Details

Time bar (total: 37.5s)

sample71.0ms

Algorithm
intervals
Results
40.0ms100×body1280valid
9.0ms123×body80valid
6.0ms19×body640valid
3.0ms10×body320valid
1.0ms4×body160valid

simplify20.0ms

Counts
1 → 1
Iterations
IterNodes
425
325
223
119
09

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1 x)
0.0b
(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(/ 1/2 (hypot 1 x))
1.3b
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite46.0ms

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:
0.0ms
(hypot 1 x)
6.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
4.0ms
(/ 1/2 (hypot 1 x))
34.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series345.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(hypot 1 x)
65.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
60.0ms
(/ 1/2 (hypot 1 x))
151.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify2.9s

Counts
117 → 117
Iterations
IterNodes
32870
21149
1492
0212

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1/2 (hypot 1 x))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
0.8b
(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt *-un-lft-identity
56×add-cube-cbrt
46×times-frac
39×prod-diff
8×add-cbrt-cube add-exp-log add-log-exp
6×associate-/r* associate-/l*
5×div-inv
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u distribute-lft-out
3×fma-def fma-neg
2×cbrt-undiv clear-num frac-2neg div-exp sqrt-prod difference-of-squares
1×+-commutative sum-log sub-neg flip3-+ flip3-- diff-log flip-+ flip-- distribute-lft-out--
Counts
4 → 140
Calls
4 calls:
7.0ms
(/ 1/2 (hypot 1 x))
4.0ms
(/ 1/2 (hypot 1 x))
15.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
7.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ 1/2 (hypot 1 x))
79.0ms
(/ 1/2 (hypot 1 x))
142.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
103.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify4.8s

Counts
152 → 152
Iterations
IterNodes
34209
21657
1618
0247

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1/2 (sqrt (hypot 1 x))) (sqrt (hypot 1 x)))
0.2b
(/ (/ 1/2 (sqrt (hypot 1 x))) (sqrt (hypot 1 x)))
0.8b
(- 1/2 (/ (/ 1/2 (sqrt (hypot 1 x))) (sqrt (hypot 1 x))))
28.5b
(fma (/ -1 (sqrt (hypot 1 x))) (/ 1/2 (sqrt (hypot 1 x))) (/ (/ 1/2 (sqrt (hypot 1 x))) (sqrt (hypot 1 x))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
1246×times-frac
808×add-sqr-sqrt
786×*-un-lft-identity
784×add-cube-cbrt
629×sqrt-prod
408×prod-diff
44×associate-/l*
37×div-inv
14×add-cbrt-cube add-exp-log
12×associate-/r*
7×difference-of-squares
6×cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×fma-neg
2×clear-num frac-2neg associate-/l/
1×sub-neg flip3-- diff-log fma-udef flip-- distribute-lft-out--
Counts
4 → 801
Calls
4 calls:
14.0ms
(/ (/ 1/2 (sqrt (hypot 1 x))) (sqrt (hypot 1 x)))
10.0ms
(/ (/ 1/2 (sqrt (hypot 1 x))) (sqrt (hypot 1 x)))
19.0ms
(- 1/2 (/ (/ 1/2 (sqrt (hypot 1 x))) (sqrt (hypot 1 x))))
0.0ms
(fma (/ -1 (sqrt (hypot 1 x))) (/ 1/2 (sqrt (hypot 1 x))) (/ (/ 1/2 (sqrt (hypot 1 x))) (sqrt (hypot 1 x))))

series607.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(/ (/ 1/2 (sqrt (hypot 1 x))) (sqrt (hypot 1 x)))
81.0ms
(/ (/ 1/2 (sqrt (hypot 1 x))) (sqrt (hypot 1 x)))
94.0ms
(- 1/2 (/ (/ 1/2 (sqrt (hypot 1 x))) (sqrt (hypot 1 x))))
349.0ms
(fma (/ -1 (sqrt (hypot 1 x))) (/ 1/2 (sqrt (hypot 1 x))) (/ (/ 1/2 (sqrt (hypot 1 x))) (sqrt (hypot 1 x))))

simplify2.9s

Counts
813 → 813
Iterations
IterNodes
12657
0981

prune13.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
0.0b
(/ (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
0.1b
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
0.7b
(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
57×add-sqr-sqrt
56×times-frac
43×add-cube-cbrt
18×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
11×pow1
9×distribute-lft-out
8×add-log-exp
6×difference-of-squares
5×cbrt-undiv div-exp div-inv
4×expm1-log1p-u associate-/r* prod-exp cbrt-unprod insert-posit16 log1p-expm1-u associate-/l* unswap-sqr
3×fma-def
2×flip3-+ flip3-- associate-/r/ sqrt-prod flip-+ flip-- associate-/l/
1×pow2 frac-times +-commutative clear-num sum-log sub-neg frac-2neg pow-plus fma-neg diff-log div-sub prod-diff pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 152
Calls
4 calls:
15.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
27.0ms
(/ (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
13.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
8.0ms
(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))

series477.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
156.0ms
(/ (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
100.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
100.0ms
(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))

simplify3.3s

Counts
164 → 164
Iterations
IterNodes
22943
1853
0279

prune1.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes162.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.2b

bsearch3.0ms

simplify9.0ms

Iterations
IterNodes
232
132
026

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.2s2870×body1280valid
398.0ms4019×body80valid
293.0ms641×body640valid
95.0ms322×body320valid
26.0ms148×body160valid