Details

Time bar (total: 5.3s)

sample20.0ms

Algorithm
intervals
Results
6.0ms56×body1280valid
3.0ms44×body640valid
3.0ms125×body80valid
1.0ms20×body320valid
0.0ms11×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.3b
(cbrt (+ x 1.0))
0.5b
(cbrt x)
3.0b
(- (cbrt (+ x 1.0)) (cbrt x))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
14×*-un-lft-identity
13×add-sqr-sqrt
5×add-cube-cbrt add-log-exp
4×difference-of-squares
3×pow1 add-exp-log add-cbrt-cube distribute-lft-out--
2×cbrt-div pow1/3 distribute-lft-out
1×sub-neg flip3-- flip3-+ diff-log flip-- flip-+
Counts
3 → 44
Calls
3 calls:
4.0ms
(cbrt (+ x 1.0))
1.0ms
(cbrt x)
40.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

series404.0ms

Counts
3 → 9
Calls
3 calls:
83.0ms
(cbrt (+ x 1.0))
175.0ms
(cbrt x)
145.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

simplify160.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0287358
1934344
24833322
35001322

prune153.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.7b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ x 1.0))
0.5b
(cbrt x)
2.4b
(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
3.0b
(- (cbrt (+ x 1.0)) (cbrt x))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity
23×cbrt-prod
11×log-pow
10×exp-prod
8×add-cube-cbrt difference-of-squares
6×distribute-lft-out-- add-log-exp
5×pow1 log-prod
4×add-exp-log add-cbrt-cube
3×distribute-lft-out
2×sub-neg cbrt-div pow1/3 exp-sum
1×log-div flip3-- flip3-+ exp-diff diff-log rem-log-exp flip-- flip-+
Counts
4 → 69
Calls
4 calls:
4.0ms
(cbrt (+ x 1.0))
1.0ms
(cbrt x)
86.0ms
(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
42.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

series547.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(cbrt (+ x 1.0))
181.0ms
(cbrt x)
139.0ms
(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
141.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

simplify37.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0336568
11025536
25001505

prune246.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
0.5b
(cbrt x)
2.4b
(log (exp (/ (- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ x 1.0)) (cbrt x)))))
3.0b
(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
31×log-pow
30×exp-prod
24×times-frac
22×cbrt-prod
18×add-sqr-sqrt add-cube-cbrt
16×distribute-lft-out
7×difference-of-squares
6×add-log-exp
5×pow1
4×add-exp-log add-cbrt-cube
3×log-prod
2×pow1/3 associate-/r/
1×sub-neg log-div flip3-- flip3-+ exp-diff diff-log div-sub rem-log-exp flip-- flip-+ div-inv
Counts
4 → 78
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
130.0ms
(log (exp (/ (- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ x 1.0)) (cbrt x)))))
23.0ms
(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series889.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(cbrt x)
172.0ms
(cbrt x)
375.0ms
(log (exp (/ (- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x))) (+ (cbrt (+ x 1.0)) (cbrt x)))))
170.0ms
(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify94.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
07501315
133891203
250011200

prune314.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.7b

localize14.0ms

Local error

Found 4 expressions with local error:

2.4b
(log (exp (* (* (cbrt (- (cbrt (+ x 1.0)) (cbrt x))) (cbrt (- (cbrt (+ x 1.0)) (cbrt x)))) (cbrt (- (cbrt (+ x 1.0)) (cbrt x))))))
3.0b
(- (cbrt (+ x 1.0)) (cbrt x))
3.0b
(- (cbrt (+ x 1.0)) (cbrt x))
3.0b
(- (cbrt (+ x 1.0)) (cbrt x))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
26×*-un-lft-identity
24×cbrt-prod
12×difference-of-squares
11×add-log-exp
9×distribute-lft-out--
5×pow1 add-cube-cbrt
4×add-exp-log add-cbrt-cube
3×sub-neg log-prod flip3-- diff-log log-pow flip-- distribute-lft-out
1×exp-prod exp-to-pow rem-log-exp
Counts
4 → 71
Calls
4 calls:
3.0ms
(log (exp (* (* (cbrt (- (cbrt (+ x 1.0)) (cbrt x))) (cbrt (- (cbrt (+ x 1.0)) (cbrt x)))) (cbrt (- (cbrt (+ x 1.0)) (cbrt x))))))
40.0ms
(- (cbrt (+ x 1.0)) (cbrt x))
39.0ms
(- (cbrt (+ x 1.0)) (cbrt x))
42.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

series553.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(log (exp (* (* (cbrt (- (cbrt (+ x 1.0)) (cbrt x))) (cbrt (- (cbrt (+ x 1.0)) (cbrt x)))) (cbrt (- (cbrt (+ x 1.0)) (cbrt x))))))
140.0ms
(- (cbrt (+ x 1.0)) (cbrt x))
134.0ms
(- (cbrt (+ x 1.0)) (cbrt x))
139.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

simplify128.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
02491046
1786915
24045759
35002759

prune292.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.7b

regimes106.0ms

Accuracy

99.2% (0.2b remaining)

Error of 12.1b against oracle of 11.9b and baseline of 30.5b

bsearch273.0ms

Steps
ItersRangePoint
7
7.803840110207806e-07
0.00015704816827310668
1.0345682363291832e-06
10
-8.58470807685748e+66
-3.383504290440664e+54
-4.4332874833874156e+61

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06136
16636
26636

end0.0ms

sample527.0ms

Algorithm
intervals
Results
179.0ms1801×body1280valid
100.0ms1269×body640valid
79.0ms4003×body80valid
33.0ms601×body320valid
14.0ms326×body160valid