Details

Time bar (total: 3.1s)

analyze828.0ms

Algorithm
search
sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 75.012207%

sample67.0ms

Algorithm
intervals
Results
33.0ms74×body1280valid
14.0ms51×body640valid
5.0ms15×body2560valid
3.0ms19×body320valid
3.0ms75×body80valid
2.0ms22×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095
195

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 51.1b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

1.2b
(+ x (sqrt (+ (* x x) 1.0)))
4.2b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.9b
(sqrt (+ (* x x) 1.0))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod
3×flip3-+ sqrt-prod add-cbrt-cube flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 42
Calls
3 calls:
5.0ms
(+ x (sqrt (+ (* x x) 1.0)))
5.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series19.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ x (sqrt (+ (* x x) 1.0)))
11.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

simplify139.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (133.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune116.0ms

Filtered
42 candidates to 51 candidates (-21.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New47451
Fresh000
Picked101
Done000
Total48452

Merged error: 0.0b

Counts
52 → 4

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.3b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
182×add-sqr-sqrt
140×unpow-prod-down cube-prod
118×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×add-exp-log unswap-sqr
10×prod-exp
9×div-exp
7×add-cbrt-cube
6×pow-to-exp pow-exp add-log-exp
4×pow1
3×associate-*r/ associate-*l*
2×diff-log frac-sub cbrt-unprod
1×cbrt-undiv sub-neg flip3-- flip3-+ pow-prod-down associate--l+ sum-log *-commutative flip-- flip-+ div-inv
Counts
2 → 286
Calls
2 calls:
12.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
49.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series32.0ms

Counts
2 → 6
Calls
2 calls:
16.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
15.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify115.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08542083
146421650
250021650

prune395.0ms

Filtered
111 candidates to 292 candidates (-163.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2911292
Fresh033
Picked011
Done000
Total2915296

Merged error: 0.0b

Counts
296 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
0.0b
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.3b
(/ 0.125 (pow x 3))
9.5b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
43×add-sqr-sqrt
40×times-frac
30×add-cube-cbrt
18×add-log-exp
13×unpow-prod-down cube-prod
12×associate-/r*
10×add-exp-log
9×distribute-lft-out
6×log-prod add-cbrt-cube distribute-lft-out--
5×pow1 sum-log difference-of-squares sqr-pow
4×cube-mult diff-log unpow3
3×associate-+r+ flip3-+ div-exp flip-+ associate-/l*
2×sub-neg log-div associate--l+ frac-sub
1×cbrt-undiv +-commutative pow-to-exp associate-+r- flip3-- frac-2neg rem-log-exp pow-exp clear-num log-pow flip-- div-inv
Counts
4 → 125
Calls
4 calls:
19.0ms
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
18.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
5.0ms
(/ 0.125 (pow x 3))
21.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series25.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
4.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
4.0ms
(/ 0.125 (pow x 3))
12.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify79.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
0505968
12347911
25002911

prune176.0ms

Filtered
80 candidates to 137 candidates (-71.3%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1370137
Fresh033
Picked011
Done011
Total1375142

Merged error: 0.0b

Counts
142 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (neg 0.0625) (pow x 5))
0.3b
(/ 0.125 (pow x 3))
11.4b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
17.9b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
110×*-un-lft-identity
102×add-sqr-sqrt
76×add-cube-cbrt
47×unpow-prod-down
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
19×associate-/r*
17×sqr-pow
15×add-exp-log
14×cube-prod distribute-lft-out--
13×associate-/l*
12×log-prod
10×difference-of-squares
9×add-log-exp
8×neg-mul-1 frac-sub add-cbrt-cube
6×div-exp
5×pow1 log-div
4×cube-mult flip3-- unpow3 flip--
3×diff-log associate--r+
2×cbrt-undiv neg-sub0 pow-to-exp sub-neg frac-2neg div-sub pow-exp clear-num div-inv associate--r-
1×distribute-frac-neg rem-log-exp log-pow
Counts
4 → 223
Calls
4 calls:
6.0ms
(/ (neg 0.0625) (pow x 5))
5.0ms
(/ 0.125 (pow x 3))
68.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
68.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

series24.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ (neg 0.0625) (pow x 5))
4.0ms
(/ 0.125 (pow x 3))
10.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
5.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

simplify105.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
08371963
137941884
250021876

prune441.0ms

Filtered
152 candidates to 235 candidates (-54.6%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New2350235
Fresh022
Picked011
Done022
Total2355240

Merged error: 0.0b

Counts
240 → 5

regimes139.0ms

bsearch0.0ms

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