Details

Time bar (total: 37.6s)

sample104.0ms

Algorithm
intervals
Results
53.0ms268×body80valid
13.0ms105×body80nan

simplify341.0ms

Counts
1 → 1
Iterations
IterNodes
done170
7170
6168
5164
4157
3134
275
139
020

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize245.0ms

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))))
22.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite168.0ms

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:
20.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
29.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series556.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(- (* b b) (* (* 4.0 a) c))
158.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
135.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
172.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify5.9s

Counts
152 → 152
Iterations
IterNodes
done5000
33959
21124
1425
0181

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.3b

localize233.0ms

Local error

Found 4 expressions with local error:

13.0b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
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×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
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:
28.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
29.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series643.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
154.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
155.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
182.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify6.1s

Counts
100 → 100
Iterations
IterNodes
done5001
32854
2822
1281
0115

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.3b

localize254.0ms

Local error

Found 4 expressions with local error:

10.0b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite123.0ms

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:
29.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
29.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
35.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series678.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
160.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
156.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
178.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.9s

Counts
88 → 88
Iterations
IterNodes
done5001
33191
2792
1247
090

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.3b

localize268.0ms

Local error

Found 4 expressions with local error:

10.0b
(+ (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) (- b))
22.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
2×sum-log
1×+-commutative neg-sub0 associate-+r- fma-def flip3-+ unsub-neg neg-log flip-+
Counts
4 → 69
Calls
4 calls:
94.0ms
(+ (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) (- b))
28.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
33.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series679.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(+ (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) (- b))
172.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
157.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
159.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify5.6s

Counts
81 → 81
Iterations
IterNodes
done5002
33191
2814
1247
091

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.3b

regimes642.0ms

Accuracy

91.6% (1.1b remaining)

Error of 7.7b against oracle of 6.5b and baseline of 20.1b

bsearch493.0ms

Steps
ItersRangePoint
7
6.896997489231346e+142
2.39218470372122e+144
1.9447999356225615e+143
9
-8.380652639018829e+71
-9.051599321779201e+64
-6.91867689254058e+70

simplify34.0ms

Iterations
IterNodes
done61
161
049

end0.0ms

sample3.4s

Algorithm
intervals
Results
2.4s8710×body80valid
420.0ms2825×body80nan