Details

Time bar (total: 5.0s)

sample65.0ms

Algorithm
intervals
Results
36.0ms75×body1280valid
13.0ms53×body640valid
4.0ms33×body320valid
2.0ms80×body80valid
2.0ms99×body80nan
1.0ms15×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
052
152

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 41.6b

Counts
2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

5.0b
(log (+ 1.0 x))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
4×log-prod *-un-lft-identity
2×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt log-div
1×flip3-+ rem-log-exp log-pow add-cbrt-cube flip-+ distribute-lft-out add-log-exp
Counts
1 → 15
Calls
1 calls:
3.0ms
(log (+ 1.0 x))

series43.0ms

Counts
1 → 3
Calls
1 calls:
43.0ms
(log (+ 1.0 x))

simplify44.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (37.0ms)

IterNodesCost
012295
132786
2116181
3500278

prune40.0ms

Filtered
18 candidates to 13 candidates (72.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New13518
Fresh000
Picked101
Done000
Total14519

Merged error: 0.2b

Counts
19 → 5

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
70×add-sqr-sqrt
68×associate-*r*
56×unpow-prod-down
36×add-cube-cbrt *-un-lft-identity
25×add-exp-log
24×unpow2 sqr-pow
17×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 → 126
Calls
2 calls:
23.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
6.0ms
(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

series100.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
43.0ms
(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

simplify74.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0676882
12962760
25001756

prune257.0ms

Filtered
132 candidates to 81 candidates (61.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1302132
Fresh044
Picked011
Done000
Total1307137

Merged error: 0.2b

Counts
137 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (pow x 2))
0.1b
(* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))
9.8b
(- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))
23.1b
(/ (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))) (* (- (* 1.0 x) (log 1.0)) (pow 1.0 2)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
20×associate-*l/
16×add-sqr-sqrt add-cbrt-cube
13×prod-exp
12×flip3-- flip--
10×add-cube-cbrt *-un-lft-identity
9×associate-*r*
8×frac-sub
6×pow1 associate-*l* associate-/l/ add-log-exp
5×cbrt-unprod
4×unpow-prod-down div-exp unswap-sqr
3×pow-to-exp times-frac pow-exp associate-/l*
2×cbrt-undiv associate-/r/ *-commutative unpow2 sqr-pow
1×sub-neg frac-2neg diff-log div-sub pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 96
Calls
4 calls:
6.0ms
(* 1/2 (pow x 2))
9.0ms
(* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))
11.0ms
(- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))
20.0ms
(/ (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))) (* (- (* 1.0 x) (log 1.0)) (pow 1.0 2)))

series568.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* 1/2 (pow x 2))
258.0ms
(* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))
121.0ms
(- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))
163.0ms
(/ (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))) (* (- (* 1.0 x) (log 1.0)) (pow 1.0 2)))

simplify114.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
06511875
135211601
250021575

prune322.0ms

Filtered
108 candidates to 73 candidates (67.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1053108
Fresh145
Picked101
Done011
Total1078115

Merged error: 0.2b

Counts
115 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

2.0b
(exp (log (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))))
9.8b
(- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))
20.3b
(/ (exp (log (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))))) (* (- (* 1.0 x) (log 1.0)) (pow 1.0 2)))
20.9b
(log (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
34×associate-*l/
21×flip3-- flip--
18×log-div
16×frac-sub
12×log-prod exp-diff
11×add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×exp-sum add-cbrt-cube
6×pow1 times-frac associate-/l/ associate-/l* add-log-exp
4×exp-prod div-exp
3×prod-exp
2×cbrt-undiv associate-/r/ log-pow
1×pow-to-exp sub-neg frac-2neg diff-log rem-log-exp pow-exp clear-num associate-/r* cbrt-unprod div-inv rem-exp-log
Counts
4 → 92
Calls
4 calls:
14.0ms
(exp (log (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))))
12.0ms
(- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))
22.0ms
(/ (exp (log (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))))) (* (- (* 1.0 x) (log 1.0)) (pow 1.0 2)))
12.0ms
(log (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))))

series646.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(exp (log (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))))
122.0ms
(- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))
166.0ms
(/ (exp (log (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))))) (* (- (* 1.0 x) (log 1.0)) (pow 1.0 2)))
228.0ms
(log (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))))

simplify105.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
06993355
133232971
250012904

prune400.0ms

Filtered
104 candidates to 79 candidates (76.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1022104
Fresh156
Picked101
Done011
Total1048112

Merged error: 0.2b

Counts
112 → 8

regimes198.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.5b

bsearch3.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02316
12316

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.0s2195×body1280valid
395.0ms1696×body640valid
105.0ms867×body320valid
79.0ms2812×body80valid
49.0ms2660×body80nan
31.0ms430×body160valid