Details

Time bar (total: 16.0s)

sample37.0ms

Algorithm
intervals
Results
9.0ms45×body1280valid
8.0ms48×body640valid
6.0ms137×body80valid
2.0ms13×body320valid
1.0ms13×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.3b
(cbrt (+ x 1.0))
0.6b
(cbrt x)
4.1b
(- (cbrt (+ x 1.0)) (cbrt x))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
64×cbrt-prod
56×*-un-lft-identity
42×prod-diff
41×add-sqr-sqrt
33×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
5×add-log-exp
4×difference-of-squares
3×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u distribute-lft-out--
2×cbrt-div pow1/3
1×sub-neg flip3-- flip3-+ diff-log flip-- flip-+
Counts
3 → 99
Calls
3 calls:
8.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt x)
103.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

series627.0ms

Counts
3 → 9
Calls
3 calls:
131.0ms
(cbrt (+ x 1.0))
273.0ms
(cbrt x)
222.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

simplify2.6s

Counts
108 → 108
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01942160
14331776
29941468
329991265
done50001254

prune348.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (log1p (- (cbrt (+ x 1.0)) (cbrt x))))
0.3b
(cbrt (+ x 1.0))
0.6b
(cbrt x)
4.1b
(- (cbrt (+ x 1.0)) (cbrt x))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
64×cbrt-prod
57×*-un-lft-identity
42×add-sqr-sqrt prod-diff
34×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u difference-of-squares
3×distribute-lft-out--
2×cbrt-div pow1/3
1×sub-neg expm1-log1p flip3-- flip3-+ diff-log flip-- flip-+ expm1-udef
Counts
4 → 110
Calls
4 calls:
1.0ms
(expm1 (log1p (- (cbrt (+ x 1.0)) (cbrt x))))
9.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt x)
85.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

series1.0s

Counts
4 → 12
Calls
4 calls:
373.0ms
(expm1 (log1p (- (cbrt (+ x 1.0)) (cbrt x))))
112.0ms
(cbrt (+ x 1.0))
335.0ms
(cbrt x)
227.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.3s

Counts
122 → 122
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02412520
15652078
214491738
done50001511

prune461.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cbrt (+ x 1.0)))
0.3b
(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
0.6b
(cbrt x)
28.4b
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-div
15×cbrt-prod
9×*-un-lft-identity
7×add-sqr-sqrt add-cube-cbrt flip3-+ flip-+
4×pow1 add-exp-log expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
2×associate-*r/ associate-*l/
1×fma-udef distribute-lft-out
Counts
4 → 61
Calls
4 calls:
19.0ms
(cbrt (cbrt (+ x 1.0)))
28.0ms
(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
2.0ms
(cbrt x)
1.0ms
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series1.1s

Counts
4 → 12
Calls
4 calls:
145.0ms
(cbrt (cbrt (+ x 1.0)))
174.0ms
(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
385.0ms
(cbrt x)
364.0ms
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify2.3s

Counts
73 → 73
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02221223
14661176
211891091
334591034
done50001032

prune469.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
28.2b
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)
0.0ms
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
281.0ms
(cbrt x)
306.0ms
(cbrt x)
299.0ms
(cbrt x)
443.0ms
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))))

simplify2.0s

Counts
61 → 61
Iterations

Useful iterations: done (2.0s)

IterNodesCost
0101718
1228695
2585556
31799495
done5001482

prune382.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.3b

regimes96.0ms

Accuracy

97.4% (0.6b remaining)

Error of 9.2b against oracle of 8.6b and baseline of 29.7b

bsearch249.0ms

Steps
ItersRangePoint
8
3.974799646785555e-07
0.0030847216915828425
7.166887942762203e-06
11
-30636816361710.875
-9.292394687435822e-10
-1.014356783985294

simplify23.0ms

Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
074146
189144
done89144

end0.0ms

sample1.4s

Algorithm
intervals
Results
562.0ms4135×body80valid
331.0ms1683×body1280valid
208.0ms1256×body640valid
58.0ms608×body320valid
20.0ms318×body160valid