Details

sample34.0ms

Algorithm

intervals

Results

15.0ms	278×	body	80	valid
4.0ms	76×	body	80	nan

simplify97.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	20	38
1	36	38
2	66	37
3	122	37
4	151	37
5	165	37
6	166	37
done	166	37

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.6b

localize119.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
53×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
37×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 140

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify604.0ms

Counts

152 → 152

Iterations

Useful iterations: done (599.0ms)

Iter	Nodes	Cost
0	181	6137
1	422	4178
2	1313	3279
done	5000	3272

prune582.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.0b

localize119.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.7b	(/ (* a c) b)
5.0b	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
60×	`prod-diff`
55×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
34×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
14×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`times-frac` `add-log-exp`
7×	`neg-mul-1`
6×	`associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r*` `log1p-expm1-u` `distribute-lft-out`
2×	`neg-sub0` `flip3--` `frac-2neg` `sqrt-div` `diff-log` `div-sub` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `associate-+l-` `associate-+r-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 161

Calls

4 calls:

19.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(/ (* a c) b)
62.0ms	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(/ (* a c) b)
59.0ms	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify867.0ms

Counts

173 → 173

Iterations

Useful iterations: done (860.0ms)

Iter	Nodes	Cost
0	265	6492
1	665	4520
2	2480	3539
done	5000	3538

prune487.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize112.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.4b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
52×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`pow1` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `diff-log` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `neg-log` `*-commutative`

Counts

4 → 143

Calls

4 calls:

7.0ms	(* (* 4.0 a) c)
3.0ms	(- (* b b) (* (* 4.0 a) c))
19.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 4.0 a) c)
47.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify752.0ms

Counts

155 → 155

Iterations

Useful iterations: 2 (163.0ms)

Iter	Nodes	Cost
0	212	5999
1	498	4070
2	1695	3162
done	5001	3162

prune390.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize122.0ms

Local error

Found 4 expressions with local error:

15.6b	(cbrt (* (* 4.0 a) c))
15.6b	(cbrt (* (* 4.0 a) c))
15.6b	(cbrt (* (* 4.0 a) c))
24.7b	(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 50

Calls

4 calls:

5.0ms	(cbrt (* (* 4.0 a) c))
5.0ms	(cbrt (* (* 4.0 a) c))
5.0ms	(cbrt (* (* 4.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

series424.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (* (* 4.0 a) c))
97.0ms	(cbrt (* (* 4.0 a) c))
97.0ms	(cbrt (* (* 4.0 a) c))
132.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

simplify927.0ms

Counts

62 → 62

Iterations

Useful iterations: done (925.0ms)

Iter	Nodes	Cost
0	92	1075
1	217	987
2	603	590
3	2159	581
done	5000	574

prune298.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.6b

regimes204.0ms

Accuracy

92.2% (1.1b remaining)

Error of 7.9b against oracle of 6.8b and baseline of 21.1b

bsearch212.0ms

Steps

Iters	Range		Point
8	1.5276508475467709e+44	4.1560730947117816e+46	4.047592289682709e+46
11	-1.829086240692416e+154	-2.187052964502477e+134	-8.555281377770497e+140

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	139
1	61	139
done	61	139

end0.0ms

sample866.0ms

Algorithm

intervals

Results

473.0ms	8732×	body	80	valid
137.0ms	2861×	body	80	nan