Details

Time bar (total: 8.7s)

analyze1.0ms

Algorithm
search
sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 100%

sample44.0ms

Algorithm
intervals
Results
27.0ms106×body1280valid
4.0ms115×body80valid
3.0ms19×body640valid
2.0ms11×body320valid
0.0ms5×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0196
1246
2286
3306
4356
5376
6376

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.3b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.5b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×times-frac
6×pow1
5×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
3 → 54
Calls
3 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(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))))))

series34.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(/ 1.0 (hypot 1.0 x))
13.0ms
(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))))))

simplify61.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0200410
1601393
21983391
35001391

prune110.0ms

Filtered
45 candidates to 63 candidates (-40.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New61263
Fresh000
Picked101
Done000
Total62264

Merged error: 14.9b

Counts
64 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
21×add-sqr-sqrt add-cube-cbrt times-frac
8×add-exp-log associate-*r/ add-cbrt-cube add-log-exp
7×associate-/r*
6×associate-/l*
5×distribute-lft-out
4×pow1 flip3-- associate--l+ frac-sub flip-- associate-/l/
3×sub-neg
2×cbrt-undiv distribute-rgt-in frac-2neg distribute-lft-in flip3-+ div-exp clear-num associate-/r/ flip-+ div-inv
1×+-commutative diff-log div-sub sum-log
Counts
4 → 95
Calls
4 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
11.0ms
(/ (- (* 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 (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))))

series60.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ 1.0 (hypot 1.0 x))
35.0ms
(/ (- (* 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)))))))
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))))

simplify50.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04231277
116411179
250011174

prune257.0ms

Filtered
77 candidates to 107 candidates (-39.0%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1061107
Fresh101
Picked011
Done000
Total1072109

Merged error: 14.9b

Counts
109 → 2

localize23.0ms

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
(* (+ (* (* 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)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.1b
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
2.0b
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
793×associate-*r/
352×frac-times
312×frac-add
212×flip3-- flip--
152×associate-*l/
127×flip3-+ flip-+
13×add-sqr-sqrt *-un-lft-identity
12×add-exp-log add-cbrt-cube
9×pow1
8×add-log-exp
7×add-cube-cbrt
5×cube-div sqr-pow
4×associate-*r* difference-of-squares
3×pow-unpow associate-*l* pow-exp prod-exp cbrt-unprod rem-cube-cbrt
2×pow-pow pow-prod-down frac-sub distribute-lft-out
1×difference-cubes cbrt-undiv +-commutative distribute-rgt-in cube-mult pow-to-exp sub-neg unpow-prod-down distribute-lft-in diff-log unpow3 cube-prod div-exp sum-log *-commutative distribute-lft-out-- unswap-sqr
Counts
4 → 302
Calls
4 calls:
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
30.0ms
(* (+ (* (* 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)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
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))

series83.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
44.0ms
(* (+ (* (* 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)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
10.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
15.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify195.0ms

Algorithm
egg-herbie
Counts
314 → 314
Iterations

Useful iterations: 1 (60.0ms)

IterNodesCost
0383015113
1500315026

prune5.8s

Filtered
214 candidates to 314 candidates (-46.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New3122314
Fresh000
Picked101
Done011
Total3133316

Merged error: 14.6b

Counts
316 → 3

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3) 3)
0.1b
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
2.0b
(- (pow (* 1.0 (- 1.0 0.5)) 3) (cbrt (pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3) 3)))
6.1b
(cbrt (pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3) 3))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
34×cbrt-prod
26×add-sqr-sqrt
25×unpow-prod-down cube-prod
20×sqr-pow
17×add-exp-log
14×difference-of-squares
13×*-un-lft-identity
11×cube-div add-cube-cbrt pow-exp add-cbrt-cube
7×pow1 cube-mult unpow3 associate-*r/
6×pow-unpow add-log-exp
4×prod-exp rem-cube-cbrt
3×pow-to-exp cbrt-div pow-pow
2×flip3-- div-exp frac-sub flip-- cbrt-unprod
1×cbrt-undiv sub-neg pow1/3 diff-log pow-prod-down rem-cbrt-cube distribute-lft-out--
Counts
4 → 124
Calls
4 calls:
4.0ms
(pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3) 3)
6.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
17.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (cbrt (pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3) 3)))
4.0ms
(cbrt (pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3) 3))

series60.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3) 3)
10.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
16.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (cbrt (pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3) 3)))
17.0ms
(cbrt (pow (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3) 3))

simplify76.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
04131138
119061042
250011031

prune431.0ms

Filtered
68 candidates to 136 candidates (-100.0%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1360136
Fresh011
Picked011
Done011
Total1363139

Merged error: 14.6b

Counts
139 → 3

regimes108.0ms

Accuracy

0% (0.2b remaining)

Error of 14.2b against oracle of 13.9b and baseline of 14.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01913
11913

end0.0ms

analyze1.0ms

Algorithm
search
sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 100%

sample1.0s

Algorithm
intervals
Results
619.0ms2880×body1280valid
160.0ms4093×body80valid
99.0ms567×body640valid
36.0ms308×body320valid
12.0ms152×body160valid

Profiling

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