Details

Time bar (total: 5.3s)

sample76.0ms

Algorithm
intervals
Results
39.0ms81×body1280valid
10.0ms37×body640valid
9.0ms28×body2560valid
5.0ms30×body320valid
3.0ms67×body80valid
1.0ms13×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: 52.6b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.6b
(+ x (sqrt (+ (* x x) 1.0)))
3.2b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.5b
(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))

series17.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(+ x (sqrt (+ (* x x) 1.0)))
9.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

simplify132.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (127.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune114.0ms

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

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New46551
Fresh000
Picked101
Done000
Total47552

Merged error: 0.0b

Counts
52 → 5

localize11.0ms

Local error

Found 1 expressions with local error:

0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
181×add-sqr-sqrt
140×unpow-prod-down cube-prod
117×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×unswap-sqr
24×add-exp-log
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×cbrt-unprod
1×cbrt-undiv associate-*r/ pow-prod-down *-commutative div-inv add-log-exp
Counts
1 → 270
Calls
1 calls:
49.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series15.0ms

Counts
1 → 3
Calls
1 calls:
15.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify85.0ms

Algorithm
egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
07251757
138321368
250011368

prune319.0ms

Filtered
95 candidates to 273 candidates (-187.4%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2730273
Fresh044
Picked011
Done000
Total2735278

Merged error: 0.0b

Counts
278 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (neg 0.0625) (pow x 5))
0.5b
(/ 0.125 (pow x 3))
12.2b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
18.8b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite155.0ms

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:
8.0ms
(/ (neg 0.0625) (pow x 5))
5.0ms
(/ 0.125 (pow x 3))
65.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
67.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

series22.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ (neg 0.0625) (pow x 5))
3.0ms
(/ 0.125 (pow x 3))
9.0ms
(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))))

simplify95.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
08371963
137941884
250021876

prune444.0ms

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

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2341235
Fresh033
Picked101
Done011
Total2355240

Merged error: 0.0b

Counts
240 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

2.1b
(sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
12.2b
(log (* (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))) (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))))
18.8b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))
18.8b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite371.0ms

Algorithm
rewrite-expression-head
Rules
65×sqrt-div
60×frac-sub
56×*-un-lft-identity
45×add-sqr-sqrt
35×log-div
30×flip3-- times-frac flip--
25×frac-times
21×pow1 distribute-lft-out--
15×difference-of-squares
14×log-pow add-log-exp
12×sqrt-prod
9×sqrt-pow1 pow1/2
7×add-exp-log
6×diff-log associate--r+
5×add-cube-cbrt associate-*r/ associate-*l/ pow-prod-up
4×sub-neg add-cbrt-cube associate--r-
3×unpow-prod-down distribute-rgt-neg-in cube-prod pow-prod-down pow-sqr sqr-pow
2×neg-sub0 div-sub rem-log-exp
1×pow2 rem-sqrt-square log-prod pow-plus prod-exp
Counts
4 → 144
Calls
4 calls:
68.0ms
(sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
152.0ms
(log (* (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))) (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))))
71.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))
71.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

series31.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
14.0ms
(log (* (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))) (sqrt (- (/ 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))))
5.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

simplify79.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06923941
121093621
250013597

prune762.0ms

Filtered
109 candidates to 156 candidates (-43.1%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1560156
Fresh033
Picked011
Done011
Total1565161

Merged error: 0.0b

Counts
161 → 5

regimes95.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.5b

bsearch31.0ms

Steps
ItersRangePoint
10
0.0364262917160445
547825979.610153
0.8888458567017814
8
-442.47528987694835
-0.030191044061917315
-1.0249618612351965

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04338
14338

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.1s2366×body1280valid
451.0ms1578×body640valid
282.0ms826×body2560valid
132.0ms757×body320valid
88.0ms2082×body80valid
39.0ms391×body160valid

Profiling

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