Details

Time bar (total: 4.4s)

analyze313.0ms

Algorithm
search

sample53.0ms

Algorithm
intervals
Results
14.0ms176×body80valid
11.0ms33×body640valid
9.0ms13×body1280valid
4.0ms20×body320valid
2.0ms14×body160valid
1.0msbody80nan
0.0msbody80invalid

simplify23.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1307
2397
3457
4607
5887
61257
71767
82087
92257
102937
112937

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 9.0b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* z (log (- 1.0 y)))
0.0b
(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
0.2b
(* x (log y))
4.8b
(log (- 1.0 y))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
21×log-prod *-un-lft-identity
13×add-cube-cbrt
11×pow1
add-exp-log add-log-exp
distribute-rgt-in distribute-lft-in associate-*r* add-cbrt-cube
associate-*l*
distribute-lft-out-- difference-of-squares
log-pow
log-div flip3-- diff-log pow-prod-down prod-exp *-commutative flip-- cbrt-unprod unswap-sqr
sub-neg rem-log-exp associate--l+ sum-log
Counts
4 → 86
Calls
4 calls:
6.0ms
(* z (log (- 1.0 y)))
6.0ms
(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
5.0ms
(* x (log y))
3.0ms
(log (- 1.0 y))

series40.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* z (log (- 1.0 y)))
20.0ms
(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
7.0ms
(* x (log y))
3.0ms
(log (- 1.0 y))

simplify47.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0458643
11650563
25002529

prune172.0ms

Filtered
66 candidates to 98 candidates (-48.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New90898
Fresh000
Picked101
Done000
Total91899

Merged error: 0.1b

Counts
99 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
0.0b
(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.0b
(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.2b
(* x (log y))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt log-prod
21×*-un-lft-identity
16×distribute-rgt-in add-cube-cbrt distribute-lft-in
13×associate--l+
11×add-log-exp
10×pow1 associate-+r+ associate-*r*
add-exp-log add-cbrt-cube
associate-+l+ associate-*l*
sub-neg
distribute-lft-out--
flip3-- diff-log associate-*r/ pow-prod-down prod-exp sum-log log-pow *-commutative flip-- cbrt-unprod difference-of-squares unswap-sqr
+-commutative flip3-+ flip-+
Counts
4 → 101
Calls
4 calls:
6.0ms
(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
6.0ms
(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
9.0ms
(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
4.0ms
(* x (log y))

series90.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
27.0ms
(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
18.0ms
(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
7.0ms
(* x (log y))

simplify55.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04441211
116861142
250021110

prune262.0ms

Filtered
75 candidates to 113 candidates (-50.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1103113
Fresh167
Picked101
Done000
Total1129121

Merged error: 0.0b

Counts
121 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.5 (* z (pow y 2)))
0.0b
(+ (* 1.0 (* z y)) (* 0.5 (* z (pow y 2))))
0.2b
(* x (log y))
7.6b
(* z (pow y 2))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
21×add-exp-log
20×add-sqr-sqrt
13×associate-*r* add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity
11×prod-exp
pow1 associate-*l*
log-prod add-log-exp
cbrt-unprod unswap-sqr
unpow-prod-down
distribute-rgt-in distribute-lft-in *-commutative
pow-to-exp pow-prod-down pow-exp unpow2 sqr-pow
+-commutative flip3-+ sum-log log-pow flip-+
Counts
4 → 82
Calls
4 calls:
5.0ms
(* 0.5 (* z (pow y 2)))
5.0ms
(+ (* 1.0 (* z y)) (* 0.5 (* z (pow y 2))))
4.0ms
(* x (log y))
5.0ms
(* z (pow y 2))

series36.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(* 0.5 (* z (pow y 2)))
15.0ms
(+ (* 1.0 (* z y)) (* 0.5 (* z (pow y 2))))
7.0ms
(* x (log y))
7.0ms
(* z (pow y 2))

simplify47.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0338451
11407391
25002379

prune159.0ms

Filtered
56 candidates to 94 candidates (-67.9%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New94094
Fresh088
Picked011
Done000
Total949103

Merged error: 0.0b

Counts
103 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.6b
(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.6b
(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.6b
(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
58×cbrt-prod
52×*-un-lft-identity
37×add-sqr-sqrt
22×pow1 distribute-lft-out--
18×cbrt-div
15×add-cube-cbrt swap-sqr
11×log-pow
flip3-- pow1/3 associate-*r* associate-*l* flip--
difference-of-squares
add-exp-log
frac-times add-cbrt-cube add-log-exp unswap-sqr
associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 111
Calls
4 calls:
14.0ms
(* (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
5.0ms
(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
5.0ms
(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
5.0ms
(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

series51.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
12.0ms
(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
14.0ms
(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
12.0ms
(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

simplify87.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05082897
118772762
250022441

prune721.0ms

Filtered
81 candidates to 123 candidates (-51.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1230123
Fresh077
Picked011
Done011
Total1239132

Merged error: 0.0b

Counts
132 → 9

regimes376.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02813
12813

end0.0ms

analyze326.0ms

Algorithm
search

sample1.3s

Algorithm
intervals
Results
354.0ms5580×body80valid
284.0ms854×body640valid
251.0ms398×body1280valid
148.0ms697×body320valid
68.0ms471×body160valid
15.0ms234×body80nan
2.0ms39×body80invalid

Profiling

Loading profile data...