Details

Time bar (total: 27.9s)

sample98.0ms

Algorithm
intervals
Results
65.0ms650×body80valid

simplify6.0s

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01217
12616
25015
38615
415115
530315
693215
7396115
done500115

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
0.0b
(fma a a (* b b))
0.4b
(pow (fma a a (* b b)) 2.0)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log
3×expm1-log1p-u unpow-prod-down pow-unpow add-cbrt-cube log1p-expm1-u add-log-exp
2×fma-udef
1×pow-to-exp pow-pow pow-exp sqr-pow
Counts
3 → 39
Calls
3 calls:
0.0ms
(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
0.0ms
(fma a a (* b b))
3.0ms
(pow (fma a a (* b b)) 2.0)

series326.0ms

Counts
3 → 9
Calls
3 calls:
107.0ms
(fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))
46.0ms
(fma a a (* b b))
173.0ms
(pow (fma a a (* b b)) 2.0)

simplify3.0s

Counts
48 → 48
Iterations

Useful iterations: 4 (1.5s)

IterNodesCost
079580
1148561
2367493
31089488
43747485
done5000485

prune263.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))) (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))))
13.1b
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
13.1b
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
13.1b
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
32.0ms
(* (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))) (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))))
2.0ms
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
2.0ms
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
2.0ms
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

series1.3s

Counts
4 → 12
Calls
4 calls:
297.0ms
(* (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))) (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0))))
300.0ms
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
348.0ms
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
326.0ms
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

simplify1.5s

Counts
93 → 93
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01062580
12082420
25302217
314491816
done50011778

prune537.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

12.5b
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
12.5b
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
13.1b
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
13.1b
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
3.0ms
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
3.0ms
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
2.0ms
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
2.0ms
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
230.0ms
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
214.0ms
(sqrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
274.0ms
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
363.0ms
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

simplify3.8s

Counts
68 → 68
Iterations

Useful iterations: 4 (1.6s)

IterNodesCost
0821324
11651244
23871160
310781106
444101094
done50011094

prune410.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (sqrt (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))) 3)
13.1b
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
13.1b
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
13.1b
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×sqrt-prod
9×unpow-prod-down cube-prod
6×pow1
5×add-exp-log add-cbrt-cube
4×expm1-log1p-u pow-pow pow1/3 log1p-expm1-u add-log-exp
3×pow-unpow
2×sqrt-pow1
1×cube-mult pow-to-exp pow1/2 unpow3 pow-exp sqrt-pow2 rem-cube-cbrt sqr-pow
Counts
4 → 80
Calls
4 calls:
8.0ms
(pow (sqrt (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))) 3)
1.0ms
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
1.0ms
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
1.0ms
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
412.0ms
(pow (sqrt (cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))) 3)
286.0ms
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
247.0ms
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))
276.0ms
(cbrt (fma (* 4.0 b) b (pow (fma a a (* b b)) 2.0)))

simplify4.2s

Counts
92 → 92
Iterations

Useful iterations: done (4.2s)

IterNodesCost
01212200
12861990
27641824
341681670
done50001652

prune539.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

regimes272.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11215
done1215

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.4s20563×body80valid