Details

Time bar (total: 16.1s)

sample96.0ms

Algorithm
intervals
Results
45.0ms61×body10240exit
17.0ms264×body80valid
6.0ms13×body640valid
4.0ms4×body1280valid
2.0ms8×body320valid
1.0ms3×body160valid

simplify23.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
089
1129
2199
3239
done239

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (log (+ 1.0 (exp x))) (* x y))
0.5b
(log (+ 1.0 (exp x)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×log-prod
6×add-sqr-sqrt add-cube-cbrt
5×pow1
4×log-div fma-neg prod-diff associate--l+
3×add-exp-log log-pow add-log-exp
2×associate--l- expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
1×sub-neg flip3-- diff-log rem-log-exp flip--
Counts
2 → 45
Calls
2 calls:
19.0ms
(- (log (+ 1.0 (exp x))) (* x y))
7.0ms
(log (+ 1.0 (exp x)))

series191.0ms

Counts
2 → 6
Calls
2 calls:
85.0ms
(- (log (+ 1.0 (exp x))) (* x y))
106.0ms
(log (+ 1.0 (exp x)))

simplify3.5s

Counts
51 → 51
Iterations

Useful iterations: done (3.5s)

IterNodesCost
094602
1207571
2482528
31331511
42980484
done5000480

prune140.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize9.0ms

Local error

Found 1 expressions with local error:

0.5b
(log (+ 1.0 (exp x)))

rewrite7.0ms

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×expm1-log1p-u flip3-+ rem-log-exp log-pow add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out add-log-exp
Counts
1 → 17
Calls
1 calls:
6.0ms
(log (+ 1.0 (exp x)))

series91.0ms

Counts
1 → 3
Calls
1 calls:
90.0ms
(log (+ 1.0 (exp x)))

simplify3.5s

Counts
20 → 20
Iterations

Useful iterations: done (3.5s)

IterNodesCost
054192
1108182
2220168
3464166
4900164
51716163
63227162
done5001161

prune63.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (log (+ (pow 1.0 3) (pow (exp x) 3))) (log (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0)))))
0.7b
(log (+ (pow 1.0 3) (pow (exp x) 3)))
3.3b
(- (exp x) 1.0)
4.0b
(log (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0))))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
50×*-un-lft-identity
28×add-sqr-sqrt
25×prod-diff
24×add-cube-cbrt log-prod
19×pow1
15×log-pow
10×distribute-lft-out
9×associate--l+
8×unpow-prod-down cube-prod
7×fma-neg
6×add-exp-log add-log-exp
5×distribute-lft-out--
4×expm1-log1p-u log-div add-cbrt-cube log1p-expm1-u
3×associate--r+
2×associate--l- sub-neg flip3-- flip3-+ diff-log rem-log-exp sum-cubes flip-- flip-+ difference-of-squares
Counts
4 → 117
Calls
4 calls:
41.0ms
(- (log (+ (pow 1.0 3) (pow (exp x) 3))) (log (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0)))))
31.0ms
(log (+ (pow 1.0 3) (pow (exp x) 3)))
16.0ms
(- (exp x) 1.0)
2.0ms
(log (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0))))

series503.0ms

Counts
4 → 12
Calls
4 calls:
221.0ms
(- (log (+ (pow 1.0 3) (pow (exp x) 3))) (log (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0)))))
131.0ms
(log (+ (pow 1.0 3) (pow (exp x) 3)))
22.0ms
(- (exp x) 1.0)
129.0ms
(log (fma 1.0 1.0 (* (exp x) (- (exp x) 1.0))))

simplify2.7s

Counts
129 → 129
Iterations

Useful iterations: done (2.7s)

IterNodesCost
02123455
14552766
211162348
340902012
done50002008

prune463.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x (+ 0.5 (* x 0.75))) (fma 1/2 (/ (pow x 2) (pow 1.0 2)) (log 2.0)))
0.1b
(* x (+ 0.5 (* x 0.75)))
0.2b
(fma 9/2 (/ (pow x 2) (pow 2.0 2)) (log 1.0))
7.5b
(- (+ (* x (+ 0.5 (* x 0.75))) (fma 1/2 (/ (pow x 2) (pow 1.0 2)) (log 2.0))) (fma 9/2 (/ (pow x 2) (pow 2.0 2)) (log 1.0)))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×*-un-lft-identity
13×add-cube-cbrt
11×add-log-exp
9×prod-diff
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×fma-neg associate-*r* associate-*l* fma-udef
2×distribute-rgt-in associate-+l+ distribute-lft-in flip3-+ diff-log associate-*r/ sum-log flip-+
1×+-commutative sub-neg associate-+r+ flip3-- fma-def pow-prod-down prod-exp associate--l+ *-commutative flip-- cbrt-unprod associate--r+ distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 82
Calls
4 calls:
12.0ms
(+ (* x (+ 0.5 (* x 0.75))) (fma 1/2 (/ (pow x 2) (pow 1.0 2)) (log 2.0)))
25.0ms
(* x (+ 0.5 (* x 0.75)))
0.0ms
(fma 9/2 (/ (pow x 2) (pow 2.0 2)) (log 1.0))
100.0ms
(- (+ (* x (+ 0.5 (* x 0.75))) (fma 1/2 (/ (pow x 2) (pow 1.0 2)) (log 2.0))) (fma 9/2 (/ (pow x 2) (pow 2.0 2)) (log 1.0)))

series640.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(+ (* x (+ 0.5 (* x 0.75))) (fma 1/2 (/ (pow x 2) (pow 1.0 2)) (log 2.0)))
93.0ms
(* x (+ 0.5 (* x 0.75)))
355.0ms
(fma 9/2 (/ (pow x 2) (pow 2.0 2)) (log 1.0))
125.0ms
(- (+ (* x (+ 0.5 (* x 0.75))) (fma 1/2 (/ (pow x 2) (pow 1.0 2)) (log 2.0))) (fma 9/2 (/ (pow x 2) (pow 2.0 2)) (log 1.0)))

simplify1.1s

Counts
94 → 94
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01562937
13962406
213872055
done50021810

prune527.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes79.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01011
1129
done129

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.2s2379×body10240exit
409.0ms8420×body80valid
89.0ms256×body640valid
76.0ms119×body1280valid
39.0ms195×body320valid
17.0ms108×body160valid