Details

Time bar (total: 22.0s)

sample114.0ms

Algorithm
intervals
Results
31.0ms255×body80nan
28.0ms125×body320valid
18.0ms511×pre80true
12.0ms83×body160valid
7.0ms20×body640valid
2.0ms28×body80valid

simplify112.0ms

Counts
1 → 1
Iterations
IterNodes
done126
5126
4118
387
243
122
012

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (fma (* -3 a) c (* b b)))
0.0b
(fma (* -3 a) c (* b b))
0.2b
(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
23.3b
(- (sqrt (fma (* -3 a) c (* b b))) b)

rewrite39.0ms

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 a) c (* b b)))
0.0ms
(fma (* -3 a) c (* b b))
24.0ms
(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
9.0ms
(- (sqrt (fma (* -3 a) c (* b b))) b)

series473.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(sqrt (fma (* -3 a) c (* b b)))
72.0ms
(fma (* -3 a) c (* b b))
163.0ms
(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
127.0ms
(- (sqrt (fma (* -3 a) c (* b b))) b)

simplify1.3s

Counts
114 → 114
Iterations
IterNodes
done5001
21256
1349
0152

prune665.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 50.2b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (* -3 a) c (* b b))
0.0b
(fma (* -3 a) c (* b b))
0.2b
(/ (fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)) (* 3 a))
52.8b
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

rewrite17.0ms

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 a) c (* b b))
0.0ms
(fma (* -3 a) c (* b b))
14.0ms
(/ (fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)) (* 3 a))
1.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

series999.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(fma (* -3 a) c (* b b))
60.0ms
(fma (* -3 a) c (* b b))
380.0ms
(/ (fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)) (* 3 a))
485.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

simplify2.3s

Counts
69 → 69
Iterations
IterNodes
done5000
33464
2722
1232
0112

prune711.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 50.2b

localize78.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)))
52.8b
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
52.8b
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
52.8b
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod fma-udef
1×pow1/3
Counts
4 → 47
Calls
4 calls:
1.0ms
(cbrt (fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)))
0.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
1.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

series1.8s

Counts
4 → 12
Calls
4 calls:
513.0ms
(cbrt (fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)))
400.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
419.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
443.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

simplify2.0s

Counts
59 → 59
Iterations
IterNodes
done5002
33182
2663
1218
0105

prune865.0ms

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 50.2b

localize94.0ms

Local error

Found 4 expressions with local error:

52.8b
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
52.8b
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
52.8b
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
52.8b
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

rewrite1.0ms

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 (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

series1.7s

Counts
4 → 12
Calls
4 calls:
397.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
441.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
462.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
399.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

simplify1.0s

Counts
56 → 56
Iterations
IterNodes
done5000
3872
2217
188
048

prune632.0ms

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 50.1b

regimes1.0s

Accuracy

0% (2.6b remaining)

Error of 51.9b against oracle of 49.3b and baseline of 51.9b

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done31
131
025

end0.0ms

sample5.9s

Algorithm
intervals
Results
1.5s3672×body320valid
1.4s8237×body80nan
1.4s16237×pre80true
687.0ms2939×body160valid
286.0ms493×body640valid
168.0ms896×body80valid