Details

Time bar (total: 4.7s)

analyze4.0ms

Algorithm
search

sample26.0ms

Algorithm
intervals
Results
9.0ms63×body1280valid
5.0ms39×body640valid
4.0ms114×body80valid
3.0ms29×body320valid
1.0ms11×body160valid

simplify18.0ms

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

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.3b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ x (+ x 1.0))
3.2b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
32×times-frac
23×add-sqr-sqrt
13×distribute-lft-out--
12×distribute-lft-out
11×add-cube-cbrt
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp difference-of-squares
3×associate-/l*
2×pow1 associate-/r/
1×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ diff-log div-exp clear-num frac-sub flip-- flip-+ div-inv
Counts
2 → 59
Calls
2 calls:
5.0ms
(/ x (+ x 1.0))
33.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series10.0ms

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

simplify118.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0266459
1872434
23573429
35001429

prune107.0ms

Filtered
44 candidates to 65 candidates (-47.7%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New61465
Fresh000
Picked101
Done000
Total62466

Merged error: 0.0b

Counts
66 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (/ (neg 1.0) (pow x 2)) (/ 3.0 x))
0.3b
(/ (neg 1.0) (pow x 2))
0.6b
(/ 3.0 (pow x 3))
5.0b
(- (- (/ (neg 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
143×times-frac
120×add-sqr-sqrt
105×*-un-lft-identity
78×add-cube-cbrt
48×unpow-prod-down
29×distribute-rgt-neg-in
27×distribute-lft-neg-in
20×associate-/r*
18×sqr-pow
15×difference-of-squares
14×add-exp-log
13×cube-prod associate-/l* unpow2
11×add-log-exp
10×distribute-lft-out--
9×neg-mul-1
8×add-cbrt-cube
6×div-exp
5×frac-sub
4×pow1 cube-mult diff-log unpow3
3×sub-neg flip3-- flip--
2×cbrt-undiv associate--l- neg-sub0 pow-to-exp frac-2neg div-sub pow-exp associate--l+ clear-num div-inv
1×distribute-frac-neg
Counts
4 → 234
Calls
4 calls:
54.0ms
(- (/ (neg 1.0) (pow x 2)) (/ 3.0 x))
7.0ms
(/ (neg 1.0) (pow x 2))
5.0ms
(/ 3.0 (pow x 3))
84.0ms
(- (- (/ (neg 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series16.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(- (/ (neg 1.0) (pow x 2)) (/ 3.0 x))
3.0ms
(/ (neg 1.0) (pow x 2))
3.0ms
(/ 3.0 (pow x 3))
4.0ms
(- (- (/ (neg 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify97.0ms

Algorithm
egg-herbie
Counts
246 → 246
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
07381746
134221585
250021567

prune307.0ms

Filtered
129 candidates to 246 candidates (-90.7%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2451246
Fresh033
Picked011
Done000
Total2455250

Merged error: 0.0b

Counts
250 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (neg 1.0) (pow x 2))
0.6b
(/ 3.0 (pow x 3))
1.5b
(log (exp (/ (neg 1.0) (pow x 2))))
8.8b
(- (- (log (exp (/ (neg 1.0) (pow x 2)))) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
200×times-frac
138×add-sqr-sqrt
132×*-un-lft-identity
125×add-cube-cbrt
86×log-pow
84×exp-prod
76×unpow-prod-down
51×distribute-lft-neg-in distribute-rgt-neg-in
26×sqr-pow
21×unpow2
20×associate-/r*
17×neg-mul-1
14×add-exp-log
13×cube-prod associate-/l*
8×associate--l+ add-cbrt-cube add-log-exp
6×pow1 log-prod div-exp
5×distribute-lft-out-- difference-of-squares
4×cube-mult unpow3
3×diff-log distribute-frac-neg div-inv
2×cbrt-undiv neg-sub0 exp-neg pow-to-exp sub-neg log-div flip3-- frac-2neg div-sub pow-exp clear-num frac-sub flip--
1×associate--l- exp-diff rem-log-exp log-rec
Counts
4 → 307
Calls
4 calls:
7.0ms
(/ (neg 1.0) (pow x 2))
5.0ms
(/ 3.0 (pow x 3))
16.0ms
(log (exp (/ (neg 1.0) (pow x 2))))
83.0ms
(- (- (log (exp (/ (neg 1.0) (pow x 2)))) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series14.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(/ (neg 1.0) (pow x 2))
3.0ms
(/ 3.0 (pow x 3))
3.0ms
(log (exp (/ (neg 1.0) (pow x 2))))
4.0ms
(- (- (log (exp (/ (neg 1.0) (pow x 2)))) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify94.0ms

Algorithm
egg-herbie
Counts
319 → 319
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
08471960
133871712
250021691

prune508.0ms

Filtered
184 candidates to 319 candidates (-73.4%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New3190319
Fresh033
Picked011
Done011
Total3195324

Merged error: 0.0b

Counts
324 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
0.0b
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b
(pow (/ x (+ x 1.0)) 3)
3.1b
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite337.0ms

Algorithm
rewrite-expression-head
Rules
1123×*-un-lft-identity
759×times-frac
571×add-sqr-sqrt
318×unpow-prod-down cube-prod
265×distribute-lft-out--
184×distribute-lft-out
180×difference-of-squares
139×add-cube-cbrt
77×associate-/l*
61×sqr-pow
35×associate-/r/
27×frac-add
24×swap-sqr
21×add-exp-log add-cbrt-cube
18×associate-*r* associate-*l*
17×frac-times associate-*r/
13×flip3-+ flip-+
12×pow1
11×associate-*l/
7×div-inv
6×cbrt-undiv div-exp add-log-exp
5×difference-cubes cube-div
4×prod-exp cbrt-unprod unswap-sqr
3×pow-unpow associate-/r* associate-/l/
2×flip3-- pow-exp frac-sub flip-- rem-cube-cbrt
1×pow2 cube-mult pow-to-exp sub-neg pow-pow frac-2neg pow-plus diff-log unpow3 div-sub pow-prod-down clear-num pow-sqr *-commutative pow-prod-up
Counts
4 → 581
Calls
4 calls:
155.0ms
(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
17.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
7.0ms
(pow (/ x (+ x 1.0)) 3)
101.0ms
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series57.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
3.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
3.0ms
(pow (/ x (+ x 1.0)) 3)
15.0ms
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify186.0ms

Algorithm
egg-herbie
Counts
593 → 593
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
0170617407
1500117140

prune1.6s

Filtered
226 candidates to 593 candidates (-162.4%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New5912593
Fresh202
Picked101
Done022
Total5944598

Merged error: 0.0b

Counts
598 → 4

regimes49.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 32.1b

bsearch45.0ms

Steps
ItersRangePoint
9
141.36685049731767
321990639.85389894
13055.080251907435
10
-2938742216479.4663
-2.952661570026046
-13121.35748737681

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04134
14134

end0.0ms

analyze4.0ms

Algorithm
search

sample719.0ms

Algorithm
intervals
Results
268.0ms1728×body1280valid
152.0ms1270×body640valid
133.0ms4135×body80valid
56.0ms601×body320valid
16.0ms266×body160valid

Profiling

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