Details

Time bar (total: 9.5s)

sample39.0ms

Algorithm
intervals
Results
18.0ms256×body80valid

simplify310.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0919
11918
23918
37718
412818
518418
621118
721618
done21618

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize25.0ms

Local error

Found 2 expressions with local error:

4.5b
(- (* x x) (* (* y 4.0) y))
31.3b
(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num div-inv
Counts
2 → 48
Calls
2 calls:
20.0ms
(- (* x x) (* (* y 4.0) y))
29.0ms
(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

series209.0ms

Counts
2 → 6
Calls
2 calls:
87.0ms
(- (* x x) (* (* y 4.0) y))
122.0ms
(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

simplify2.9s

Counts
54 → 54
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0901183
12201154
27751046
330571044
done50001043

prune229.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize1.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune12.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 2 expressions with local error:

2.8b
(fma x x (- (* y (* y 4.0))))
31.3b
(/ (fma x x (- (* y (* y 4.0)))) (fma x x (* (* y 4.0) y)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
2 → 39
Calls
2 calls:
1.0ms
(fma x x (- (* y (* y 4.0))))
11.0ms
(/ (fma x x (- (* y (* y 4.0)))) (fma x x (* (* y 4.0) y)))

series231.0ms

Counts
2 → 6
Calls
2 calls:
86.0ms
(fma x x (- (* y (* y 4.0))))
145.0ms
(/ (fma x x (- (* y (* y 4.0)))) (fma x x (* (* y 4.0) y)))

simplify1.7s

Counts
45 → 45
Iterations

Useful iterations: done (1.7s)

IterNodesCost
068985
1117976
2296886
31070886
done5001885

prune191.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (pow (/ (fma x x (- (* y (* y 4.0)))) (fma x x (* (* y 4.0) y))) 3))
0.0b
(pow (/ (fma x x (- (* y (* y 4.0)))) (fma x x (* (* y 4.0) y))) 3)
2.8b
(fma x x (- (* y (* y 4.0))))
31.3b
(/ (fma x x (- (* y (* y 4.0)))) (fma x x (* (* y 4.0) y)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
42×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
32×cbrt-prod
26×unpow-prod-down cube-prod
9×add-exp-log add-cbrt-cube
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* associate-/l*
2×cbrt-undiv cube-div cube-mult unpow3 div-exp pow-exp rem-cube-cbrt sqr-pow
1×pow-to-exp cbrt-div pow-pow frac-2neg pow1/3 clear-num rem-cbrt-cube fma-udef
Counts
4 → 131
Calls
4 calls:
13.0ms
(cbrt (pow (/ (fma x x (- (* y (* y 4.0)))) (fma x x (* (* y 4.0) y))) 3))
15.0ms
(pow (/ (fma x x (- (* y (* y 4.0)))) (fma x x (* (* y 4.0) y))) 3)
1.0ms
(fma x x (- (* y (* y 4.0))))
12.0ms
(/ (fma x x (- (* y (* y 4.0)))) (fma x x (* (* y 4.0) y)))

series475.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(cbrt (pow (/ (fma x x (- (* y (* y 4.0)))) (fma x x (* (* y 4.0) y))) 3))
128.0ms
(pow (/ (fma x x (- (* y (* y 4.0)))) (fma x x (* (* y 4.0) y))) 3)
90.0ms
(fma x x (- (* y (* y 4.0))))
133.0ms
(/ (fma x x (- (* y (* y 4.0)))) (fma x x (* (* y 4.0) y)))

simplify1.2s

Counts
143 → 143
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01494354
13483915
211003533
done50013399

prune591.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.3b

regimes154.0ms

Accuracy

54.4% (14.3b remaining)

Error of 14.6b against oracle of 0.4b and baseline of 31.7b

bsearch147.0ms

Steps
ItersRangePoint
7
1297230358.0715733
27128352222.409004
10274298981.38737
6
-1.05219316141597e-55
-8.303856826304397e-57
-9.03291647064193e-57
8
-4.27526971693393e+82
-5.849132443619543e+79
-4.219332295965777e+82

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02133
12833
23533
done3533

end0.0ms

sample885.0ms

Algorithm
intervals
Results
585.0ms8000×body80valid