Details

Time bar (total: 5.5s)

sample37.0ms

Algorithm
intervals
Results
19.0ms92×body1280valid
5.0ms131×body80valid
3.0ms17×body640valid
1.0ms7×body320valid
1.0ms9×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: 14.5b

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))
2.2b
(- 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))))))

series196.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
73.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms
(/ 1.0 (hypot 1.0 x))
86.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify70.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0221492
1697465
22311463
35001463

prune138.0ms

Filtered
78 candidates to 55 candidates (70.5%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New75378
Fresh000
Picked011
Done000
Total75479

Merged error: 14.0b

Counts
79 → 4

localize14.0ms

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))
1.7b
(- (* 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))))

series210.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(/ (- (* 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)))))))
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
37.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify54.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04071275
115941181
250021177

prune291.0ms

Filtered
122 candidates to 88 candidates (72.1%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1166122
Fresh112
Picked101
Done101
Total1197126

Merged error: 13.9b

Counts
126 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
0.0b
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
0.2b
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
1.6b
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
288×associate-*r/
108×frac-add
76×flip3-- flip--
74×associate-/r/
72×frac-times
40×add-sqr-sqrt
30×*-un-lft-identity
27×times-frac associate-*l/
21×add-exp-log add-cbrt-cube sqr-pow
20×add-cube-cbrt difference-of-squares
19×flip3-+ flip-+
12×pow1
9×cube-div associate-/l*
7×prod-exp cbrt-unprod
6×add-log-exp
5×difference-cubes distribute-lft-out--
4×pow-prod-down frac-sub associate-/l/
3×cbrt-undiv pow-unpow div-exp associate-*r* pow-exp associate-/r* rem-cube-cbrt
2×pow-pow
1×distribute-rgt-in cube-mult pow-to-exp sub-neg unpow-prod-down frac-2neg distribute-lft-in diff-log unpow3 div-sub cube-prod associate-*l* clear-num *-commutative div-inv
Counts
4 → 206
Calls
4 calls:
32.0ms
(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
12.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
5.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
9.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

series343.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
54.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
37.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
72.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify108.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
019676759
150026583

prune910.0ms

Filtered
218 candidates to 161 candidates (73.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2135218
Fresh336
Picked101
Done000
Total2178225

Merged error: 13.7b

Counts
225 → 8

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
1.0b
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) (* (cbrt 3) (cbrt 3)))
1.3b
(pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) (* (cbrt 3) (cbrt 3))) (cbrt 3))
1.6b
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) (* (cbrt 3) (cbrt 3))) (cbrt 3)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
17×associate-*r/
16×add-sqr-sqrt
13×add-cbrt-cube
12×pow1
11×unpow-prod-down pow-exp sqr-pow
10×*-un-lft-identity
9×prod-exp
8×add-cube-cbrt difference-of-squares
7×pow-unpow
6×add-log-exp
5×cbrt-unprod
4×frac-times pow-prod-down frac-add
3×cbrt-prod pow-to-exp flip3-- pow-pow div-exp associate-*r* flip--
2×flip3-+ flip-+
1×cbrt-undiv distribute-rgt-in sub-neg distribute-lft-in diff-log associate-*l* associate-*l/ *-commutative distribute-lft-out--
Counts
4 → 94
Calls
4 calls:
12.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
5.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) (* (cbrt 3) (cbrt 3)))
4.0ms
(pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) (* (cbrt 3) (cbrt 3))) (cbrt 3))
10.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) (* (cbrt 3) (cbrt 3))) (cbrt 3)))

series1.1s

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
187.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) (* (cbrt 3) (cbrt 3)))
425.0ms
(pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) (* (cbrt 3) (cbrt 3))) (cbrt 3))
444.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) (* (cbrt 3) (cbrt 3))) (cbrt 3)))

simplify103.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
06531486
132231363
250021351

prune399.0ms

Filtered
106 candidates to 72 candidates (67.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1042106
Fresh077
Picked101
Done000
Total1059114

Merged error: 13.7b

Counts
114 → 9

regimes270.0ms

Accuracy

0% (0.3b remaining)

Error of 14.9b against oracle of 14.6b and baseline of 14.9b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03762
13762

end0.0ms

sample1.0s

Algorithm
intervals
Results
597.0ms2825×body1280valid
150.0ms4045×body80valid
107.0ms640×body640valid
37.0ms327×body320valid
12.0ms163×body160valid

Profiling

Loading profile data...