Details

Time bar (total: 22.6s)

sample140.0ms

Algorithm
intervals
Results
49.0ms148×body160valid
27.0ms306×body80nan
26.0ms562×pre80true
14.0ms49×body320valid
6.0ms59×body80valid

simplify105.0ms

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: 43.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (fma (* -3 a) c (* b b)))
0.2b
(fma (* -3 a) c (* b b))
0.3b
(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
37.9b
(- (sqrt (fma (* -3 a) c (* b b))) b)

rewrite28.0ms

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:
1.0ms
(sqrt (fma (* -3 a) c (* b b)))
0.0ms
(fma (* -3 a) c (* b b))
18.0ms
(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
7.0ms
(- (sqrt (fma (* -3 a) c (* b b))) b)

series489.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(sqrt (fma (* -3 a) c (* b b)))
73.0ms
(fma (* -3 a) c (* b b))
165.0ms
(/ (- (sqrt (fma (* -3 a) c (* b b))) b) (* 3 a))
109.0ms
(- (sqrt (fma (* -3 a) c (* b b))) b)

simplify1.3s

Counts
114 → 114
Iterations
IterNodes
done5001
21256
1349
0152

prune690.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 40.5b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (* -3 a) c (* b b))
0.2b
(fma (* -3 a) c (* b b))
0.4b
(/ (fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)) (* 3 a))
43.3b
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* 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 a) c (* b b))
0.0ms
(fma (* -3 a) c (* b b))
7.0ms
(/ (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))

series979.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(fma (* -3 a) c (* b b))
74.0ms
(fma (* -3 a) c (* b b))
441.0ms
(/ (fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)) (* 3 a))
383.0ms
(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

prune655.0ms

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 40.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ (fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)) (* 3 a)))
43.3b
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
43.3b
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
43.3b
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
7×cbrt-prod
6×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×times-frac fma-udef
1×cbrt-div pow1/3 div-inv
Counts
4 → 52
Calls
4 calls:
7.0ms
(cbrt (/ (fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)) (* 3 a)))
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))

series2.0s

Counts
4 → 12
Calls
4 calls:
790.0ms
(cbrt (/ (fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b)) (* 3 a)))
381.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
431.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
436.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))

simplify2.4s

Counts
64 → 64
Iterations
IterNodes
done5001
21160
1329
0158

prune895.0ms

Pruning

38 alts after pruning (38 fresh and 0 done)

Merged error: 40.4b

localize123.0ms

Local error

Found 4 expressions with local error:

43.3b
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
43.3b
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
43.3b
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
43.3b
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* 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 (* -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))

series1.8s

Counts
4 → 12
Calls
4 calls:
497.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
436.0ms
(fma (sqrt (sqrt (fma (* -3 a) c (* b b)))) (sqrt (sqrt (fma (* -3 a) c (* b b)))) (- b))
449.0ms
(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))

simplify1.1s

Counts
56 → 56
Iterations
IterNodes
done5000
3872
2217
188
048

prune571.0ms

Pruning

42 alts after pruning (42 fresh and 0 done)

Merged error: 40.4b

regimes1.2s

Accuracy

0% (3.2b remaining)

Error of 43.3b against oracle of 40.2b and baseline of 43.3b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done24
124
020

end0.0ms

sample5.5s

Algorithm
intervals
Results
1.5s16382×pre80true
1.2s4831×body160valid
1.0s8382×body80nan
532.0ms1395×body320valid
249.0ms1774×body80valid