Details

Time bar (total: 24.6s)

sample115.0ms

Algorithm
intervals
Results
69.0ms279×body80valid
18.0ms84×body80nan

simplify211.0ms

Counts
1 → 1
Iterations
IterNodes
done160
7160
6159
5152
4140
3108
263
136
020

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize128.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite80.0ms

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 insert-posit16 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 → 155
Calls
4 calls:
34.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
20.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series423.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
105.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
95.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
105.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify3.3s

Counts
167 → 167
Iterations
IterNodes
done5000
34570
21211
1436
0181

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize161.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4 a) c))
0.9b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite71.0ms

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 insert-posit16 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 → 144
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4 a) c))
20.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
17.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
21.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (* b b) (* (* 4 a) c))
111.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
84.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
93.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.7s

Counts
156 → 156
Iterations
IterNodes
done5000
33818
21125
1428
0183

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.3b

localize194.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4 a) c))
0.9b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
20.8b
(sqrt (fma (* -4 c) a (* b b)))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite59.0ms

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 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×flip3-- diff-log flip--
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 neg-log
Counts
4 → 142
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4 a) c))
24.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
2.0ms
(sqrt (fma (* -4 c) a (* b b)))
21.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series392.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (* b b) (* (* 4 a) c))
104.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
102.0ms
(sqrt (fma (* -4 c) a (* b b)))
108.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.8s

Counts
154 → 154
Iterations
IterNodes
done5000
34063
21160
1453
0202

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize197.0ms

Local error

Found 4 expressions with local error:

8.1b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite52.0ms

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 insert-posit16 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 → 80
Calls
4 calls:
16.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
11.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
124.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
87.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
85.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify4.4s

Counts
92 → 92
Iterations
IterNodes
done5001
33147
2801
1250
091

prune813.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.8b

regimes433.0ms

Accuracy

90.7% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 18.8b

bsearch298.0ms

Steps
ItersRangePoint
7
5.455680955858941e+61
9.381769121995126e+63
9.19242293018462e+63
10
-3.72456461250081e+89
-1.6290502733481186e+78
-5.1217249295588275e+88

simplify10.0ms

Iterations
IterNodes
done56
156
047

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.1s8750×body80valid
596.0ms3007×body80nan