Details

Time bar (total: 5.4s)

sample19.0ms

Algorithm
intervals
Results
5.0ms50×body1280valid
3.0ms49×body640valid
3.0ms127×body80valid
1.0ms22×body320valid
0.0ms8×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104
done104

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)
2.4b
(- (cbrt (+ x 1.0)) (cbrt x))

rewrite63.0ms

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:
4.0ms
(cbrt (+ x 1.0))
1.0ms
(cbrt x)
54.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

series406.0ms

Counts
3 → 9
Calls
3 calls:
88.0ms
(cbrt (+ x 1.0))
178.0ms
(cbrt x)
141.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

simplify52.0ms

Counts
108 → 108
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04301315
113941045
25001981
done5001981

prune248.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.8b

localize12.0ms

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)
30.7b
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite49.0ms

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
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod fma-udef
Counts
4 → 94
Calls
4 calls:
4.0ms
(cbrt (+ x 1.0))
41.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
1.0ms
(cbrt x)
0.0ms
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series608.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(cbrt (+ x 1.0))
100.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
177.0ms
(cbrt x)
246.0ms
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify49.0ms

Counts
106 → 106
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0479846
11610782
25001727
done5001727

prune376.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.5b
(pow (cbrt (cbrt (+ x 1.0))) 4)
0.6b
(cbrt x)
30.4b
(fma (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (pow (cbrt (cbrt (+ x 1.0))) 4))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
38×cbrt-prod
33×*-un-lft-identity
25×add-sqr-sqrt
17×add-cube-cbrt
12×pow1 cbrt-div
10×unpow-prod-down
9×swap-sqr
8×pow1/3
7×add-exp-log associate-*r* associate-*l* distribute-lft-out
6×flip3-+ flip-+
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
3×pow-unpow
2×pow-pow associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-to-exp pow-plus pow-exp prod-exp *-commutative cbrt-unprod fma-udef sqr-pow
Counts
4 → 105
Calls
4 calls:
49.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
19.0ms
(pow (cbrt (cbrt (+ x 1.0))) 4)
2.0ms
(cbrt x)
1.0ms
(fma (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (pow (cbrt (cbrt (+ x 1.0))) 4))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series674.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
146.0ms
(pow (cbrt (cbrt (+ x 1.0))) 4)
177.0ms
(cbrt x)
249.0ms
(fma (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (pow (cbrt (cbrt (+ x 1.0))) 4))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify61.0ms

Counts
117 → 117
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05991021
12102943
25002889
done5002889

prune474.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cbrt x))
0.6b
(cbrt (cbrt x))
0.6b
(cbrt (cbrt x))
31.0b
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (* (cbrt (cbrt x)) (cbrt (* (cbrt x) (cbrt x))))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
27×cbrt-prod
10×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 → 58
Calls
4 calls:
4.0ms
(cbrt (cbrt x))
1.0ms
(cbrt (cbrt x))
1.0ms
(cbrt (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 x))))))

series978.0ms

Counts
4 → 12
Calls
4 calls:
250.0ms
(cbrt (cbrt x))
245.0ms
(cbrt (cbrt x))
242.0ms
(cbrt (cbrt x))
241.0ms
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (* (cbrt (cbrt x)) (cbrt (* (cbrt x) (cbrt x))))))

simplify64.0ms

Counts
70 → 70
Iterations

Useful iterations: 3 (59.0ms)

IterNodesCost
0247549
1651494
22375480
35001477
done5001477

prune371.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 18.8b

regimes145.0ms

Accuracy

98.3% (0.2b remaining)

Error of 18.5b against oracle of 18.3b and baseline of 29.8b

bsearch96.0ms

Steps
ItersRangePoint
7
27.68840223478076
5364.146891578128
3214.257238783485
9
-7.149767289149974e+63
-1.497073903866961e+55
-4.445502958773829e+61

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06143
16143
done6143

end0.0ms

sample506.0ms

Algorithm
intervals
Results
155.0ms1654×body1280valid
92.0ms1303×body640valid
83.0ms4117×body80valid
36.0ms624×body320valid
14.0ms302×body160valid