Details

Time bar (total: 17.2s)

sample170.0ms

Algorithm
intervals
Results
58.0ms165×body160valid
34.0ms518×pre80true
33.0ms262×body80nan
13.0ms32×body320valid
8.0ms59×body80valid

simplify103.0ms

Counts
1 → 1
Iterations
IterNodes
done102
7102
6101
599
491
373
241
122
012

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (fma -3 (* c a) (* b b)))
0.1b
(fma -3 (* c a) (* b b))
0.3b
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
40.0b
(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
18×prod-diff sqrt-prod
9×add-cbrt-cube add-exp-log
6×times-frac fma-neg associate-/l* add-log-exp difference-of-squares
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp cbrt-unprod fma-udef div-inv
Counts
4 → 102
Calls
4 calls:
2.0ms
(sqrt (fma -3 (* c a) (* b b)))
0.0ms
(fma -3 (* c a) (* b b))
24.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
8.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)

series386.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(sqrt (fma -3 (* c a) (* b b)))
72.0ms
(fma -3 (* c a) (* b b))
101.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
97.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify1.1s

Counts
114 → 114
Iterations
IterNodes
done2000
32000
2940
1347
0152

prune664.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 39.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma -3 (* c a) (* b b))
0.1b
(fma -3 (* c a) (* b b))
0.3b
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
42.8b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
9×add-cbrt-cube add-exp-log
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×times-frac fma-udef associate-/l*
2×cbrt-undiv div-exp
1×clear-num associate-/r* frac-2neg prod-exp cbrt-unprod div-inv
Counts
4 → 57
Calls
4 calls:
0.0ms
(fma -3 (* c a) (* b b))
0.0ms
(fma -3 (* c a) (* b b))
7.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
0.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.2s

Counts
4 → 12
Calls
4 calls:
68.0ms
(fma -3 (* c a) (* b b))
88.0ms
(fma -3 (* c a) (* b b))
654.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
438.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.2s

Counts
69 → 69
Iterations
IterNodes
done2005
32005
2672
1231
0112

prune718.0ms

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 39.6b

localize58.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
0.5b
(cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))))
0.5b
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
42.8b
(fma (sqrt (sqrt (cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1
12×add-sqr-sqrt
11×add-cbrt-cube add-exp-log
9×*-un-lft-identity add-cube-cbrt
7×pow-plus pow-prod-up
6×associate-*r*
5×fma-udef
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×pow2 swap-sqr pow-sqr
2×distribute-rgt-in distribute-lft-in pow3 *-commutative unswap-sqr
1×cbrt-prod pow1/3 rem-cbrt-cube
Counts
4 → 87
Calls
4 calls:
38.0ms
(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
21.0ms
(cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))))
12.0ms
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
1.0ms
(fma (sqrt (sqrt (cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series800.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
84.0ms
(cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))))
87.0ms
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
452.0ms
(fma (sqrt (sqrt (cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.3s

Counts
99 → 99
Iterations
IterNodes
done2011
32011
2947
1327
0140

prune835.0ms

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 39.6b

localize96.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
0.5b
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
3.4b
(pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3)
42.8b
(fma (sqrt (sqrt (pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
50×pow1
17×add-exp-log
13×add-sqr-sqrt pow-plus pow-prod-up
12×pow-pow
11×add-cbrt-cube
10×*-un-lft-identity add-cube-cbrt
7×pow-prod-down prod-exp
6×associate-*r*
5×pow2 pow-sqr fma-udef
4×expm1-log1p-u associate-*l* cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow swap-sqr pow-exp
2×distribute-rgt-in distribute-lft-in pow3 *-commutative unswap-sqr
1×pow-to-exp unpow-prod-down unpow1/3 sqr-pow
Counts
4 → 106
Calls
4 calls:
39.0ms
(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
13.0ms
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
28.0ms
(pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3)
1.0ms
(fma (sqrt (sqrt (pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series899.0ms

Counts
4 → 12
Calls
4 calls:
201.0ms
(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
87.0ms
(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
228.0ms
(pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3)
383.0ms
(fma (sqrt (sqrt (pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.3s

Counts
118 → 118
Iterations
IterNodes
done2013
32013
21330
1443
0175

prune704.0ms

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 39.5b

regimes761.0ms

Accuracy

0% (2.6b remaining)

Error of 43.0b against oracle of 40.3b and baseline of 43.0b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done27
127
023

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.5s4798×body160valid
974.0ms8276×body80nan
885.0ms16276×pre80true
562.0ms1400×body320valid
272.0ms1802×body80valid