Details

sample88.0ms

Algorithm

intervals

Results

46.0ms	285×	body	80	valid
10.0ms	89×	body	80	nan

simplify243.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	170
7	170
6	168
5	164
4	157
3	134
2	75
1	39
0	20

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize184.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (* b b) (* (* 4.0 a) c))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

13.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (* b b) (* (* 4.0 a) c))
62.0ms	(- (* b b) (* (* 4.0 a) c))
89.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
3	2176
2	551
1	177
0	71

prune801.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.4b

localize192.0ms

Local error

Found 4 expressions with local error:

9.5b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

21.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series493.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
118.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
116.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
141.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	3221
2	793
1	247
0	90

prune998.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.4b

localize204.0ms

Local error

Found 4 expressions with local error:

10.9b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

25.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
116.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
120.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
98.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.1s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	2880
2	822
1	281
0	115

prune950.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize241.0ms

Local error

Found 4 expressions with local error:

22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
112.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

80 → 80

Iterations

Iter	Nodes
done	5005
3	1705
2	437
1	139
0	54

prune772.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

regimes504.0ms

Accuracy

92.2% (1.0b remaining)

Error of 8.1b against oracle of 7.1b and baseline of 20.4b

bsearch169.0ms

Steps

Iters	Range		Point
5	2.6243927093659187e+107	5.901159163981397e+107	3.9321910650396994e+107
4	-2.6709732094199134e+112	-1.6569790030408257e+112	-1.99047315062329e+112

simplify24.0ms

Iterations

Iter	Nodes
done	56
1	56
0	47

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.5s	8696×	body	80	valid
338.0ms	2883×	body	80	nan