Details

Time bar (total: 4.5s)

sample77.0ms

Algorithm
intervals
Results
27.0ms55×body1280valid
15.0ms50×body640valid
8.0ms145×body80valid
5.0ms24×body320valid
3.0ms81×body80nan
3.0ms18×body160valid

simplify120.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (7.0ms)

IterNodesCost
0156
1246
2516
31066
43044
57744
641424
750014

prune8.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 12.6b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x y))
0.0b
(/ (pow (/ x (+ x y)) x) x)
6.3b
(pow (/ x (+ x y)) x)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
118×*-un-lft-identity
90×unpow-prod-down
80×add-sqr-sqrt add-cube-cbrt
25×associate-/l*
19×distribute-lft-out
16×add-exp-log
12×associate-/r/
7×div-exp associate-/r* add-cbrt-cube div-inv
6×flip3-+ flip-+
5×sqr-pow
4×pow1 pow-exp
3×pow-unpow add-log-exp
2×cbrt-undiv pow-to-exp frac-2neg clear-num
1×pow-pow
Counts
3 → 172
Calls
3 calls:
9.0ms
(/ x (+ x y))
10.0ms
(/ (pow (/ x (+ x y)) x) x)
6.0ms
(pow (/ x (+ x y)) x)

series404.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(/ x (+ x y))
134.0ms
(/ (pow (/ x (+ x y)) x) x)
227.0ms
(pow (/ x (+ x y)) x)

simplify76.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
05371436
126401406
250011406

prune533.0ms

Filtered
181 candidates to 131 candidates (72.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1765181
Fresh000
Picked101
Done000
Total1775182

Merged error: 0.3b

Counts
182 → 5

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

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 frac-2neg mul-1-neg div-exp clear-num div-inv associate-/l/ add-log-exp
Counts
1 → 28
Calls
1 calls:
4.0ms
(/ (exp (* -1 y)) x)

series19.0ms

Counts
1 → 3
Calls
1 calls:
19.0ms
(/ (exp (* -1 y)) x)

simplify50.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0114186
1303172
21435169
35001169

prune95.0ms

Filtered
31 candidates to 23 candidates (74.2%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New30131
Fresh134
Picked101
Done000
Total32436

Merged error: 0.3b

Counts
36 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
11×add-exp-log
9×add-cbrt-cube
8×add-sqr-sqrt
7×pow1
6×add-cube-cbrt *-un-lft-identity
4×div-exp prod-exp
3×times-frac associate-*r* associate-*l* associate-/l*
2×cbrt-undiv rec-exp pow-flip 1-exp pow-prod-down cbrt-unprod add-log-exp
1×frac-2neg clear-num associate-/r* *-commutative div-inv inv-pow unswap-sqr
Counts
2 → 46
Calls
2 calls:
5.0ms
(/ 1 (* x (exp y)))
4.0ms
(* x (exp y))

series45.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(/ 1 (* x (exp y)))
25.0ms
(* x (exp y))

simplify94.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0173200
1786167
24230160
35002160

prune108.0ms

Filtered
52 candidates to 28 candidates (53.8%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New51152
Fresh033
Picked011
Done000
Total51556

Merged error: 0.2b

Counts
56 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (pow y 2))
0.0b
(+ (* 1/2 (pow y 2)) (+ y 1))
0.1b
(/ 1 (* x (+ (* 1/2 (pow y 2)) (+ y 1))))
2.8b
(* x (+ (* 1/2 (pow y 2)) (+ y 1)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
19×add-sqr-sqrt
13×add-cbrt-cube
11×add-cube-cbrt *-un-lft-identity associate-*r*
9×pow1 add-log-exp
7×prod-exp
6×associate-*l*
5×unswap-sqr
4×unpow-prod-down associate-*r/ div-exp
3×flip3-+ times-frac sum-log cbrt-unprod flip-+ associate-/l*
2×cbrt-undiv rec-exp pow-flip 1-exp pow-prod-down associate-/r/ *-commutative unpow2 sqr-pow
1×+-commutative distribute-rgt-in pow-to-exp associate-+r+ frac-2neg distribute-lft-in pow-exp clear-num associate-/r* div-inv inv-pow
Counts
4 → 92
Calls
4 calls:
5.0ms
(* 1/2 (pow y 2))
6.0ms
(+ (* 1/2 (pow y 2)) (+ y 1))
13.0ms
(/ 1 (* x (+ (* 1/2 (pow y 2)) (+ y 1))))
8.0ms
(* x (+ (* 1/2 (pow y 2)) (+ y 1)))

series134.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* 1/2 (pow y 2))
18.0ms
(+ (* 1/2 (pow y 2)) (+ y 1))
50.0ms
(/ 1 (* x (+ (* 1/2 (pow y 2)) (+ y 1))))
41.0ms
(* x (+ (* 1/2 (pow y 2)) (+ y 1)))

simplify69.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
0420642
12208552
25001546

prune235.0ms

Filtered
104 candidates to 62 candidates (59.6%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1040104
Fresh033
Picked011
Done011
Total1045109

Merged error: 0.2b

Counts
109 → 5

regimes120.0ms

Accuracy

87.7% (1.5b remaining)

Error of 2.0b against oracle of 0.5b and baseline of 12.4b

bsearch80.0ms

Steps
ItersRangePoint
7
4.441427088419529e-17
2.8933248776460057e-15
2.851493031640306e-15
8
-0.3117988049014286
-0.000777779614891554
-0.30757307122549704

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02916
12916

end0.0ms

sample2.1s

Algorithm
intervals
Results
750.0ms1516×body1280valid
433.0ms1437×body640valid
257.0ms4878×body80valid
163.0ms833×body320valid
117.0ms2924×body80nan
61.0ms463×body160valid

Profiling

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