Details

Time bar (total: 15.2s)

sample104.0ms

Algorithm
intervals
Results
69.0ms277×body80valid
13.0ms84×body80nan

simplify148.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.8b

localize142.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (sqrt (fma -4 (* c a) (* b b))) b)
1.7b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
23.7b
(sqrt (fma -4 (* c a) (* b b)))
23.7b
(sqrt (fma -4 (* c a) (* b b)))

rewrite36.0ms

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×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 flip--
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
8.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
17.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
5.0ms
(sqrt (fma -4 (* c a) (* b b)))

series487.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
120.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
105.0ms
(sqrt (fma -4 (* c a) (* b b)))
147.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify868.0ms

Counts
177 → 177
Iterations
IterNodes
done2000
2995
1424
0194

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.9b

localize153.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
23.7b
(sqrt (fma -4 (* c a) (* b b)))
23.7b
(sqrt (fma -4 (* c a) (* b b)))
23.7b
(sqrt (fma -4 (* c a) (* b b)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
55×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
40×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
8×add-log-exp
7×pow1 neg-mul-1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg flip3-- neg-log flip--
Counts
4 → 139
Calls
4 calls:
19.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
3.0ms
(sqrt (fma -4 (* c a) (* b b)))

series480.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
113.0ms
(sqrt (fma -4 (* c a) (* b b)))
106.0ms
(sqrt (fma -4 (* c a) (* b b)))
124.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify1.3s

Counts
151 → 151
Iterations
IterNodes
done2000
31875
2672
1314
0146

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.9b

localize537.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (sqrt (fma -4 (* c a) (* b b))) b)
23.7b
(sqrt (fma -4 (* c a) (* b b)))
23.7b
(sqrt (fma -4 (* c a) (* b b)))
23.7b
(sqrt (fma -4 (* c a) (* b b)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
23×*-un-lft-identity
22×sqrt-prod
21×add-cube-cbrt
18×prod-diff
7×pow1
6×fma-neg add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 90
Calls
4 calls:
8.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
1.0ms
(sqrt (fma -4 (* c a) (* b b)))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))

series399.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
80.0ms
(sqrt (fma -4 (* c a) (* b b)))
102.0ms
(sqrt (fma -4 (* c a) (* b b)))
102.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify815.0ms

Counts
102 → 102
Iterations
IterNodes
done2001
3908
2311
1168
085

prune931.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.9b

localize207.0ms

Local error

Found 4 expressions with local error:

23.7b
(sqrt (fma -4 (* c a) (* b b)))
24.5b
(cbrt (fma -4 (* c a) (* b b)))
24.5b
(cbrt (fma -4 (* c a) (* b b)))
24.5b
(cbrt (fma -4 (* c a) (* b b)))

rewrite7.0ms

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 insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
1.0ms
(cbrt (fma -4 (* c a) (* b b)))
1.0ms
(cbrt (fma -4 (* c a) (* b b)))
2.0ms
(cbrt (fma -4 (* c a) (* b b)))

series828.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(sqrt (fma -4 (* c a) (* b b)))
249.0ms
(cbrt (fma -4 (* c a) (* b b)))
219.0ms
(cbrt (fma -4 (* c a) (* b b)))
229.0ms
(cbrt (fma -4 (* c a) (* b b)))

simplify471.0ms

Counts
70 → 70
Iterations
IterNodes
done2017
3847
2281
1122
068

prune715.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.9b

regimes422.0ms

Accuracy

91.5% (0.6b remaining)

Error of 12.3b against oracle of 11.7b and baseline of 19.2b

bsearch139.0ms

Steps
ItersRangePoint
7
1.9723660647371773e+81
3.4101289177416236e+83
3.340270116328134e+83

simplify29.0ms

Iterations
IterNodes
done55
255
153
043

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.0s8767×body80valid
619.0ms2981×body80nan