Details

Time bar (total: 23.6s)

sample607.0ms

Algorithm
intervals
Results
63.0ms112×body320valid
28.0ms284×body80nan
25.0ms540×pre80true
18.0ms93×body160valid
7.0ms16×body640valid
4.0ms35×body80valid

simplify108.0ms

Counts
1 → 1
Iterations
IterNodes
done115
5115
4107
385
247
125
014

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (fma (* c a) -4 (* b b)))
0.1b
(fma (* c a) -4 (* b b))
0.1b
(/ (- (sqrt (fma (* c a) -4 (* b b))) b) a)
26.8b
(- (sqrt (fma (* c a) -4 (* b b))) b)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 114
Calls
4 calls:
1.0ms
(sqrt (fma (* c a) -4 (* b b)))
0.0ms
(fma (* c a) -4 (* b b))
22.0ms
(/ (- (sqrt (fma (* c a) -4 (* b b))) b) a)
14.0ms
(- (sqrt (fma (* c a) -4 (* b b))) b)

series398.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(sqrt (fma (* c a) -4 (* b b)))
71.0ms
(fma (* c a) -4 (* b b))
108.0ms
(/ (- (sqrt (fma (* c a) -4 (* b b))) b) a)
125.0ms
(- (sqrt (fma (* c a) -4 (* b b))) b)

simplify1.8s

Counts
126 → 126
Iterations
IterNodes
done5004
32760
2799
1335
0157

prune597.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 48.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (* c a) -4 (* b b))
0.1b
(fma (* c a) -4 (* b b))
0.1b
(/ (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b)) a)
51.2b
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* fma-udef associate-/l*
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 63
Calls
4 calls:
0.0ms
(fma (* c a) -4 (* b b))
0.0ms
(fma (* c a) -4 (* b b))
4.0ms
(/ (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b)) a)
0.0ms
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

series1.2s

Counts
4 → 12
Calls
4 calls:
96.0ms
(fma (* c a) -4 (* b b))
90.0ms
(fma (* c a) -4 (* b b))
560.0ms
(/ (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b)) a)
434.0ms
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

simplify1.8s

Counts
75 → 75
Iterations
IterNodes
done5000
31733
2446
1190
0110

prune759.0ms

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 48.4b

localize64.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))))
51.2b
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
51.2b
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
51.2b
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×cbrt-prod
12×*-un-lft-identity add-cube-cbrt
11×pow1
6×pow1/3 swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×fma-udef
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 76
Calls
4 calls:
24.0ms
(* (cbrt (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))))
0.0ms
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
1.0ms
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

series2.1s

Counts
4 → 12
Calls
4 calls:
874.0ms
(* (cbrt (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))))
402.0ms
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
426.0ms
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
370.0ms
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

simplify2.1s

Counts
88 → 88
Iterations
IterNodes
done5000
32850
2810
1280
0126

prune973.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 47.7b

localize123.0ms

Local error

Found 4 expressions with local error:

51.2b
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
51.2b
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
51.2b
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
51.2b
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 44
Calls
4 calls:
0.0ms
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
1.0ms
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

series1.6s

Counts
4 → 12
Calls
4 calls:
445.0ms
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
355.0ms
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
396.0ms
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
402.0ms
(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

simplify1.9s

Counts
56 → 56
Iterations
IterNodes
done5001
42659
3644
2192
188
048

prune851.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 47.7b

regimes806.0ms

Accuracy

0% (3.2b remaining)

Error of 51.8b against oracle of 48.7b and baseline of 51.8b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done25
125
022

end0.0ms

sample5.7s

Algorithm
intervals
Results
1.9s3699×body320valid
1.1s8340×body80nan
938.0ms16340×pre80true
751.0ms2924×body160valid
435.0ms893×body80valid
212.0ms484×body640valid