Details

Time bar (total: 8.7s)

sample117.0ms

Algorithm
intervals
Results
38.0ms558×body80nan
13.0ms193×body80valid
8.0ms10×body1280valid
7.0ms19×body640valid
5.0ms22×body320valid
2.0ms13×body160valid

simplify133.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0269
1499
21189
32569
45339
512509
626379
742979
845739
945889
1045889

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 7.5b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- z 1.0) (log (- 1.0 y)))
0.0b
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
0.1b
(* (- x 1.0) (log y))
5.2b
(log (- 1.0 y))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
37×log-prod
35×add-sqr-sqrt
31×*-un-lft-identity
17×add-cube-cbrt
16×distribute-rgt-in distribute-lft-in
12×associate-*l/
11×pow1
10×associate-+r+ associate-*l*
9×add-exp-log
8×associate-*r* add-cbrt-cube
7×flip3-- flip-- distribute-lft-out-- difference-of-squares
6×associate-+l+ add-log-exp
4×frac-add
3×log-pow
2×log-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-+ rem-log-exp sum-log flip-+
Counts
4 → 109
Calls
4 calls:
8.0ms
(* (- z 1.0) (log (- 1.0 y)))
11.0ms
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
7.0ms
(* (- x 1.0) (log y))
3.0ms
(log (- 1.0 y))

series47.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (- z 1.0) (log (- 1.0 y)))
25.0ms
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
12.0ms
(* (- x 1.0) (log y))
3.0ms
(log (- 1.0 y))

simplify68.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06731005
12529936
25001886

prune253.0ms

Filtered
87 candidates to 121 candidates (-39.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1138121
Fresh000
Picked101
Done000
Total1148122

Merged error: 0.0b

Counts
122 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.0b
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0b
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.1b
(* (- x 1.0) (log y))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
94×add-sqr-sqrt
80×times-frac
78×associate-*r*
57×*-un-lft-identity
56×unpow-prod-down
50×add-cube-cbrt
31×add-exp-log
27×flip3-- flip--
24×log-prod associate-*l/ unpow2 sqr-pow
19×unswap-sqr
16×distribute-rgt-in distribute-lft-in frac-add
13×associate-*l* add-cbrt-cube
12×pow1 frac-times prod-exp associate--l+
10×associate-+r+
9×div-exp
7×associate-*r/
6×pow-to-exp associate-+l+ pow-exp add-log-exp
4×sub-neg cbrt-unprod distribute-lft-out--
3×pow-prod-down *-commutative difference-of-squares
2×log-pow
1×cbrt-undiv +-commutative flip3-+ sum-log flip-+ div-inv
Counts
4 → 223
Calls
4 calls:
11.0ms
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
19.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
12.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
7.0ms
(* (- x 1.0) (log y))

series71.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
5.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
18.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
10.0ms
(* (- x 1.0) (log y))

simplify60.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013592834
150012680

prune704.0ms

Filtered
162 candidates to 235 candidates (-45.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2341235
Fresh077
Picked011
Done000
Total2349243

Merged error: 0.0b

Counts
243 → 9

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (- x 1.0) (log y)) (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.1b
(* (- x 1.0) (log y))
0.1b
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.5b
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
98×associate-*l/
88×frac-times
84×flip3-- flip--
52×frac-add
31×flip3-+ flip-+
29×add-sqr-sqrt
27×*-un-lft-identity
26×associate-*r/
20×associate-*r*
16×pow1
13×add-exp-log add-cube-cbrt add-cbrt-cube
12×log-prod sqrt-prod
11×distribute-rgt-in distribute-lft-in associate-*l*
6×associate-+l+ add-log-exp difference-of-squares
5×pow-prod-down prod-exp cbrt-unprod distribute-lft-out--
4×sub-neg associate-+r+
3×log-pow *-commutative distribute-lft-out
2×unswap-sqr
1×+-commutative sum-log
Counts
4 → 190
Calls
4 calls:
13.0ms
(+ (* (- x 1.0) (log y)) (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
6.0ms
(* (- x 1.0) (log y))
13.0ms
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
31.0ms
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series169.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(+ (* (- x 1.0) (log y)) (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
10.0ms
(* (- x 1.0) (log y))
20.0ms
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
42.0ms
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify112.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
016998416
150018107

prune2.3s

Filtered
164 candidates to 202 candidates (-23.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2020202
Fresh077
Picked011
Done011
Total2029211

Merged error: 0.0b

Counts
211 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- x 1.0) (log y))
8.0b
(+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))
11.1b
(log (- (sqrt 1.0) (sqrt y)))
11.2b
(log (+ (sqrt 1.0) (sqrt y)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
34×log-prod *-un-lft-identity
32×add-sqr-sqrt
16×sqrt-prod
13×pow1
12×add-cube-cbrt
9×associate-+r+ difference-of-squares
8×add-exp-log log-div distribute-lft-out
7×log-pow
6×add-cbrt-cube
5×associate-+l+ associate-*l* distribute-lft-out--
4×associate-*r* add-log-exp
3×distribute-rgt-in flip3-- distribute-lft-in flip3-+ flip-- flip-+
2×associate-+l- associate-+r- rem-log-exp associate-*l/
1×+-commutative pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
4 → 98
Calls
4 calls:
7.0ms
(* (- x 1.0) (log y))
14.0ms
(+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))
6.0ms
(log (- (sqrt 1.0) (sqrt y)))
5.0ms
(log (+ (sqrt 1.0) (sqrt y)))

series46.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (- x 1.0) (log y))
19.0ms
(+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))
10.0ms
(log (- (sqrt 1.0) (sqrt y)))
7.0ms
(log (+ (sqrt 1.0) (sqrt y)))

simplify56.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05941098
122721027
25001996

prune224.0ms

Filtered
74 candidates to 110 candidates (-48.6%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1100110
Fresh066
Picked011
Done022
Total1109119

Merged error: 0.0b

Counts
119 → 9

regimes651.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02815
12815

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.3s19722×body80nan
412.0ms5850×body80valid
280.0ms758×body640valid
201.0ms283×body1280valid
161.0ms699×body320valid
66.0ms434×body160valid

Profiling

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