Details

Time bar (total: 16.5s)

sample83.0ms

Algorithm
intervals
Results
40.0ms280×body80valid
9.0ms88×body80nan

simplify157.0ms

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

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize197.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (sqrt (fma (* c 4.0) (- a) (* b b))) b)
0.8b
(- (- b) (sqrt (fma (* c 4.0) (- a) (* b b))))
24.4b
(sqrt (fma (* c 4.0) (- a) (* b b)))
24.4b
(sqrt (fma (* c 4.0) (- 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 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:
9.0ms
(- (sqrt (fma (* c 4.0) (- a) (* b b))) b)
16.0ms
(- (- b) (sqrt (fma (* c 4.0) (- a) (* b b))))
1.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))
3.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))

series486.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (sqrt (fma (* c 4.0) (- a) (* b b))) b)
108.0ms
(- (- b) (sqrt (fma (* c 4.0) (- a) (* b b))))
127.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))
141.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))

simplify2.2s

Counts
173 → 173
Iterations
IterNodes
done5001
21749
1425
0193

prune874.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.5b

localize161.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b) (sqrt (fma (* c 4.0) (- a) (* b b))))
24.4b
(sqrt (fma (* c 4.0) (- a) (* b b)))
24.4b
(sqrt (fma (* c 4.0) (- a) (* b b)))
24.4b
(sqrt (fma (* c 4.0) (- a) (* b b)))

rewrite47.0ms

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:
32.0ms
(- (- 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)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(- (- b) (sqrt (fma (* c 4.0) (- a) (* b b))))
115.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))
125.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))
119.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))

simplify995.0ms

Counts
147 → 147
Iterations
IterNodes
done5000
21030
1314
0146

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.5b

localize151.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (sqrt (fma (* c 4.0) (- a) (* b b))) b)
3.0b
(/ (* 2.0 c) (fma 2.0 (/ c (/ b a)) (* -2 b)))
4.0b
(/ c (/ b a))
24.4b
(sqrt (fma (* c 4.0) (- a) (* b b)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
68×add-sqr-sqrt
65×*-un-lft-identity
63×add-cube-cbrt
18×prod-diff
16×associate-/r* sqrt-prod
14×add-cbrt-cube add-exp-log
6×fma-neg div-inv add-log-exp
5×pow1 cbrt-undiv div-exp
4×expm1-log1p-u log1p-expm1-u associate-/l*
2×clear-num frac-2neg difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log prod-exp associate-/r/ cbrt-unprod flip-- distribute-lft-out--
Counts
4 → 151
Calls
4 calls:
14.0ms
(- (sqrt (fma (* c 4.0) (- a) (* b b))) b)
8.0ms
(/ (* 2.0 c) (fma 2.0 (/ c (/ b a)) (* -2 b)))
7.0ms
(/ c (/ b a))
1.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))

series503.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(- (sqrt (fma (* c 4.0) (- a) (* b b))) b)
209.0ms
(/ (* 2.0 c) (fma 2.0 (/ c (/ b a)) (* -2 b)))
35.0ms
(/ c (/ b a))
138.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))

simplify1.2s

Counts
163 → 163
Iterations
IterNodes
done5000
22990
1664
0275

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.5b

localize248.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (sqrt (fma (* c 4.0) (- a) (* b b))) b)
3.0b
(/ (* 2.0 c) (fma 2.0 (/ (* (/ c (* (cbrt b) (cbrt b))) (* (cbrt a) (cbrt a))) (/ (cbrt b) (cbrt a))) (* -2 b)))
3.7b
(* (/ c (* (cbrt b) (cbrt b))) (* (cbrt a) (cbrt a)))
24.4b
(sqrt (fma (* c 4.0) (- a) (* b b)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt add-exp-log
25×*-un-lft-identity
23×add-cube-cbrt
20×add-cbrt-cube
18×prod-diff
16×sqrt-prod
12×prod-exp cbrt-unprod
10×pow1
7×times-frac associate-*l*
6×cbrt-undiv fma-neg div-exp add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×associate-/r* pow-prod-down
2×div-inv difference-of-squares unswap-sqr
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log associate-*r* associate-*l/ *-commutative flip-- associate-/l* distribute-lft-out--
Counts
4 → 114
Calls
4 calls:
18.0ms
(- (sqrt (fma (* c 4.0) (- a) (* b b))) b)
15.0ms
(/ (* 2.0 c) (fma 2.0 (/ (* (/ c (* (cbrt b) (cbrt b))) (* (cbrt a) (cbrt a))) (/ (cbrt b) (cbrt a))) (* -2 b)))
45.0ms
(* (/ c (* (cbrt b) (cbrt b))) (* (cbrt a) (cbrt a)))
2.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))

series1.1s

Counts
4 → 12
Calls
4 calls:
140.0ms
(- (sqrt (fma (* c 4.0) (- a) (* b b))) b)
705.0ms
(/ (* 2.0 c) (fma 2.0 (/ (* (/ c (* (cbrt b) (cbrt b))) (* (cbrt a) (cbrt a))) (/ (cbrt b) (cbrt a))) (* -2 b)))
109.0ms
(* (/ c (* (cbrt b) (cbrt b))) (* (cbrt a) (cbrt a)))
113.0ms
(sqrt (fma (* c 4.0) (- a) (* b b)))

simplify1.0s

Counts
126 → 126
Iterations
IterNodes
done5003
22192
1556
0227

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.5b

regimes561.0ms

Accuracy

82.2% (1.3b remaining)

Error of 13.7b against oracle of 12.4b and baseline of 19.7b

bsearch151.0ms

Steps
ItersRangePoint
10
4.0721326822252617e+40
3.6590220876252264e+50
3.628799960716312e+50

simplify5.0ms

Iterations
IterNodes
done32
132
030

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.2s8758×body80valid
311.0ms2839×body80nan