Details

Time bar (total: 19.3s)

sample89.0ms

Algorithm
intervals
Results
47.0ms273×body80valid
11.0ms92×body80nan

simplify263.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
02038
13638
26637
312237
416137
517437
617637
done17637

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.0b

localize179.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite176.0ms

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:
62.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
55.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
28.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
131.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
118.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
177 → 177
Iterations

Useful iterations: 2 (590.0ms)

IterNodesCost
02086992
15084619
226663570
done50003570

prune780.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.4b

localize154.0ms

Local error

Found 4 expressions with local error:

21.9b
(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite85.0ms

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:
1.0ms
(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
34.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series617.0ms

Counts
4 → 12
Calls
4 calls:
209.0ms
(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))
128.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
140.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
139.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts
73 → 73
Iterations

Useful iterations: done (3.1s)

IterNodesCost
0711269
11741005
2677906
33809906
done5000903

prune494.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.6b

localize141.0ms

Local error

Found 4 expressions with local error:

7.0b
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))
24.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
8×add-log-exp
6×cbrt-prod distribute-lft-neg-in distribute-rgt-neg-in
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×sqrt-prod
2×neg-mul-1 pow1/3 sqrt-div diff-log
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 83
Calls
4 calls:
32.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.0ms
(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)))

series525.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
112.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
127.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
148.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
95 → 95
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01782699
14522598
219502248
done50012216

prune822.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.6b

localize115.0ms

Local error

Found 4 expressions with local error:

23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))
24.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))
24.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u 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:
30.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series603.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
157.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
141.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
191.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.3s

Counts
74 → 74
Iterations

Useful iterations: done (3.3s)

IterNodesCost
0941258
12241190
27501076
339761058
done50001057

prune541.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.6b

regimes330.0ms

Accuracy

86.1% (1.9b remaining)

Error of 8.4b against oracle of 6.6b and baseline of 19.9b

bsearch329.0ms

Steps
ItersRangePoint
10
1.3113650301339767e-12
0.01077406869848718
0.010648423176581222
7
-4.1637922183371475e+115
-1.3908068482385633e+114
-3.028200009108188e+115

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
042122
148122
done48122

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.1s8732×body80valid
279.0ms3047×body80nan