Details

Time bar (total: 2.4s)

analyze884.0ms

Algorithm
search
sampling

Space saved by range analysis: 0.097632%

Space saved by search: 24.292737%

Guaranteed chance to sample good point: 64.497423%

sample57.0ms

Algorithm
intervals
Results
32.0ms136×body5120exit
7.0ms196×body80valid
3.0ms19×body640valid
3.0ms26×body320valid
1.0ms15×body160valid
0.0ms1×body80invalid

simplify46.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (5.0ms)

IterNodesCost
0209
1489
21079
32248
415148
550028

prune9.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.1b

Counts
2 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ wj (+ wj 1))
0.0b
(/ x (+ wj 1))
0.0b
(/ (/ x (+ wj 1)) (exp wj))
3.6b
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
127×times-frac
118×*-un-lft-identity
78×add-sqr-sqrt
73×add-cube-cbrt
24×associate-/l*
21×distribute-lft-out
13×add-cbrt-cube
12×associate-/r/
11×add-exp-log associate-/r*
9×add-log-exp
7×flip3-+ flip-+ div-inv
5×cbrt-undiv div-exp
4×pow1
3×frac-2neg clear-num
2×diff-log frac-sub distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- associate--l+ sum-log flip-- associate-/l/
Counts
4 → 176
Calls
4 calls:
5.0ms
(/ wj (+ wj 1))
7.0ms
(/ x (+ wj 1))
9.0ms
(/ (/ x (+ wj 1)) (exp wj))
28.0ms
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series32.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(/ wj (+ wj 1))
5.0ms
(/ x (+ wj 1))
11.0ms
(/ (/ x (+ wj 1)) (exp wj))
14.0ms
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify78.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
07211524
133031471
250021469

prune247.0ms

Filtered
138 candidates to 188 candidates (-36.2%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1844188
Fresh101
Picked101
Done000
Total1864190

Merged error: 0.1b

Counts
190 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (pow wj 2))
0.0b
(* 2 (* wj x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
5×*-un-lft-identity
4×add-log-exp
3×add-sqr-sqrt add-cube-cbrt associate-*l* pow-prod-down prod-exp cbrt-unprod
1×+-commutative flip3-+ associate-*r* sum-log *-commutative flip-+ distribute-lft-out
Counts
2 → 30
Calls
2 calls:
4.0ms
(+ x (pow wj 2))
6.0ms
(* 2 (* wj x))

series9.0ms

Counts
2 → 6
Calls
2 calls:
6.0ms
(+ x (pow wj 2))
3.0ms
(* 2 (* wj x))

simplify66.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0149122
1550108
22362107
35001107

prune58.0ms

Filtered
21 candidates to 36 candidates (-71.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New33336
Fresh033
Picked011
Done000
Total33740

Merged error: 0.1b

Counts
40 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (+ wj 1))
0.0b
(/ (/ x (+ wj 1)) (exp wj))
0.0b
(* (/ wj (- (* wj wj) 1)) (- wj 1))
3.6b
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (* (/ wj (- (* wj wj) 1)) (- wj 1)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
133×times-frac
113×*-un-lft-identity
87×add-sqr-sqrt
75×add-cube-cbrt
24×associate-*l*
21×associate-/l*
16×add-cbrt-cube distribute-lft-out
14×add-exp-log
12×associate-/r/
10×flip3-+ frac-sub flip-+
9×add-log-exp
8×flip3-- flip-- difference-of-squares
7×associate-*r* associate-/r* div-inv
6×pow1 frac-times associate-*r/
5×cbrt-undiv sub-neg div-exp
4×distribute-rgt-in distribute-lft-in difference-of-sqr-1 associate--r+
3×associate-*l/
2×frac-2neg diff-log prod-exp clear-num cbrt-unprod unswap-sqr
1×pow-prod-down associate--l+ sum-log *-commutative associate-/l/ distribute-lft-out--
Counts
4 → 206
Calls
4 calls:
5.0ms
(/ x (+ wj 1))
11.0ms
(/ (/ x (+ wj 1)) (exp wj))
14.0ms
(* (/ wj (- (* wj wj) 1)) (- wj 1))
24.0ms
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (* (/ wj (- (* wj wj) 1)) (- wj 1)))

series43.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ x (+ wj 1))
11.0ms
(/ (/ x (+ wj 1)) (exp wj))
4.0ms
(* (/ wj (- (* wj wj) 1)) (- wj 1))
24.0ms
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (* (/ wj (- (* wj wj) 1)) (- wj 1)))

simplify52.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010412170
150012090

prune322.0ms

Filtered
161 candidates to 218 candidates (-35.4%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2162218
Fresh055
Picked011
Done011
Total2169225

Merged error: 0.1b

Counts
225 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (pow wj 2))
0.0b
(+ x (pow wj 2))
0.0b
(* 2 (* wj x))
0.2b
(* (sqrt (+ x (pow wj 2))) (sqrt (+ x (pow wj 2))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
26×sqrt-prod
25×add-sqr-sqrt
24×pow1
13×add-cube-cbrt
12×sqrt-div
11×add-exp-log swap-sqr add-cbrt-cube
10×associate-*l*
8×sqrt-pow1 flip3-+ pow1/2 associate-*r* flip-+ distribute-lft-out add-log-exp
6×pow-prod-down
5×pow-prod-up
4×frac-times prod-exp cbrt-unprod unswap-sqr
3×pow-sqr
2×+-commutative associate-*r/ associate-*l/ sum-log *-commutative
1×pow2 pow-plus sqrt-unprod rem-square-sqrt
Counts
4 → 104
Calls
4 calls:
4.0ms
(+ x (pow wj 2))
4.0ms
(+ x (pow wj 2))
5.0ms
(* 2 (* wj x))
13.0ms
(* (sqrt (+ x (pow wj 2))) (sqrt (+ x (pow wj 2))))

series21.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(+ x (pow wj 2))
6.0ms
(+ x (pow wj 2))
3.0ms
(* 2 (* wj x))
6.0ms
(* (sqrt (+ x (pow wj 2))) (sqrt (+ x (pow wj 2))))

simplify45.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0243531
11082477
25002463

prune131.0ms

Filtered
54 candidates to 116 candidates (-114.8%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1151116
Fresh156
Picked011
Done022
Total1169125

Merged error: 0.1b

Counts
125 → 9

regimes146.0ms

bsearch1.0ms

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