Details

Time bar (total: 10.0s)

sample1.5s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 68.75%

Guaranteed chance to sample good point: 41.210938%

Results
13.0ms184×body80valid
9.0ms12×body1280valid
8.0ms20×body640valid
6.0ms25×body320valid
6.0ms78×body80nan
2.0ms15×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: 7.2b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
0.0b
(* (- z 1.0) (log (- 1.0 y)))
0.1b
(* (- x 1.0) (log y))
6.0b
(log (- 1.0 y))

rewrite36.0ms

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:
14.0ms
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
8.0ms
(* (- z 1.0) (log (- 1.0 y)))
6.0ms
(* (- x 1.0) (log y))
3.0ms
(log (- 1.0 y))

series43.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
6.0ms
(* (- z 1.0) (log (- 1.0 y)))
9.0ms
(* (- x 1.0) (log y))
3.0ms
(log (- 1.0 y))

simplify67.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06731005
12529936
25001886

prune214.0ms

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

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1156121
Fresh000
Picked101
Done000
Total1166122

Merged error: 0.1b

Counts
122 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 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
(+ (* (- x 1.0) (log y)) (* (- 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))

rewrite59.0ms

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:
12.0ms
(* (- 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)))
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)))))))
7.0ms
(* (- x 1.0) (log y))

series67.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(* (- 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)))
36.0ms
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
14.0ms
(* (- x 1.0) (log y))

simplify57.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013592834
150012680

prune767.0ms

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

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2305235
Fresh235
Picked101
Done000
Total2338241

Merged error: 0.1b

Counts
241 → 8

localize25.0ms

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

rewrite68.0ms

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:
16.0ms
(+ (* (- 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))))))))
13.0ms
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
6.0ms
(* (- x 1.0) (log y))
21.0ms
(* (* (- 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)))))))

series157.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(+ (* (- 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))))))))
18.0ms
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
9.0ms
(* (- x 1.0) (log y))
37.0ms
(* (* (- 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)))))))

simplify107.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
016998416
150018107

prune2.3s

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

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2020202
Fresh077
Picked011
Done000
Total2028210

Merged error: 0.1b

Counts
210 → 8

localize226.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt y) (cbrt y))
0.6b
(cbrt y)
0.6b
(cbrt y)
0.6b
(cbrt y)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
5.0ms
(* (cbrt y) (cbrt y))
1.0ms
(cbrt y)
1.0ms
(cbrt y)
1.0ms
(cbrt y)

series92.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (cbrt y) (cbrt y))
26.0ms
(cbrt y)
21.0ms
(cbrt y)
22.0ms
(cbrt y)

simplify72.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0148349
1471322
22276265
35002252

prune154.0ms

Filtered
56 candidates to 85 candidates (-51.8%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New84185
Fresh066
Picked011
Done011
Total84993

Merged error: 0.1b

Counts
93 → 9

regimes573.0ms

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
03428
13428

end0.0ms

sample3.2s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 68.75%

Guaranteed chance to sample good point: 41.210938%

Results
421.0ms5839×body80valid
266.0ms731×body640valid
188.0ms271×body1280valid
159.0ms676×body320valid
144.0ms1941×body80nan
69.0ms483×body160valid
2.0ms33×body80invalid

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