Details

Time bar (total: 18.9s)

sample100.0ms

Algorithm
intervals
Results
54.0ms283×body80valid
11.0ms94×body80nan

simplify187.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize156.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (* b b) (* (* 4.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite52.0ms

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:
14.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(- (* b b) (* (* 4.0 a) c))
113.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
133.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts
78 → 78
Iterations
IterNodes
done5000
32176
2551
1177
071

prune605.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.0b

localize173.0ms

Local error

Found 4 expressions with local error:

9.3b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite66.0ms

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:
18.0ms
(+ (- 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)))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
156.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
82.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
101.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts
88 → 88
Iterations
IterNodes
done5000
33221
2793
1247
090

prune996.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.0b

localize198.0ms

Local error

Found 4 expressions with local error:

9.8b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite45.0ms

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:
12.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
12.0ms
(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)))

series435.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
111.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.3s

Counts
100 → 100
Iterations
IterNodes
done5000
32880
2822
1281
0115

prune806.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.5b

localize187.0ms

Local error

Found 4 expressions with local error:

22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite329.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log log1p-expm1-u flip-- 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:
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
304.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series480.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
121.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
120.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
140.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
74 → 74
Iterations
IterNodes
done5001
32150
2610
1216
094

prune820.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.5b

regimes338.0ms

Accuracy

92.4% (1.0b remaining)

Error of 7.9b against oracle of 6.9b and baseline of 20.3b

bsearch244.0ms

Steps
ItersRangePoint
5
6.972240796235003e+85
2.4695855038465726e+86
2.216005534325193e+86
9
-6.117539429929052e+154
-3.6285784997486435e+148
-4.501750666080754e+151

simplify20.0ms

Iterations
IterNodes
done58
158
049

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.1s8725×body80valid
328.0ms2954×body80nan