Details

Time bar (total: 5.9s)

sample66.0ms

Algorithm
intervals
Results
21.0ms48×body1280valid
12.0ms44×body640valid
7.0ms41×body320valid
7.0ms148×body80valid
4.0ms101×body80nan
2.0ms16×body160valid

simplify111.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (9.0ms)

IterNodesCost
0156
1246
2516
31086
43104
57924
641924
750024

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (exp (* x (log (/ x (+ x y))))) x)
0.0b
(/ x (+ x y))
0.1b
(* x (log (/ x (+ x y))))
7.1b
(log (/ x (+ x y)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
261×times-frac
221×*-un-lft-identity
198×log-prod
149×add-sqr-sqrt
147×add-cube-cbrt
144×exp-sum
90×distribute-rgt-in distribute-lft-in
42×associate-/l*
37×distribute-lft-out
24×associate-/r/
13×div-inv
12×add-exp-log flip3-+ flip-+
10×add-cbrt-cube
8×pow1
7×associate-/r*
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×div-exp associate-*l*
2×cbrt-undiv frac-2neg rem-log-exp clear-num log-pow
1×log-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 296
Calls
4 calls:
52.0ms
(/ (exp (* x (log (/ x (+ x y))))) x)
10.0ms
(/ x (+ x y))
22.0ms
(* x (log (/ x (+ x y))))
6.0ms
(log (/ x (+ x y)))

series264.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (exp (* x (log (/ x (+ x y))))) x)
34.0ms
(/ x (+ x y))
69.0ms
(* x (log (/ x (+ x y))))
49.0ms
(log (/ x (+ x y)))

simplify90.0ms

Algorithm
egg-herbie
Counts
308 → 308
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
08383073
128872638
250022622

prune952.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b
(/ (exp (* -1 y)) x)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
3×associate-/r* add-cbrt-cube associate-/l*
2×add-exp-log
1×pow1 cbrt-undiv exp-neg expm1-log1p-u frac-2neg mul-1-neg div-exp clear-num log1p-expm1-u div-inv associate-/l/ add-log-exp
Counts
1 → 30
Calls
1 calls:
9.0ms
(/ (exp (* -1 y)) x)

series20.0ms

Counts
1 → 3
Calls
1 calls:
20.0ms
(/ (exp (* -1 y)) x)

simplify47.0ms

Algorithm
egg-herbie
Counts
33 → 33
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
0118194
1313179
21512177
35001177

prune93.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (sqrt (exp (* -1 y))) x)
0.0b
(* (sqrt (exp (* -1 y))) (/ (sqrt (exp (* -1 y))) x))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
40×times-frac
32×add-cube-cbrt *-un-lft-identity
29×sqrt-prod
22×associate-*r*
9×add-exp-log add-cbrt-cube
6×associate-*l* associate-/l* unswap-sqr
4×pow1
3×exp-neg mul-1-neg sqrt-div associate-/r*
2×cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
2 → 94
Calls
2 calls:
9.0ms
(/ (sqrt (exp (* -1 y))) x)
33.0ms
(* (sqrt (exp (* -1 y))) (/ (sqrt (exp (* -1 y))) x))

series47.0ms

Counts
2 → 6
Calls
2 calls:
30.0ms
(/ (sqrt (exp (* -1 y))) x)
17.0ms
(* (sqrt (exp (* -1 y))) (/ (sqrt (exp (* -1 y))) x))

simplify42.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0274908
11191784
25001740

prune337.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (sqrt (exp (* -1 y))))
0.0b
(* (sqrt (exp (* -1 y))) (/ (sqrt 1) (/ x (sqrt (exp (* -1 y))))))
0.0b
(/ (sqrt 1) (/ x (sqrt (exp (* -1 y)))))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
558×times-frac
348×add-sqr-sqrt
301×sqrt-prod
290×*-un-lft-identity
284×add-cube-cbrt
143×associate-*r*
29×associate-/r*
20×unswap-sqr
19×add-exp-log add-cbrt-cube
16×exp-neg mul-1-neg sqrt-div associate-/r/ div-inv
9×associate-/l*
7×cbrt-undiv div-exp
6×associate-*l*
5×pow1
3×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
3 → 415
Calls
3 calls:
10.0ms
(/ x (sqrt (exp (* -1 y))))
79.0ms
(* (sqrt (exp (* -1 y))) (/ (sqrt 1) (/ x (sqrt (exp (* -1 y))))))
17.0ms
(/ (sqrt 1) (/ x (sqrt (exp (* -1 y)))))

series90.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(/ x (sqrt (exp (* -1 y))))
25.0ms
(* (sqrt (exp (* -1 y))) (/ (sqrt 1) (/ x (sqrt (exp (* -1 y))))))
28.0ms
(/ (sqrt 1) (/ x (sqrt (exp (* -1 y)))))

simplify72.0ms

Algorithm
egg-herbie
Counts
424 → 424
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
09895430
150024541

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes54.0ms

Accuracy

97.5% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 11.9b

bsearch122.0ms

Steps
ItersRangePoint
10
4.04762297915196e-13
0.007285382865895221
0.007220371088777497
10
-1.2585567989575416e+20
-3013496178.120658
-11605909410.296701

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02620
12620

end0.0ms

sample2.0s

Algorithm
intervals
Results
717.0ms1541×body1280valid
411.0ms1448×body640valid
242.0ms4874×body80valid
160.0ms875×body320valid
114.0ms3072×body80nan
50.0ms422×body160valid