Details

Time bar (total: 5.2s)

sample51.0ms

Algorithm
intervals
Results
27.0ms67×body10240exit
10.0ms271×body80valid
2.0ms7×body640valid
1.0ms5×body320valid
1.0ms1×body1280valid
0.0ms4×body160valid

simplify6.0ms

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: 0.5b

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)))

rewrite10.0ms

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:
6.0ms
(- (log (+ 1.0 (exp x))) (* x y))
3.0ms
(log (+ 1.0 (exp x)))

series118.0ms

Counts
2 → 6
Calls
2 calls:
56.0ms
(- (log (+ 1.0 (exp x))) (* x y))
62.0ms
(log (+ 1.0 (exp x)))

simplify58.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0206339
1587310
21945308
35001281

prune118.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
172×associate-+r+
171×prod-diff
152×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
144×times-frac
86×distribute-rgt-in distribute-lft-in
54×unpow-prod-down
18×unpow2 sqr-pow
10×add-log-exp
6×div-inv
3×pow1 add-exp-log expm1-log1p-u sub-neg fma-def fma-neg add-cbrt-cube log1p-expm1-u
2×diff-log sum-log fma-udef
1×+-commutative associate-+l+ flip3-- flip3-+ associate--l+ flip-- flip-+
Counts
3 → 221
Calls
3 calls:
15.0ms
(- (+ (fma x 0.5 (log 2.0)) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* x y))
0.0ms
(fma x 0.5 (log 2.0))
33.0ms
(+ (fma x 0.5 (log 2.0)) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))

series301.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(- (+ (fma x 0.5 (log 2.0)) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* x y))
167.0ms
(fma x 0.5 (log 2.0))
60.0ms
(+ (fma x 0.5 (log 2.0)) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))

simplify97.0ms

Algorithm
egg-herbie
Counts
230 → 230
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
012763322
145582635
250012634

prune848.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (log (+ (exp x) 1.0)) (* x y))
0.5b
(log (+ (exp x) 1.0))
0.7b
(pow (- (log (+ (exp x) 1.0)) (* x y)) 3)
14.7b
(cbrt (pow (- (log (+ (exp x) 1.0)) (* x y)) 3))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
14×add-sqr-sqrt add-cube-cbrt
12×cbrt-prod
8×pow1 log-prod
6×add-exp-log unpow-prod-down cube-prod
5×add-cbrt-cube add-log-exp
4×cube-div expm1-log1p-u log-div fma-neg prod-diff associate--l+ log1p-expm1-u
3×pow-unpow flip3-- log-pow flip--
2×associate--l- cube-mult cbrt-div flip3-+ unpow3 flip-+ distribute-lft-out sqr-pow
1×pow-to-exp sub-neg pow-pow pow1/3 diff-log rem-log-exp pow-exp rem-cbrt-cube rem-cube-cbrt
Counts
4 → 97
Calls
4 calls:
7.0ms
(- (log (+ (exp x) 1.0)) (* x y))
3.0ms
(log (+ (exp x) 1.0))
4.0ms
(pow (- (log (+ (exp x) 1.0)) (* x y)) 3)
4.0ms
(cbrt (pow (- (log (+ (exp x) 1.0)) (* x y)) 3))

series305.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(- (log (+ (exp x) 1.0)) (* x y))
57.0ms
(log (+ (exp x) 1.0))
130.0ms
(pow (- (log (+ (exp x) 1.0)) (* x y)) 3)
57.0ms
(cbrt (pow (- (log (+ (exp x) 1.0)) (* x y)) 3))

simplify50.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0396899
11469837
25002827

prune259.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (log 2.0) 2)
1.0b
(pow (log 2.0) 2)
1.0b
(pow (log 2.0) 3)
8.0b
(cbrt (fma (* 0.375 (pow (log 2.0) 2)) (pow x 2) (+ (fma 1.5 (* (pow (log 2.0) 2) x) (* 0.75 (* (log 2.0) (pow x 2)))) (pow (log 2.0) 3))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt unpow-prod-down *-un-lft-identity
11×pow1
9×pow-unpow
7×add-exp-log
5×add-cbrt-cube
4×expm1-log1p-u cube-prod log-pow log1p-expm1-u add-log-exp
3×cbrt-prod pow-to-exp pow-pow pow-exp sqr-pow
2×unpow2
1×cube-mult pow1/3 unpow3 rem-cube-cbrt
Counts
4 → 82
Calls
4 calls:
1.0ms
(pow (log 2.0) 2)
1.0ms
(pow (log 2.0) 2)
2.0ms
(pow (log 2.0) 3)
1.0ms
(cbrt (fma (* 0.375 (pow (log 2.0) 2)) (pow x 2) (+ (fma 1.5 (* (pow (log 2.0) 2) x) (* 0.75 (* (log 2.0) (pow x 2)))) (pow (log 2.0) 3))))

series615.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(pow (log 2.0) 2)
0.0ms
(pow (log 2.0) 2)
0.0ms
(pow (log 2.0) 3)
615.0ms
(cbrt (fma (* 0.375 (pow (log 2.0) 2)) (pow x 2) (+ (fma 1.5 (* (pow (log 2.0) 2) x) (* 0.75 (* (log 2.0) (pow x 2)))) (pow (log 2.0) 3))))

simplify58.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0351781
11721702
25002692

prune301.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes104.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0105
1105

end0.0ms

sample1.7s

Algorithm
intervals
Results
995.0ms2440×body10240exit
321.0ms8379×body80valid
72.0ms271×body640valid
50.0ms100×body1280valid
30.0ms190×body320valid
12.0ms123×body160valid