Details

Time bar (total: 12.3s)

sample99.0ms

Algorithm
intervals
Results
26.0ms36×body2560valid
22.0ms187×body80valid
15.0ms26×body1280valid
9.0ms84×body80nan
5.0ms12×body640valid
2.0ms3×body5120valid
2.0ms8×body320valid
1.0ms5×body160valid

simplify114.0ms

Counts
1 → 1
Iterations
IterNodes
done102
7102
6101
599
491
373
241
122
012

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
1.0b
(- (* b b) (* (* 3 a) c))
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
23.7b
(sqrt (- (* b b) (* (* 3 a) c)))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-cube-cbrt add-log-exp
9×add-cbrt-cube add-exp-log
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×neg-sub0 cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-+l- flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 94
Calls
4 calls:
61.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
16.0ms
(- (* b b) (* (* 3 a) c))
31.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
20.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series821.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
86.0ms
(- (* b b) (* (* 3 a) c))
117.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
504.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

simplify803.0ms

Counts
106 → 106
Iterations
IterNodes
done2004
21430
1442
0170

prune560.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* a c) -3)
1.1b
(- (sqrt (fma b b (* (* a c) -3))) b)
1.3b
(fma b b (* (* a c) -3))
23.7b
(sqrt (fma b b (* (* a c) -3)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
16×sqrt-prod
10×pow1
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log associate-*l* *-commutative fma-udef flip-- distribute-lft-out--
Counts
4 → 90
Calls
4 calls:
31.0ms
(* (* a c) -3)
16.0ms
(- (sqrt (fma b b (* (* a c) -3))) b)
0.0ms
(fma b b (* (* a c) -3))
3.0ms
(sqrt (fma b b (* (* a c) -3)))

series325.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (* a c) -3)
139.0ms
(- (sqrt (fma b b (* (* a c) -3))) b)
65.0ms
(fma b b (* (* a c) -3))
94.0ms
(sqrt (fma b b (* (* a c) -3)))

simplify657.0ms

Counts
102 → 102
Iterations
IterNodes
done2000
2846
1333
0145

prune481.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* a c) -3)
1.1b
(- (sqrt (fma b b (* (* a c) -3))) b)
1.3b
(fma b b (* (* a c) -3))
23.7b
(sqrt (fma b b (* (* a c) -3)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
16×sqrt-prod
10×pow1
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log associate-*l* *-commutative fma-udef flip-- distribute-lft-out--
Counts
4 → 90
Calls
4 calls:
30.0ms
(* (* a c) -3)
16.0ms
(- (sqrt (fma b b (* (* a c) -3))) b)
0.0ms
(fma b b (* (* a c) -3))
3.0ms
(sqrt (fma b b (* (* a c) -3)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (* a c) -3)
88.0ms
(- (sqrt (fma b b (* (* a c) -3))) b)
85.0ms
(fma b b (* (* a c) -3))
100.0ms
(sqrt (fma b b (* (* a c) -3)))

simplify675.0ms

Counts
102 → 102
Iterations
IterNodes
done2000
2846
1333
0145

prune481.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 1/3 (/ (- (sqrt (fma b b (* (* a c) -3))) b) a))
1.1b
(- (sqrt (fma b b (* (* a c) -3))) b)
1.3b
(fma b b (* (* a c) -3))
23.7b
(sqrt (fma b b (* (* a c) -3)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
38×*-un-lft-identity
30×add-cube-cbrt
22×associate-*r*
19×times-frac sqrt-prod
18×prod-diff
9×add-cbrt-cube add-exp-log
8×difference-of-squares
7×pow1
6×fma-neg add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out--
3×associate-*l*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log div-exp pow-prod-down associate-*r/ *-commutative fma-udef div-inv flip--
Counts
4 → 113
Calls
4 calls:
31.0ms
(* 1/3 (/ (- (sqrt (fma b b (* (* a c) -3))) b) a))
12.0ms
(- (sqrt (fma b b (* (* a c) -3))) b)
0.0ms
(fma b b (* (* a c) -3))
3.0ms
(sqrt (fma b b (* (* a c) -3)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(* 1/3 (/ (- (sqrt (fma b b (* (* a c) -3))) b) a))
107.0ms
(- (sqrt (fma b b (* (* a c) -3))) b)
58.0ms
(fma b b (* (* a c) -3))
107.0ms
(sqrt (fma b b (* (* a c) -3)))

simplify728.0ms

Counts
125 → 125
Iterations
IterNodes
done2002
21387
1477
0197

prune456.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

regimes547.0ms

Accuracy

84.2% (4.5b remaining)

Error of 9.8b against oracle of 5.3b and baseline of 33.9b

bsearch374.0ms

Steps
ItersRangePoint
8
2.469533614662255e-16
6.384179586440732e-13
2.8123237256202247e-16
9
2.201345904528094e-30
9.673336284784144e-25
1.56232019487653e-25
10
5.0092461758030895e-88
5.0325836698121444e-76
1.4064974064077476e-77
6
-1.2289413495061505e+143
-2.1289603692599492e+142
-3.0165216367200194e+142

simplify10.0ms

Iterations
IterNodes
done55
155
042

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.3s1103×body2560valid
880.0ms5759×body80valid
565.0ms957×body1280valid
362.0ms2979×body80nan
264.0ms482×body640valid
147.0ms115×body5120valid
100.0ms222×body320valid
28.0ms127×body160valid