Details

Time bar (total: 16.3s)

sample106.0ms

Algorithm
intervals
Results
57.0ms88×body1280valid
16.0ms138×body80valid
12.0ms16×body640valid
4.0ms10×body320valid
1.0ms4×body160valid

simplify124.0ms

Counts
1 → 1
Iterations
IterNodes
done114
6114
5111
489
369
243
121
09

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b
(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(/ 1/2 (hypot 1 x))
2.2b
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
45×*-un-lft-identity
42×add-sqr-sqrt
28×add-cube-cbrt
21×prod-diff
20×sqrt-prod
10×times-frac
8×add-log-exp
6×add-cbrt-cube add-exp-log distribute-lft-out
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×associate-/r* fma-def fma-neg associate-/l* distribute-lft-out--
2×flip3-+ sqrt-div flip-+ hypot-def
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log div-exp div-inv flip--
Counts
4 → 115
Calls
4 calls:
16.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
13.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
7.0ms
(/ 1/2 (hypot 1 x))
26.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
64.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
81.0ms
(/ 1/2 (hypot 1 x))
142.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.4s

Counts
127 → 127
Iterations
IterNodes
done2001
32001
21398
1507
0213

prune459.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(/ 1/2 (hypot 1 x))
1.6b
(- (- 1 (/ 1/2 (hypot 1 x))) 1/2)

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
103×add-sqr-sqrt
93×*-un-lft-identity
67×add-cube-cbrt
63×prod-diff
53×times-frac
41×associate--l+
17×difference-of-squares
11×add-log-exp
8×add-cbrt-cube fma-neg add-exp-log
7×distribute-lft-out--
6×associate-/r* associate-/l*
5×div-inv
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u distribute-lft-out
3×fma-def diff-log
2×cbrt-undiv clear-num sub-neg frac-2neg div-exp sqrt-prod
1×associate--l- +-commutative sum-log flip3-+ flip3-- flip-+ flip--
Counts
4 → 173
Calls
4 calls:
14.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
4.0ms
(/ 1/2 (hypot 1 x))
4.0ms
(/ 1/2 (hypot 1 x))
81.0ms
(- (- 1 (/ 1/2 (hypot 1 x))) 1/2)

series385.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
101.0ms
(/ 1/2 (hypot 1 x))
81.0ms
(/ 1/2 (hypot 1 x))
97.0ms
(- (- 1 (/ 1/2 (hypot 1 x))) 1/2)

simplify975.0ms

Counts
185 → 185
Iterations
IterNodes
done2000
22000
1675
0257

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ -1/2 (hypot 1 x))
0.0b
(* (+ (/ -1/2 (hypot 1 x)) 1) (+ (/ -1/2 (hypot 1 x)) 1))
0.0b
(/ (- (* (* (+ (/ -1/2 (hypot 1 x)) 1) (+ (/ -1/2 (hypot 1 x)) 1)) (+ (/ -1/2 (hypot 1 x)) 1)) 1/8) (fma (+ (/ -1/2 (hypot 1 x)) 1) (+ (/ -1/2 (hypot 1 x)) 1) (fma 1/2 (+ (/ -1/2 (hypot 1 x)) 1) 1/4)))
1.6b
(- (* (* (+ (/ -1/2 (hypot 1 x)) 1) (+ (/ -1/2 (hypot 1 x)) 1)) (+ (/ -1/2 (hypot 1 x)) 1)) 1/8)

rewrite455.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
27×add-sqr-sqrt
25×add-cube-cbrt
18×times-frac
11×pow1
10×add-cbrt-cube add-exp-log
6×associate-/r* flip3-+ swap-sqr flip-+ distribute-lft-out associate-/l* add-log-exp
4×expm1-log1p-u frac-times associate-*r* associate-*l* insert-posit16 log1p-expm1-u
3×prod-diff
2×distribute-rgt-in cbrt-undiv clear-num frac-2neg distribute-lft-in flip3-- div-exp associate-*l/ associate--l+ associate-*r/ div-inv flip-- associate-/l/
1×pow2 sub-neg pow-plus fma-neg diff-log div-sub pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
Counts
4 → 127
Calls
4 calls:
8.0ms
(/ -1/2 (hypot 1 x))
93.0ms
(* (+ (/ -1/2 (hypot 1 x)) 1) (+ (/ -1/2 (hypot 1 x)) 1))
253.0ms
(/ (- (* (* (+ (/ -1/2 (hypot 1 x)) 1) (+ (/ -1/2 (hypot 1 x)) 1)) (+ (/ -1/2 (hypot 1 x)) 1)) 1/8) (fma (+ (/ -1/2 (hypot 1 x)) 1) (+ (/ -1/2 (hypot 1 x)) 1) (fma 1/2 (+ (/ -1/2 (hypot 1 x)) 1) 1/4)))
97.0ms
(- (* (* (+ (/ -1/2 (hypot 1 x)) 1) (+ (/ -1/2 (hypot 1 x)) 1)) (+ (/ -1/2 (hypot 1 x)) 1)) 1/8)

