Details

Time bar (total: 19.4s)

sample92.0ms

Algorithm
intervals
Results
35.0ms273×body80valid
14.0ms103×body80nan

simplify228.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
02038
13638
26637
312237
416137
517437
617637
done17637

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.2b

localize144.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite227.0ms

Algorithm
rewrite-expression-head
Rules
78×prod-diff
71×add-sqr-sqrt
67×*-un-lft-identity
61×add-cube-cbrt
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×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 difference-of-squares
3×diff-log distribute-lft-out--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
105.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
54.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series444.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
121.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
111.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts
177 → 177
Iterations

Useful iterations: 2 (544.0ms)

IterNodesCost
02086992
15084619
226663570
done50003570

prune880.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.7b

localize157.0ms

Local error

Found 4 expressions with local error:

20.7b
(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
1×fma-udef
Counts
4 → 61
Calls
4 calls:
0.0ms
(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series445.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
127.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
83.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.0s

Counts
73 → 73
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0711269
11741005
2677906
33809906
done5000903

prune677.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.9b

localize185.0ms

Local error

Found 4 expressions with local error:

22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log expm1-log1p-u cbrt-div flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 64
Calls
4 calls:
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series469.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
88.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
141.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
121.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.1s

Counts
76 → 76
Iterations

Useful iterations: done (3.1s)

IterNodesCost
0941248
12241156
27501052
339761040
done50001038

prune924.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.9b

localize147.0ms

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))))))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite77.0ms

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:
16.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
27.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
127.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
118.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
100 → 100
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01152639
12931655
212111574
done50011554

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 6.9b

regimes395.0ms

Accuracy

92.2% (1.0b remaining)

Error of 7.2b against oracle of 6.2b and baseline of 19.5b

bsearch399.0ms

Steps
ItersRangePoint
9
9.357224410271438e+98
8.450543925883448e+104
6.215531586102827e+101
9
-3.6488347205826883e+132
-1.6867412280479856e+126
-1.2969712652290727e+130

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
047135
154135
done54135

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.2s8732×body80valid
431.0ms2889×body80nan