Details

Time bar (total: 18.7s)

sample91.0ms

Algorithm
intervals
Results
37.0ms281×body80valid
10.0ms89×body80nan

simplify214.0ms

Counts
1 → 1
Iterations
IterNodes
done193
6193
5189
4179
3143
279
139
020

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.5b

localize182.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log sqrt-pow1 pow1/2 diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×associate--l- +-commutative sub-neg flip3-+ associate-+l- flip-+
Counts
4 → 151
Calls
4 calls:
34.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series477.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
124.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
107.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
113.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts
163 → 163
Iterations
IterNodes
done5001
21833
1440
0179

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize149.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite76.0ms

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×expm1-log1p-u flip3-- add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u flip--
3×diff-log
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 neg-log
Counts
4 → 140
Calls
4 calls:
11.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (* b b) (* (* 4.0 a) c))
142.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
87.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
115.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
152 → 152
Iterations
IterNodes
done5000
21954
1433
0181

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize271.0ms

Local error

Found 4 expressions with local error:

23.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(cbrt (fma b b (* (- c) (* 4.0 a))))
23.8b
(cbrt (fma b b (* (- c) (* 4.0 a))))
23.8b
(cbrt (fma b b (* (- c) (* 4.0 a))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
Counts
4 → 56
Calls
4 calls:
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
1.0ms
(cbrt (fma b b (* (- c) (* 4.0 a))))
1.0ms
(cbrt (fma b b (* (- c) (* 4.0 a))))
1.0ms
(cbrt (fma b b (* (- c) (* 4.0 a))))

series562.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
167.0ms
(cbrt (fma b b (* (- c) (* 4.0 a))))
160.0ms
(cbrt (fma b b (* (- c) (* 4.0 a))))
154.0ms
(cbrt (fma b b (* (- c) (* 4.0 a))))

simplify3.0s

Counts
68 → 68
Iterations
IterNodes
done5000
34272
2789
1233
098

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize242.0ms

Local error

Found 4 expressions with local error:

23.8b
(cbrt (fma (* 4.0 a) (- c) (* b b)))
23.8b
(cbrt (fma (* 4.0 a) (- c) (* b b)))
23.8b
(cbrt (fma b b (* (- c) (* 4.0 a))))
23.8b
(cbrt (fma b b (* (- c) (* 4.0 a))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log log1p-expm1-u add-log-exp
Counts
4 → 52
Calls
4 calls:
1.0ms
(cbrt (fma (* 4.0 a) (- c) (* b b)))
1.0ms
(cbrt (fma (* 4.0 a) (- c) (* b b)))
1.0ms
(cbrt (fma b b (* (- c) (* 4.0 a))))
1.0ms
(cbrt (fma b b (* (- c) (* 4.0 a))))

series998.0ms

Counts
4 → 12
Calls
4 calls:
337.0ms
(cbrt (fma (* 4.0 a) (- c) (* b b)))
360.0ms
(cbrt (fma (* 4.0 a) (- c) (* b b)))
151.0ms
(cbrt (fma b b (* (- c) (* 4.0 a))))
149.0ms
(cbrt (fma b b (* (- c) (* 4.0 a))))

simplify862.0ms

Counts
64 → 64
Iterations
IterNodes
done5001
32058
2488
1187
094

prune996.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

regimes490.0ms

Accuracy

90% (1.4b remaining)

Error of 6.9b against oracle of 5.5b and baseline of 19.6b

bsearch318.0ms

Steps
ItersRangePoint
10
4.0721326822252617e+40
3.6590220876252264e+50
3.628799960716312e+50
7
-9.685109581380507e+154
-1.5171851739610474e+153
-1.2278935470827574e+154

simplify19.0ms

Iterations
IterNodes
done74
374
268
165
055

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.2s8698×body80valid
291.0ms2819×body80nan