series939.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ -1/2 (hypot 1 x))
99.0ms
(* (+ (/ -1/2 (hypot 1 x)) 1) (+ (/ -1/2 (hypot 1 x)) 1))
537.0ms
(/ (- (* (* (+ (/ -1/2 (hypot 1 x)) 1) (+ (/ -1/2 (hypot 1 x)) 1)) (+ (/ -1/2 (hypot 1 x)) 1)) 1/8) (fma (+ (/ -1/2 (hypot 1 x)) 1) (+ (/ -1/2 (hypot 1 x)) 1) (fma 1/2 (+ (/ -1/2 (hypot 1 x)) 1) 1/4)))
239.0ms
(- (* (* (+ (/ -1/2 (hypot 1 x)) 1) (+ (/ -1/2 (hypot 1 x)) 1)) (+ (/ -1/2 (hypot 1 x)) 1)) 1/8)

simplify1.2s

Counts
139 → 139
Iterations
IterNodes
done2001
22001
1715
0258

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize96.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x))))
0.0b
(/ (fma (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x))) (fma 1/2 (+ 1 (/ -1/2 (hypot 1 x))) 1/4)) (fma (* (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x)))) (+ 1 (/ -1/2 (hypot 1 x))) -1/8))
0.0b
(/ 1 (/ (fma (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x))) (fma 1/2 (+ 1 (/ -1/2 (hypot 1 x))) 1/4)) (fma (* (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x)))) (+ 1 (/ -1/2 (hypot 1 x))) -1/8)))
1.6b
(fma (* (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x)))) (+ 1 (/ -1/2 (hypot 1 x))) -1/8)

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
72×*-un-lft-identity
60×add-sqr-sqrt
58×add-cube-cbrt
19×add-exp-log
16×associate-/r*
13×add-cbrt-cube
12×pow1
8×div-exp
6×flip3-+ swap-sqr flip-+ div-inv distribute-lft-out associate-/l*
4×expm1-log1p-u frac-times cbrt-undiv associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×rec-exp clear-num frac-2neg 1-exp associate-*l/ associate-*r/
1×pow2 distribute-rgt-in distribute-lft-in pow-plus pow-prod-down prod-exp associate-/r/ pow-sqr *-commutative pow-prod-up cbrt-unprod fma-udef pow-flip inv-pow unswap-sqr
Counts
4 → 163
Calls
4 calls:
70.0ms
(* (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x))))
8.0ms
(/ (fma (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x))) (fma 1/2 (+ 1 (/ -1/2 (hypot 1 x))) 1/4)) (fma (* (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x)))) (+ 1 (/ -1/2 (hypot 1 x))) -1/8))
10.0ms
(/ 1 (/ (fma (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x))) (fma 1/2 (+ 1 (/ -1/2 (hypot 1 x))) 1/4)) (fma (* (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x)))) (+ 1 (/ -1/2 (hypot 1 x))) -1/8)))
0.0ms
(fma (* (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x)))) (+ 1 (/ -1/2 (hypot 1 x))) -1/8)

series1.2s

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x))))
412.0ms
(/ (fma (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x))) (fma 1/2 (+ 1 (/ -1/2 (hypot 1 x))) 1/4)) (fma (* (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x)))) (+ 1 (/ -1/2 (hypot 1 x))) -1/8))
508.0ms
(/ 1 (/ (fma (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x))) (fma 1/2 (+ 1 (/ -1/2 (hypot 1 x))) 1/4)) (fma (* (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x)))) (+ 1 (/ -1/2 (hypot 1 x))) -1/8)))
172.0ms
(fma (* (+ 1 (/ -1/2 (hypot 1 x))) (+ 1 (/ -1/2 (hypot 1 x)))) (+ 1 (/ -1/2 (hypot 1 x))) -1/8)

simplify1.3s

Counts
175 → 175
Iterations
IterNodes
done2002
22002
1759
0274

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes206.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.3b

bsearch239.0ms

Steps
ItersRangePoint
11
5.037382729650074e-10
1937402784720.5117
0.011674747997097862
6
-0.09018726350273112
-0.009521407882115243
-0.012079716481524932

simplify19.0ms

Iterations
IterNodes
done57
157
049

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.7s2845×body1280valid
678.0ms603×body640valid
488.0ms4095×body80valid
114.0ms306×body320valid
27.0ms151×body160valid