Details

Time bar (total: 28.9s)

sample107.0ms

Algorithm
intervals
Results
59.0ms89×body1280valid
15.0ms126×body80valid
10.0ms19×body640valid
7.0ms19×body320valid
1.0ms3×body160valid

simplify24.0ms

Counts
1 → 1
Iterations
IterNodes
425
325
223
119
09

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
35×add-sqr-sqrt
27×add-cube-cbrt
21×prod-diff
16×sqrt-prod
9×times-frac
8×add-log-exp
6×add-cbrt-cube add-exp-log
5×distribute-lft-out
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u difference-of-squares
3×associate-/r* fma-def fma-neg associate-/l* distribute-lft-out--
1×cbrt-undiv +-commutative hypot-udef clear-num sum-log sub-neg frac-2neg flip3-+ flip3-- diff-log div-exp flip-+ div-inv flip--
Counts
4 → 105
Calls
4 calls:
7.0ms
(/ 1/2 (hypot 1 x))
0.0ms
(hypot 1 x)
12.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
44.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series396.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ 1/2 (hypot 1 x))
85.0ms
(hypot 1 x)
72.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
133.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify3.0s

Counts
117 → 117
Iterations
IterNodes
32900
21147
1492
0212

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1 x)
0.0b
(hypot 1 x)
0.0b
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
1.7b
(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt *-un-lft-identity
40×add-cube-cbrt
39×prod-diff
28×times-frac
8×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u distribute-lft-out
3×fma-def fma-neg div-inv
2×hypot-udef sqrt-prod difference-of-squares
1×+-commutative sum-log sub-neg flip3-+ flip3-- diff-log flip-+ flip-- distribute-lft-out--
Counts
4 → 102
Calls
4 calls:
0.0ms
(hypot 1 x)
0.0ms
(hypot 1 x)
28.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
13.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(hypot 1 x)
81.0ms
(hypot 1 x)
129.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
92.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify5.2s

Counts
114 → 114
Iterations
IterNodes
34216
21627
1595
0236

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (- 1/2 (/ 1/2 (hypot 1 x))))
0.0b
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
0.1b
(exp (log (- 1/2 (/ 1/2 (hypot 1 x)))))
1.7b
(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
54×*-un-lft-identity
43×add-cube-cbrt
39×prod-diff
30×times-frac
12×log-prod
8×add-log-exp
6×pow1 exp-sum difference-of-squares
5×add-exp-log
4×expm1-log1p-u log-div exp-prod add-cbrt-cube insert-posit16 log1p-expm1-u distribute-lft-out
3×fma-def flip3-- fma-neg div-inv flip-- distribute-lft-out--
2×exp-diff log-pow sqrt-prod
1×+-commutative sum-log sub-neg flip3-+ diff-log rem-log-exp flip-+ rem-exp-log
Counts
4 → 123
Calls
4 calls:
6.0ms
(log (- 1/2 (/ 1/2 (hypot 1 x))))
14.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
10.0ms
(exp (log (- 1/2 (/ 1/2 (hypot 1 x)))))
7.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(log (- 1/2 (/ 1/2 (hypot 1 x))))
132.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
90.0ms
(exp (log (- 1/2 (/ 1/2 (hypot 1 x)))))
99.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify4.7s

Counts
135 → 135
Iterations
IterNodes
34159
21708
1657
0282

prune1.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
0.0b
(* (hypot 1 x) (* (hypot 1 x) (hypot 1 x)))
0.2b
(/ 1/8 (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x))))
1.7b
(- 1/8 (/ 1/8 (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x)))))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
29×*-un-lft-identity
27×add-sqr-sqrt
22×add-cube-cbrt
21×prod-diff
18×pow1 add-cbrt-cube add-exp-log
12×times-frac
8×add-log-exp
6×prod-exp cbrt-unprod
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv distribute-lft-out
3×cbrt-undiv hypot-udef fma-def fma-neg div-exp associate-*l* pow-prod-down associate-/l*
2×sqrt-unprod sqrt-prod
1×pow2 +-commutative clear-num associate-/r* sum-log sub-neg frac-2neg flip3-+ pow-plus flip3-- diff-log cube-unmult associate-*r* pow-sqr *-commutative flip-+ flip-- distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 115
Calls
4 calls:
27.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
23.0ms
(* (hypot 1 x) (* (hypot 1 x) (hypot 1 x)))
20.0ms
(/ 1/8 (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x))))
19.0ms
(- 1/8 (/ 1/8 (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x)))))

series422.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
88.0ms
(* (hypot 1 x) (* (hypot 1 x) (hypot 1 x)))
98.0ms
(/ 1/8 (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x))))
101.0ms
(- 1/8 (/ 1/8 (* (hypot 1 x) (* (hypot 1 x) (hypot 1 x)))))

simplify5.0s

Counts
127 → 127
Iterations
IterNodes
36693
21853
1621
0246

prune1.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes86.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.6b

bsearch1.0ms

simplify7.0ms

Iterations
IterNodes
230
130
025

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.8s2877×body1280valid
791.0ms3970×body80valid
346.0ms667×body640valid
102.0ms341×body320valid
63.0ms145×body160valid