Details

Time bar (total: 5.1s)

sample20.0ms

Algorithm
intervals
Results
5.0ms48×body1280valid
3.0ms44×body640valid
3.0ms126×body80valid
2.0ms27×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: 30.8b

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b
(cbrt (+ x 1.0))
0.6b
(cbrt x)
3.1b
(- (cbrt (+ x 1.0)) (cbrt x))

rewrite13.0ms

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:
3.0ms
(cbrt (+ x 1.0))
1.0ms
(cbrt x)
8.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

series437.0ms

Counts
3 → 9
Calls
3 calls:
92.0ms
(cbrt (+ x 1.0))
189.0ms
(cbrt x)
156.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

simplify165.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0287358
1934344
24833322
35001322

prune160.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ x 1.0))
0.3b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.6b
(cbrt x)
9.9b
(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
31×cbrt-prod
30×*-un-lft-identity
22×add-sqr-sqrt
14×add-cube-cbrt cbrt-div
11×pow1
9×swap-sqr
8×pow1/3
7×flip3-+ associate-*r* associate-*l* flip-+ distribute-lft-out
6×add-exp-log add-log-exp
4×frac-times add-cbrt-cube unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 sub-neg flip3-- pow-plus diff-log prod-exp *-commutative flip-- cbrt-unprod
Counts
4 → 90
Calls
4 calls:
3.0ms
(cbrt (+ x 1.0))
10.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
1.0ms
(cbrt x)
17.0ms
(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series546.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(cbrt (+ x 1.0))
108.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
183.0ms
(cbrt x)
162.0ms
(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify54.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0420880
11572820
25001760

prune318.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.6b
(cbrt x)
9.9b
(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))))) (cbrt x))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
51×cbrt-prod
49×*-un-lft-identity
37×add-sqr-sqrt
24×cbrt-div
21×add-cube-cbrt
18×pow1 swap-sqr
14×associate-*r* associate-*l*
13×pow1/3
12×flip3-+ flip-+ distribute-lft-out
8×add-exp-log frac-times unswap-sqr
6×add-log-exp
4×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up add-cbrt-cube
2×pow2 pow-plus prod-exp *-commutative cbrt-unprod
1×sub-neg flip3-- diff-log flip--
Counts
4 → 129
Calls
4 calls:
10.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
10.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
1.0ms
(cbrt x)
36.0ms
(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))))) (cbrt x))

series561.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
108.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
189.0ms
(cbrt x)
158.0ms
(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))))) (cbrt x))

simplify56.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04101332
115301241
250011136

prune487.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(* (cbrt x) (cbrt x))
9.9b
(- (* (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))))) (* (cbrt x) (cbrt x)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
22×cbrt-prod add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
11×pow1
8×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l* add-log-exp
4×add-cbrt-cube unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 sub-neg flip3-- pow-plus diff-log prod-exp *-commutative flip-- cbrt-unprod difference-of-squares
Counts
4 → 75
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
6.0ms
(* (cbrt x) (cbrt x))
98.0ms
(- (* (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))))) (* (cbrt x) (cbrt x)))

series960.0ms

Counts
4 → 12
Calls
4 calls:
381.0ms
(cbrt x)
180.0ms
(cbrt x)
202.0ms
(* (cbrt x) (cbrt x))
197.0ms
(- (* (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))))) (* (cbrt x) (cbrt x)))

simplify57.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0301785
11301659
25001608

prune289.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.9b

regimes86.0ms

Accuracy

99.1% (0.2b remaining)

Error of 12.0b against oracle of 11.8b and baseline of 29.9b

bsearch111.0ms

Steps
ItersRangePoint
10
1.4316099847845607e-10
21.660028671588154
0.0001936421456613118
10
-1.828180551810585e+69
-1.9710212454209794e+59
-4.462890112366947e+61

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06547
17047
27047

end0.0ms

sample516.0ms

Algorithm
intervals
Results
182.0ms1746×body1280valid
107.0ms1226×body640valid
85.0ms4099×body80valid
36.0ms610×body320valid
12.0ms319×body160valid