Details

Time bar (total: 2.4s)

analyze1.0ms

Algorithm
search

sample35.0ms

Algorithm
intervals
Results
17.0ms81×body1280valid
5.0ms140×body80valid
5.0ms28×body640valid
1.0ms6×body320valid
0.0ms1×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0196
1246
2286
3306
4356
5376
6376

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.6b

Counts
2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(hypot 1.0 x)
0.8b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt
9×times-frac
7×pow1
6×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×sqrt-pow1 sqrt-div associate-*r/
1×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ pow1/2 diff-log div-exp pow-prod-down clear-num sqrt-prod flip-- flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 61
Calls
4 calls:
10.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms
(/ 1.0 (hypot 1.0 x))
1.0ms
(hypot 1.0 x)
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series32.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
4.0ms
(/ 1.0 (hypot 1.0 x))
1.0ms
(hypot 1.0 x)
14.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify58.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0201433
1602413
21986411
35001411

prune309.0ms

Filtered
52 candidates to 73 candidates (-40.4%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New72173
Fresh000
Picked101
Done000
Total73174

Merged error: 15.1b

Counts
74 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.2b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
20×add-sqr-sqrt add-cube-cbrt
18×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r* associate-/l*
4×pow1 associate-*r/ associate--l+
3×sub-neg
2×cbrt-undiv distribute-rgt-in flip3-- frac-2neg distribute-lft-in div-exp clear-num frac-sub flip-- div-inv
1×+-commutative flip3-+ diff-log sum-log flip-+ distribute-lft-out
Counts
4 → 84
Calls
4 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series30.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
4.0ms
(/ 1.0 (hypot 1.0 x))
14.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify141.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0306616
11080568
24837560
35001560

prune201.0ms

Filtered
69 candidates to 96 candidates (-39.1%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New95196
Fresh000
Picked011
Done000
Total95297

Merged error: 15.0b

Counts
97 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.2b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
1.0b
(* (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
26×sqrt-prod
24×add-sqr-sqrt
19×pow1
12×add-cube-cbrt sqrt-div
11×swap-sqr
10×add-log-exp
8×sqrt-pow1 flip3-+ pow1/2 flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log associate-*r/ add-cbrt-cube
5×pow-prod-up
4×frac-times associate--l+ unswap-sqr
3×sub-neg pow-prod-down pow-sqr
2×+-commutative distribute-rgt-in flip3-- distribute-lft-in associate-*l/ sum-log frac-sub flip--
1×pow2 pow-plus sqrt-unprod diff-log prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 104
Calls
4 calls:
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
10.0ms
(* (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

series49.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
16.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
14.0ms
(* (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

simplify53.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03261259
112001141
250021097

prune278.0ms

Filtered
62 candidates to 116 candidates (-87.1%)
Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1160116
Fresh000
Picked011
Done011
Total1162118

Merged error: 15.0b

Counts
118 → 2

regimes86.0ms

Accuracy

0% (0.0b remaining)

Error of 15.5b against oracle of 15.5b and baseline of 15.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01913
11913

end0.0ms

analyze1.0ms

Algorithm
search

sample1.1s

Algorithm
intervals
Results
630.0ms2873×body1280valid
158.0ms4036×body80valid
108.0ms611×body640valid
40.0ms329×body320valid
12.0ms151×body160valid

Profiling

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