Details

Time bar (total: 4.1s)

sample59.0ms

Algorithm
intervals
Results
35.0ms81×body1280valid
10.0ms51×body640valid
3.0ms28×body320valid
2.0ms88×body80valid
1.0ms96×body80nan
0.0ms8×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
052
152

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.5b

localize4.0ms

Local error

Found 1 expressions with local error:

2.9b
(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))

series46.0ms

Counts
1 → 3
Calls
1 calls:
46.0ms
(log (+ 1.0 x))

simplify37.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (34.0ms)

IterNodesCost
012295
132786
2116181
3500278

prune41.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

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))))

rewrite31.0ms

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:
19.0ms
(* 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))))

series93.0ms

Counts
2 → 6
Calls
2 calls:
48.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
44.0ms
(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

simplify70.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0676882
12962760
25001756

prune286.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cbrt (log (+ 1.0 x))) (cbrt (log (+ 1.0 x))))
2.9b
(log (+ 1.0 x))
2.9b
(log (+ 1.0 x))
2.9b
(log (+ 1.0 x))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
23×add-sqr-sqrt *-un-lft-identity
20×pow1
15×add-cube-cbrt
12×log-prod
9×add-exp-log swap-sqr log-pow
7×associate-*r* associate-*l*
6×log-div pow1/3
4×add-cbrt-cube add-log-exp unswap-sqr
3×flip3-+ rem-log-exp flip-+ distribute-lft-out
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 90
Calls
4 calls:
6.0ms
(* (cbrt (log (+ 1.0 x))) (cbrt (log (+ 1.0 x))))
3.0ms
(log (+ 1.0 x))
3.0ms
(log (+ 1.0 x))
3.0ms
(log (+ 1.0 x))

series337.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(* (cbrt (log (+ 1.0 x))) (cbrt (log (+ 1.0 x))))
49.0ms
(log (+ 1.0 x))
47.0ms
(log (+ 1.0 x))
42.0ms
(log (+ 1.0 x))

simplify53.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0438840
11662774
25002664

prune223.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
0.1b
(* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
8.8b
(- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
36.1b
(/ (- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (+ (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
534×add-exp-log
341×prod-exp
199×div-exp
132×pow-to-exp pow-exp
101×associate-*r/
48×frac-sub
43×pow1
42×add-cbrt-cube
41×frac-times
40×flip3-+ flip-+
29×associate-*l/
26×associate-/l/
21×cbrt-unprod
17×pow-prod-down
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×times-frac
10×add-log-exp
7×cbrt-undiv
5×difference-of-squares
4×frac-add associate-/r/ pow-sqr pow-prod-up associate-/l*
3×associate-/r* sum-log
2×flip3-- pow-plus associate--l+ flip--
1×+-commutative pow2 distribute-rgt-in sub-neg associate-+l+ frac-2neg distribute-lft-in diff-log div-sub swap-sqr associate-*r* associate-*l* clear-num *-commutative div-inv
Counts
4 → 275
Calls
4 calls:
6.0ms
(+ (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
21.0ms
(* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
12.0ms
(- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
24.0ms
(/ (- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (+ (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series351.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(+ (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
80.0ms
(* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
90.0ms
(- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
136.0ms
(/ (- (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0))) (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (+ (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify69.0ms

Algorithm
egg-herbie
Counts
287 → 287
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010644712
150014284

prune511.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes90.0ms

Accuracy

98.2% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 21.7b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02111
12111

end0.0ms

sample1.7s

Algorithm
intervals
Results
985.0ms2278×body1280valid
338.0ms1626×body640valid
86.0ms846×body320valid
61.0ms2845×body80valid
33.0ms2695×body80nan
24.0ms405×body160valid