Details

sample209.0ms

Algorithm

intervals

Results

13.0ms	190×	body	80	valid
11.0ms	38×	body	2560	valid
9.0ms	36×	body	1280	valid
4.0ms	79×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
2	22	12
3	25	12
4	27	12
5	29	12
done	29	12

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
0.8b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

104.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (* b_2 b_2) (* a c))
39.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series475.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
66.0ms	(- (* b_2 b_2) (* a c))
117.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
135.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

92 → 92

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	151	1534
1	378	1440
2	1557	1268
done	5001	1260

prune343.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.9b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
7.7b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite306.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
158×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
89×	`add-cube-cbrt`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 206

Calls

4 calls:

32.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
129.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
108.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series653.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
240.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
233.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
89.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

218 → 218

Iterations

Useful iterations: 2 (759.0ms)

Iter	Nodes	Cost
0	307	6418
1	777	5561
2	4237	5359
done	5000	5359

prune881.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.9b	(/ (* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
7.7b	(* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
28×	`add-exp-log`
27×	`associate-r`
26×	`times-frac`
19×	`add-cube-cbrt`
18×	`add-cbrt-cube`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`associate-/l/`
5×	`cbrt-undiv`
4×	`frac-times` `distribute-rgt-neg-in` `flip3-+` `associate-*l/` `cbrt-unprod` `flip-+`
3×	`flip3--` `associate-l` `associate-/r*` `flip--` `unswap-sqr`
2×	`rec-exp` `sqrt-div` `diff-log` `1-exp` `associate-*r/` `associate-/r/` `un-div-inv` `div-inv`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `clear-num` `-commutative` `associate-/l`

Counts

4 → 118

Calls

4 calls:

26.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
49.0ms	(/ (* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
171.0ms	(* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series622.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
201.0ms	(/ (* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
231.0ms	(* (+ 0 (* a c)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.4s

Counts

130 → 130

Iterations

Useful iterations: 2 (969.0ms)

Iter	Nodes	Cost
0	236	2749
1	652	2226
2	4443	1942
done	5001	1942

prune437.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize36.0ms

Local error

Found 4 expressions with local error:

8.8b	(sqrt (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
8.8b	(sqrt (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
21.3b	(sqrt (- (* b_2 b_2) (* a c)))
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
22×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
14×	`times-frac`
10×	`add-cube-cbrt`
8×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `add-cbrt-cube` `flip--` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`distribute-rgt-neg-in` `div-inv`

Counts

4 → 78

Calls

4 calls:

51.0ms	(sqrt (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
59.0ms	(sqrt (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series763.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(sqrt (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
275.0ms	(sqrt (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))
111.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify827.0ms

Counts

90 → 90

Iterations

Useful iterations: done (822.0ms)

Iter	Nodes	Cost
0	127	1758
1	286	1548
2	1162	1488
done	5001	1464

prune520.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes210.0ms

Accuracy

83.3% (4.5b remaining)

Error of 10.4b against oracle of 5.9b and baseline of 33.0b

bsearch145.0ms

Steps

Iters	Range		Point
9	3.58845601849977e-79	3.3299624871078663e-72	4.603517726908401e-74
9	-4.955433086253459e+131	-5.661938264600021e+124	-3.4127765686872833e+126

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	26	38
1	32	38
done	32	38

end0.0ms

sample3.0s

Algorithm

intervals

Results

665.0ms	1056×	body	2560	valid
451.0ms	5921×	body	80	valid
424.0ms	85×	body	5120	valid
402.0ms	903×	body	1280	valid
263.0ms	2891×	body	80	nan
108.0ms	460×	body	640	valid
39.0ms	221×	body	320	valid
16.0ms	119×	body	160	valid