Details

Time bar (total: 3.5s)

sample41.0ms

Algorithm
intervals
Results
22.0ms104×body1280valid
5.0ms123×body80valid
3.0ms16×body640valid
1.0ms8×body320valid
0.0ms5×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0196
1246
2286
3306
4356
5376
6376

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.0b

Counts
2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(/ 1.0 (hypot 1.0 x))
2.0b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
7×pow1
6×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg pow1/2 diff-log div-exp pow-prod-down clear-num sum-log sqrt-prod flip-- div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 66
Calls
4 calls:
6.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms
(/ 1.0 (hypot 1.0 x))
4.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series198.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
75.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms
(/ 1.0 (hypot 1.0 x))
89.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify72.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0221492
1697465
22311463
35001463

prune147.0ms

Filtered
78 candidates to 55 candidates (70.5%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New76278
Fresh000
Picked101
Done000
Total77279

Merged error: 14.6b

Counts
79 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
1.4b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
30×times-frac
29×add-sqr-sqrt add-cube-cbrt
10×add-exp-log associate-/r* add-cbrt-cube
9×associate-/l*
8×associate-*r/
6×add-log-exp
4×pow1 flip3-- associate--l+ frac-sub flip-- associate-/l/ distribute-lft-out
3×cbrt-undiv sub-neg frac-2neg div-exp clear-num div-inv
2×distribute-rgt-in distribute-lft-in associate-/r/
1×flip3-+ diff-log div-sub flip-+
Counts
4 → 110
Calls
4 calls:
12.0ms
(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series206.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
6.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(/ 1.0 (hypot 1.0 x))
33.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify56.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04071275
115941181
250021177

prune254.0ms

Filtered
122 candidates to 88 candidates (72.1%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1202122
Fresh011
Picked101
Done000
Total1213124

Merged error: 14.6b

Counts
124 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
1.4b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt *-un-lft-identity
32×times-frac
29×add-cube-cbrt
18×associate-*r*
17×add-exp-log
13×associate-*r/ add-cbrt-cube
6×pow1 flip3-- associate-/r* frac-sub flip-- associate-/l* add-log-exp
4×frac-times div-exp associate-*l/ prod-exp associate--l+
3×cbrt-undiv sub-neg associate-*l* div-inv distribute-lft-out unswap-sqr
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r/ cbrt-unprod
1×rec-exp flip3-+ diff-log 1-exp pow-prod-down un-div-inv *-commutative flip-+
Counts
4 → 121
Calls
4 calls:
16.0ms
(* (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series209.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(* (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
6.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(/ 1.0 (hypot 1.0 x))
36.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify66.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05091401
122341263
250011246

prune286.0ms

Filtered
133 candidates to 94 candidates (70.7%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1321133
Fresh022
Picked011
Done000
Total1324136

Merged error: 14.6b

Counts
136 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.1b
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
1.3b
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
87×associate-*r/
44×add-exp-log add-cbrt-cube
43×pow1
24×frac-sub
21×frac-times prod-exp cbrt-unprod
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
19×flip3-- flip--
18×times-frac
17×pow-prod-down
15×associate-*l/
8×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate--l+
6×associate-/r* associate-/l* add-log-exp
5×sub-neg
4×pow-sqr pow-prod-up
2×frac-2neg pow-plus clear-num div-inv
1×pow2 diff-log swap-sqr associate-*r* associate-*l* *-commutative difference-of-squares
Counts
4 → 146
Calls
4 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(/ 1.0 (hypot 1.0 x))
11.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
15.0ms
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

series96.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(/ 1.0 (hypot 1.0 x))
29.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
55.0ms
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

simplify100.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
07061704
135911480
250021479

prune300.0ms

Filtered
158 candidates to 82 candidates (51.9%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1553158
Fresh022
Picked101
Done011
Total1566162

Merged error: 14.2b

Counts
162 → 6

regimes222.0ms

Accuracy

0% (0.2b remaining)

Error of 14.4b against oracle of 14.1b and baseline of 14.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02414
12414

end0.0ms

sample1.0s

Algorithm
intervals
Results
617.0ms2860×body1280valid
158.0ms4106×body80valid
100.0ms596×body640valid
37.0ms281×body320valid
12.0ms157×body160valid

Profiling

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