body	320	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	9
1	34	9
2	38	9
3	40	9
4	41	9
5	41	9
done	41	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize11.0ms

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

rewrite161.0ms

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:

53.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
28.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
54.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
59.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
79.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify72.0ms

Counts

93 → 93

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	280	888
1	816	840
2	2500	828
3	5001	827
done	5001	827

prune277.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
0.5b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.5b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite488.0ms

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:

202.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
53.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
208.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
82.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify112.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	202	567
1	613	507
2	1609	506
3	3883	506
4	5001	506
done	5001	506

prune253.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.3b

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)))))
3.4b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite112.0ms

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:

7.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
74.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
23.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

278.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
60.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
80.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify48.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	390	900
1	1684	818
2	5001	784
done	5001	784

prune288.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.2b	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.4b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
23×	`*-un-lft-identity`
22×	`times-frac`
21×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`add-log-exp`
5×	`log-pow` `unswap-sqr`
4×	`exp-prod` `sqrt-div` `prod-exp`
3×	`log-prod` `flip3-+` `associate-l` `flip-+`
2×	`div-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 91

Calls

4 calls:

72.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
5.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
27.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series657.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
463.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
75.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
63.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify43.0ms

Counts

103 → 103

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	399	962
1	1650	851
2	5002	816
done	5002	816

prune304.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.3b

regimes188.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	14
1	28	14
done	28	14

end0.0ms

sample858.0ms

Algorithm

intervals

Results

211.0ms	6055×	body	80	valid
170.0ms	809×	body	2560	valid
104.0ms	589×	body	1280	valid
102.0ms	8000×	pre	80	true
46.0ms	323×	body	640	valid
15.0ms	146×	body	320	valid
5.0ms	78×	body	160	valid