Details

Time bar (total: 19.8s)

sample124.0ms

Algorithm
intervals
Results
72.0ms277×body80valid
21.0ms86×body80nan

simplify189.0ms

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

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.5b

localize162.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (sqrt (fma -4 (* c a) (* b b))) b)
1.2b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
23.5b
(sqrt (fma -4 (* c a) (* b b)))
23.5b
(sqrt (fma -4 (* c a) (* b b)))

rewrite51.0ms

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:
16.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
22.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
4.0ms
(sqrt (fma -4 (* c a) (* b b)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
99.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
80.0ms
(sqrt (fma -4 (* c a) (* b b)))
130.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify1.1s

Counts
177 → 177
Iterations
IterNodes
done2000
32000
2995
1424
0194

prune3.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.7b

localize162.0ms

Local error

Found 4 expressions with local error:

9.8b
(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
23.5b
(sqrt (fma -4 (* c a) (* b b)))
23.5b
(sqrt (fma -4 (* c a) (* b b)))
23.5b
(sqrt (fma -4 (* c a) (* b b)))

rewrite27.0ms

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
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg flip3-- neg-log flip-- difference-of-squares
Counts
4 → 86
Calls
4 calls:
19.0ms
(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (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)))
2.0ms
(sqrt (fma -4 (* c a) (* b b)))

series416.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(- (- b) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))))
92.0ms
(sqrt (fma -4 (* c a) (* b b)))
116.0ms
(sqrt (fma -4 (* c a) (* b b)))
110.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify1.2s

Counts
98 → 98
Iterations
IterNodes
done2016
42016
31432
2519
1207
097

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.7b

localize195.0ms

Local error

Found 4 expressions with local error:

21.3b
(fma (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))) (- b))
23.5b
(sqrt (fma -4 (* c a) (* b b)))
23.5b
(sqrt (fma -4 (* c a) (* b b)))
23.5b
(sqrt (fma -4 (* c a) (* b b)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×fma-udef
Counts
4 → 59
Calls
4 calls:
0.0ms
(fma (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b 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)))

series657.0ms

Counts
4 → 12
Calls
4 calls:
359.0ms
(fma (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))) (- b))
97.0ms
(sqrt (fma -4 (* c a) (* b b)))
101.0ms
(sqrt (fma -4 (* c a) (* b b)))
99.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify928.0ms

Counts
71 → 71
Iterations
IterNodes
done2006
42006
3715
2243
1112
065

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.7b

localize205.0ms

Local error

Found 4 expressions with local error:

23.5b
(sqrt (fma -4 (* c a) (* b b)))
24.2b
(cbrt (fma -4 (* c a) (* b b)))
24.2b
(cbrt (fma -4 (* c a) (* b b)))
24.2b
(cbrt (fma -4 (* c a) (* b b)))

rewrite18.0ms

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:
3.0ms
(sqrt (fma -4 (* c a) (* b b)))
11.0ms
(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)))

series963.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(sqrt (fma -4 (* c a) (* b b)))
291.0ms
(cbrt (fma -4 (* c a) (* b b)))
285.0ms
(cbrt (fma -4 (* c a) (* b b)))
276.0ms
(cbrt (fma -4 (* c a) (* b b)))

simplify1.0s

Counts
70 → 70
Iterations
IterNodes
done2017
42017
3847
2281
1122
068

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.7b

regimes485.0ms

Accuracy

88.9% (0.7b remaining)

Error of 13.1b against oracle of 12.3b and baseline of 19.0b

bsearch152.0ms

Steps
ItersRangePoint
8
2.231296991249122e+66
2.5939819947174796e+69
4.1813913858897907e+68

simplify13.0ms

Iterations
IterNodes
done29
129
027

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.4s8699×body80valid
545.0ms2954×body80nan