Details

sample77.0ms

Algorithm

intervals

Results

32.0ms	277×	body	80	valid
11.0ms	107×	body	80	nan

simplify377.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	157
7	157
6	156
5	149
4	137
3	110
2	62
1	36
0	20

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.2b

localize231.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
2.4b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite157.0ms

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:

23.0ms	(- (* b b) (* (* 4.0 a) c))
64.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
38.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series620.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(- (* b b) (* (* 4.0 a) c))
167.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
153.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
206.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify5.7s

Counts

152 → 152

Iterations

Iter	Nodes
done	5000
3	3959
2	1124
1	425
0	181

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.4b

localize251.0ms

Local error

Found 4 expressions with local error:

11.1b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `rem-sqrt-square` `flip3--` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `flip-+`

Counts

4 → 76

Calls

4 calls:

34.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
27.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series666.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
152.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
154.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
191.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.9s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
3	3191
2	792
1	247
0	90

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.4b

localize359.0ms

Local error

Found 4 expressions with local error:

21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

24.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series883.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
252.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
244.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
236.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify4.5s

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
3	2132
2	610
1	216
0	94

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.4b

localize321.0ms

Local error

Found 4 expressions with local error:

21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

27.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series834.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
212.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
223.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
251.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.9s

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
3	2132
2	610
1	216
0	94

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.4b

regimes680.0ms

Accuracy

92.1% (1.1b remaining)

Error of 7.6b against oracle of 6.6b and baseline of 20.1b

bsearch497.0ms

Steps

Iters	Range		Point
7	6.896997489231346e+142	2.39218470372122e+144	1.3596302420465967e+143
10	-5.6310187782355484e+91	-8.514648891065421e+79	-5.024722505568395e+88

simplify35.0ms

Iterations

Iter	Nodes
done	61
1	61
0	49

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.7s	8692×	body	80	valid
403.0ms	2818×	body	80	nan