Details

Time bar (total: 15.9s)

sample46.0ms

Algorithm
intervals
Results
18.0ms271×body80valid
7.0ms102×body80nan

simplify132.0ms

Counts
1 → 1
Iterations
IterNodes
done176
6176
5174
4161
3122
266
136
020

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize149.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (fma (* c 4.0) (- a) (* b b))) b)
2.0b
(- (- b) (sqrt (fma (* c 4.0) (- a) (* b b))))
22.9b
(sqrt (fma (* c 4.0) (- a) (* b b)))
22.9b
(sqrt (fma (* c 4.0) (- a) (* b b)))

rewrite68.0ms

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 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 → 161
Calls
4 calls:
17.0ms
(- (sqrt (fma (* c 4.0) (- a) (* b b))) b)
30.0ms
(- (- b) (sqrt (fma (* c 4.0) (- a) (* b b))))
2.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))
6.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))

series486.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(- (sqrt (fma (* c 4.0) (- a) (* b b))) b)
120.0ms
(- (- b) (sqrt (fma (* c 4.0) (- a) (* b b))))
109.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))
142.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))

simplify2.1s

Counts
173 → 173
Iterations
IterNodes
done5001
21749
1425
0193

prune876.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.4b

localize163.0ms

Local error

Found 4 expressions with local error:

7.1b
(- (- b) (* (fabs (cbrt (fma (* c 4.0) (- a) (* b b)))) (sqrt (cbrt (fma (* c 4.0) (- a) (* b b))))))
22.9b
(sqrt (fma (* c 4.0) (- a) (* b b)))
23.8b
(cbrt (fma (* c 4.0) (- a) (* b b)))
23.8b
(cbrt (fma (* c 4.0) (- a) (* b b)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
10×fma-neg prod-diff
8×add-log-exp
6×cbrt-prod distribute-lft-neg-in distribute-rgt-neg-in
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
3×sqrt-prod
2×neg-mul-1 pow1/3 diff-log
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 neg-log flip--
Counts
4 → 77
Calls
4 calls:
23.0ms
(- (- b) (* (fabs (cbrt (fma (* c 4.0) (- a) (* b b)))) (sqrt (cbrt (fma (* c 4.0) (- a) (* b b))))))
2.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))
1.0ms
(cbrt (fma (* c 4.0) (- a) (* b b)))
2.0ms
(cbrt (fma (* c 4.0) (- a) (* b b)))

series916.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(- (- b) (* (fabs (cbrt (fma (* c 4.0) (- a) (* b b)))) (sqrt (cbrt (fma (* c 4.0) (- a) (* b b))))))
112.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))
315.0ms
(cbrt (fma (* c 4.0) (- a) (* b b)))
363.0ms
(cbrt (fma (* c 4.0) (- a) (* b b)))

simplify956.0ms

Counts
89 → 89
Iterations
IterNodes
done5000
21349
1368
0164

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.4b

localize163.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

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 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 → 135
Calls
4 calls:
31.0ms
(- (- b) (sqrt (fma (* c 4.0) (- a) (* b b))))
2.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))
2.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))
3.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))

series547.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (- b) (sqrt (fma (* c 4.0) (- a) (* b b))))
143.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))
153.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))
135.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))

simplify874.0ms

Counts
147 → 147
Iterations
IterNodes
done5000
21030
1314
0146

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.4b

localize184.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

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 log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
1.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))
1.0ms
(cbrt (fma b b (* c (* 4.0 (- a)))))
1.0ms
(cbrt (fma b b (* c (* 4.0 (- a)))))
1.0ms
(cbrt (fma (* c 4.0) (- a) (* b b)))

series699.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))
138.0ms
(cbrt (fma b b (* c (* 4.0 (- a)))))
136.0ms
(cbrt (fma b b (* c (* 4.0 (- a)))))
292.0ms
(cbrt (fma (* c 4.0) (- a) (* b b)))

simplify1.1s

Counts
66 → 66
Iterations
IterNodes
done5001
32133
2524
1206
0108

prune903.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.4b

regimes398.0ms

Accuracy

87.5% (0.9b remaining)

Error of 13.7b against oracle of 12.7b and baseline of 20.1b

bsearch162.0ms

Steps
ItersRangePoint
7
1.9371672431899034e+133
5.16149553175908e+134
3.756010775197467e+134

simplify9.0ms

Iterations
IterNodes
done55
355
251
143
036

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.7s8769×body80valid
335.0ms2946×body80nan