Details

Time bar (total: 3.4s)

sample25.0ms

Algorithm
intervals
Results
8.0ms53×body1280valid
5.0ms44×body640valid
4.0ms129×body80valid
1.0ms16×body320valid
1.0ms14×body160valid

simplify17.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0126
1166
2196
3216
4276
5396
6586
7796
81076
91606
102776
113036
123036

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.1b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ x 1.0) (- x 1.0))
3.5b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
40×times-frac
35×add-sqr-sqrt
18×distribute-lft-out--
14×distribute-lft-out
13×add-cube-cbrt
9×difference-of-squares
5×associate-/r*
4×add-exp-log add-cbrt-cube associate-/l* add-log-exp
2×pow1 flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-exp clear-num frac-sub flip-+ div-inv
Counts
2 → 71
Calls
2 calls:
7.0ms
(/ (+ x 1.0) (- x 1.0))
29.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series10.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(/ (+ x 1.0) (- x 1.0))
7.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify145.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0317591
11003565
24494559
35003559

prune123.0ms

Filtered
50 candidates to 77 candidates (-54.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New73477
Fresh000
Picked101
Done000
Total74478

Merged error: 0.2b

Counts
78 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x 1.0) (+ x 1.0))
0.0b
(/ 1 (/ (- x 1.0) (+ x 1.0)))
3.5b
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
199×times-frac
191×*-un-lft-identity
156×add-sqr-sqrt
81×add-cube-cbrt
31×difference-of-squares
30×associate-/r*
27×distribute-lft-out
25×distribute-lft-out--
16×add-exp-log
11×associate-/r/
10×add-cbrt-cube
8×div-exp associate-/l*
7×div-inv
5×flip3-+ flip-+ add-log-exp
4×pow1 cbrt-undiv
2×rec-exp flip3-- frac-2neg 1-exp clear-num flip-- associate-/l/
1×sub-neg pow-flip diff-log div-sub frac-sub inv-pow
Counts
3 → 201
Calls
3 calls:
7.0ms
(/ (- x 1.0) (+ x 1.0))
11.0ms
(/ 1 (/ (- x 1.0) (+ x 1.0)))
69.0ms
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

series13.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(/ (- x 1.0) (+ x 1.0))
3.0ms
(/ 1 (/ (- x 1.0) (+ x 1.0)))
7.0ms
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

simplify71.0ms

Algorithm
egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
06801910
130271602
250011593

prune185.0ms

Filtered
99 candidates to 210 candidates (-112.1%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2091210
Fresh033
Picked101
Done000
Total2104214

Merged error: 0.2b

Counts
214 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cbrt (- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))) (cbrt (- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))))
3.5b
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
3.5b
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
3.5b
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

rewrite378.0ms

Algorithm
rewrite-expression-head
Rules
251×add-sqr-sqrt
158×*-un-lft-identity
155×times-frac
88×cbrt-prod
70×difference-of-squares
40×distribute-lft-out--
28×swap-sqr
24×cbrt-div
20×associate-*r* associate-*l*
12×add-cube-cbrt
11×pow1 flip3-- frac-sub flip-- div-inv
10×add-log-exp
9×frac-times distribute-lft-out
6×add-exp-log pow1/3
4×add-cbrt-cube unswap-sqr
3×sub-neg diff-log associate-*r/ associate-*l/
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 186
Calls
4 calls:
152.0ms
(* (cbrt (- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))) (cbrt (- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))))
71.0ms
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
70.0ms
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
71.0ms
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

series40.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (cbrt (- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))) (cbrt (- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))))
7.0ms
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
7.0ms
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
7.0ms
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

simplify77.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05293912
118813683
250023423

prune643.0ms

Filtered
127 candidates to 198 candidates (-55.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1971198
Fresh033
Picked101
Done000
Total1984202

Merged error: 0.2b

Counts
202 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (* 2 (log (cbrt (- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))))))
3.2b
(log (cbrt (- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))))
3.5b
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
3.5b
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

rewrite303.0ms

Algorithm
rewrite-expression-head
Rules
175×add-sqr-sqrt
105×times-frac
90×*-un-lft-identity
60×log-prod
51×cbrt-prod
50×difference-of-squares
40×exp-sum
20×distribute-rgt-in distribute-lft-in distribute-lft-out--
10×add-cube-cbrt add-log-exp
5×pow1 add-exp-log div-inv distribute-lft-out
4×add-cbrt-cube
3×log-div cbrt-div flip3-- frac-sub flip--
2×sub-neg diff-log log-pow
1×exp-prod exp-to-pow pow1/3 rem-log-exp rem-exp-log
Counts
4 → 137
Calls
4 calls:
77.0ms
(exp (* 2 (log (cbrt (- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))))))
72.0ms
(log (cbrt (- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))))
71.0ms
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
71.0ms
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

series47.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(exp (* 2 (log (cbrt (- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))))))
15.0ms
(log (cbrt (- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))))
7.0ms
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
7.0ms
(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

simplify70.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
07992515
127072301
250012267

prune306.0ms

Filtered
87 candidates to 149 candidates (-71.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1481149
Fresh033
Picked101
Done000
Total1494153

Merged error: 0.2b

Counts
153 → 4

regimes41.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 29.4b

bsearch27.0ms

Steps
ItersRangePoint
10
0.0364262917160445
547825979.610153
1.009120764653964
8
-340480.61858828116
-442.47528987694835
-18521.583028075464

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04731
14731

end0.0ms

sample724.0ms

Algorithm
intervals
Results
253.0ms1702×body1280valid
136.0ms1181×body640valid
129.0ms4170×body80valid
59.0ms638×body320valid
18.0ms309×body160valid

Profiling

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