Details

Time bar (total: 4.4s)

sample57.0ms

Algorithm
intervals
Results
28.0ms70×body10240exit
12.0ms265×body80valid
3.0ms11×body640valid
2.0ms4×body1280valid
1.0ms8×body320valid
0.0ms3×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1195
2235
3235

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt log-prod
6×pow1 add-log-exp
4×add-exp-log log-div fma-neg prod-diff associate--l+
3×expm1-log1p-u fma-def flip3-+ log-pow add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
2×associate--l-
1×+-commutative sub-neg flip3-- diff-log rem-log-exp sum-log flip--
Counts
3 → 62
Calls
3 calls:
6.0ms
(- (log (+ 1.0 (exp x))) (* x y))
3.0ms
(+ 1.0 (exp x))
3.0ms
(log (+ 1.0 (exp x)))

series130.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(- (log (+ 1.0 (exp x))) (* x y))
7.0ms
(+ 1.0 (exp x))
65.0ms
(log (+ 1.0 (exp x)))

simplify59.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0236404
1702369
22284367
35002340

prune168.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (log (+ 1.0 (exp x))))
0.0b
(+ 1.0 (exp x))
0.0b
(expm1 (log1p (log (+ 1.0 (exp x)))))
1.0b
(log (+ 1.0 (exp x)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
6×add-sqr-sqrt add-cube-cbrt add-log-exp
5×pow1 add-exp-log expm1-log1p-u
4×log-prod add-cbrt-cube log1p-expm1-u
3×fma-def
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative log1p-udef expm1-log1p log1p-expm1 rem-log-exp sum-log log-pow expm1-udef
Counts
4 → 56
Calls
4 calls:
0.0ms
(log1p (log (+ 1.0 (exp x))))
3.0ms
(+ 1.0 (exp x))
0.0ms
(expm1 (log1p (log (+ 1.0 (exp x)))))
3.0ms
(log (+ 1.0 (exp x)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(log1p (log (+ 1.0 (exp x))))
8.0ms
(+ 1.0 (exp x))
239.0ms
(expm1 (log1p (log (+ 1.0 (exp x)))))
64.0ms
(log (+ 1.0 (exp x)))

simplify88.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (77.0ms)

IterNodesCost
0251370
1777332
22932322
35001321

prune181.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- (+ (log (+ (exp x) 1.0)) 1) 1) (* x y))
0.0b
(+ (exp x) 1.0)
0.9b
(- (+ (log (+ (exp x) 1.0)) 1) 1)
1.0b
(log (+ (exp x) 1.0))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
74×*-un-lft-identity
39×prod-diff
37×add-sqr-sqrt
25×add-cube-cbrt
22×distribute-lft-out
20×associate--l+
18×add-log-exp
15×pow1
14×fma-neg
11×log-pow
9×distribute-lft-out--
7×diff-log
6×add-exp-log difference-of-squares
4×expm1-log1p-u log-div log-prod add-cbrt-cube log1p-expm1-u
3×associate--l- sub-neg fma-def flip3-+ difference-of-sqr-1 sum-log flip-+
2×associate-+l- flip3-- flip--
1×+-commutative expm1-def rem-log-exp
Counts
4 → 132
Calls
4 calls:
133.0ms
(- (- (+ (log (+ (exp x) 1.0)) 1) 1) (* x y))
4.0ms
(+ (exp x) 1.0)
32.0ms
(- (+ (log (+ (exp x) 1.0)) 1) 1)
4.0ms
(log (+ (exp x) 1.0))

series201.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(- (- (+ (log (+ (exp x) 1.0)) 1) 1) (* x y))
8.0ms
(+ (exp x) 1.0)
66.0ms
(- (+ (log (+ (exp x) 1.0)) 1) 1)
61.0ms
(log (+ (exp x) 1.0))

simplify47.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03881069
11502735
25001613

prune272.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (log 2.0) (- (fma 0.25 (pow x 2) (* 0.5 x)) (* 1/2 (/ (pow x 2) (pow 2.0 2)))))
0.0b
(fma 0.25 (pow x 2) (* 0.5 x))
0.0b
(- (+ (log 2.0) (- (fma 0.25 (pow x 2) (* 0.5 x)) (* 1/2 (/ (pow x 2) (pow 2.0 2))))) (* x y))
7.0b
(- (fma 0.25 (pow x 2) (* 0.5 x)) (* 1/2 (/ (pow x 2) (pow 2.0 2))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
16×add-log-exp
11×add-sqr-sqrt add-cube-cbrt prod-diff
8×pow1 fma-neg
6×associate-+r+ diff-log distribute-lft-out
4×add-exp-log expm1-log1p-u fma-def sum-log log-pow add-cbrt-cube log1p-expm1-u
3×sub-neg associate-+l+ log-prod associate--l+ fma-udef
2×associate-+r- flip3-- flip--
1×+-commutative associate--l- flip3-+ flip-+
Counts
4 → 89
Calls
4 calls:
7.0ms
(+ (log 2.0) (- (fma 0.25 (pow x 2) (* 0.5 x)) (* 1/2 (/ (pow x 2) (pow 2.0 2)))))
0.0ms
(fma 0.25 (pow x 2) (* 0.5 x))
61.0ms
(- (+ (log 2.0) (- (fma 0.25 (pow x 2) (* 0.5 x)) (* 1/2 (/ (pow x 2) (pow 2.0 2))))) (* x y))
3.0ms
(- (fma 0.25 (pow x 2) (* 0.5 x)) (* 1/2 (/ (pow x 2) (pow 2.0 2))))

series331.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(+ (log 2.0) (- (fma 0.25 (pow x 2) (* 0.5 x)) (* 1/2 (/ (pow x 2) (pow 2.0 2)))))
58.0ms
(fma 0.25 (pow x 2) (* 0.5 x))
71.0ms
(- (+ (log 2.0) (- (fma 0.25 (pow x 2) (* 0.5 x)) (* 1/2 (/ (pow x 2) (pow 2.0 2))))) (* x y))
145.0ms
(- (fma 0.25 (pow x 2) (* 0.5 x)) (* 1/2 (/ (pow x 2) (pow 2.0 2))))

simplify46.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03241091
112741007
25001989

prune311.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes33.0ms

Accuracy

84.9% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 1.0b

bsearch38.0ms

Steps
ItersRangePoint
8
-0.008763241487176904
-2.653200281950173e-06
-0.00041498737468865604

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03719
13719

end0.0ms

sample1.6s

Algorithm
intervals
Results
938.0ms2344×body10240exit
309.0ms8425×body80valid
57.0ms220×body640valid
56.0ms113×body1280valid
31.0ms203×body320valid
8.0ms87×body160valid