Details

Time bar (total: 18.4s)

sample129.0ms

Algorithm
intervals
Results
37.0ms272×body80nan
23.0ms162×body160valid
16.0ms528×pre80true
9.0ms46×body320valid
3.0ms48×body80valid

simplify101.0ms

Counts
1 → 1
Iterations
IterNodes
done128
5128
4119
386
246
125
014

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.7b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (fma (- a) (* 4.0 c) (* b b)))
0.1b
(fma (- a) (* 4.0 c) (* b b))
0.2b
(/ (- (sqrt (fma (- a) (* 4.0 c) (* b b))) b) a)
41.0b
(- (sqrt (fma (- a) (* 4.0 c) (* b b))) b)

rewrite52.0ms

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 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 → 110
Calls
4 calls:
1.0ms
(sqrt (fma (- a) (* 4.0 c) (* b b)))
0.0ms
(fma (- a) (* 4.0 c) (* b b))
28.0ms
(/ (- (sqrt (fma (- a) (* 4.0 c) (* b b))) b) a)
18.0ms
(- (sqrt (fma (- a) (* 4.0 c) (* b b))) b)

series485.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(sqrt (fma (- a) (* 4.0 c) (* b b)))
93.0ms
(fma (- a) (* 4.0 c) (* b b))
157.0ms
(/ (- (sqrt (fma (- a) (* 4.0 c) (* b b))) b) a)
122.0ms
(- (sqrt (fma (- a) (* 4.0 c) (* b b))) b)

simplify878.0ms

Counts
122 → 122
Iterations
IterNodes
done5001
21064
1336
0152

prune734.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))
0.1b
(fma 4.0 (* c (- a)) (* b b))
0.2b
(/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b)))))
0.2b
(/ (/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))) a)

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
99×*-un-lft-identity
65×add-sqr-sqrt add-cube-cbrt
21×associate-/l*
17×distribute-lft-out
11×add-cbrt-cube add-exp-log
10×associate-/r/
7×associate-/r*
6×flip3-+ flip-+ div-inv add-log-exp
4×expm1-log1p-u pow1 cbrt-undiv div-exp log1p-expm1-u
3×fma-def
2×clear-num frac-2neg
1×+-commutative sum-log fma-udef associate-/l/
Counts
4 → 154
Calls
4 calls:
5.0ms
(+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))
0.0ms
(fma 4.0 (* c (- a)) (* b b))
11.0ms
(/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b)))))
42.0ms
(/ (/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))) a)

series880.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))
70.0ms
(fma 4.0 (* c (- a)) (* b b))
333.0ms
(/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b)))))
351.0ms
(/ (/ (fma (- (* a 4.0)) c 0) (+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))) a)

simplify1.2s

Counts
166 → 166
Iterations
IterNodes
done5000
22553
1606
0251

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ b (sqrt (fma (- a) (* 4.0 c) (* b b))))
0.1b
(fma (- a) (* 4.0 c) (* b b))
0.1b
(* a (+ b (sqrt (fma (- a) (* 4.0 c) (* b b)))))
0.4b
(/ (- (* a (* 4.0 c))) (* a (+ b (sqrt (fma (- a) (* 4.0 c) (* b b))))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×add-sqr-sqrt add-cbrt-cube add-exp-log
9×add-cube-cbrt
6×pow1 times-frac associate-/l* add-log-exp
4×expm1-log1p-u associate-*r* associate-*r/ log1p-expm1-u
3×fma-def flip3-+ associate-*l* flip-+
2×distribute-lft-neg-in cbrt-undiv neg-mul-1 distribute-rgt-neg-in div-exp prod-exp associate-/r/ cbrt-unprod distribute-lft-out
1×neg-sub0 distribute-rgt-in +-commutative clear-num associate-/r* sum-log frac-2neg distribute-lft-in div-sub pow-prod-down distribute-frac-neg *-commutative fma-udef div-inv unswap-sqr
Counts
4 → 85
Calls
4 calls:
5.0ms
(+ b (sqrt (fma (- a) (* 4.0 c) (* b b))))
0.0ms
(fma (- a) (* 4.0 c) (* b b))
19.0ms
(* a (+ b (sqrt (fma (- a) (* 4.0 c) (* b b)))))
23.0ms
(/ (- (* a (* 4.0 c))) (* a (+ b (sqrt (fma (- a) (* 4.0 c) (* b b))))))

series585.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(+ b (sqrt (fma (- a) (* 4.0 c) (* b b))))
66.0ms
(fma (- a) (* 4.0 c) (* b b))
128.0ms
(* a (+ b (sqrt (fma (- a) (* 4.0 c) (* b b)))))
268.0ms
(/ (- (* a (* 4.0 c))) (* a (+ b (sqrt (fma (- a) (* 4.0 c) (* b b))))))

simplify1.1s

Counts
97 → 97
Iterations
IterNodes
done5000
22286
1421
0152

prune768.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ b (sqrt (fma c (* 4.0 (- a)) (* b b)))) (- (* 4.0 a)))
0.1b
(fma c (* 4.0 (- a)) (* b b))
0.2b
(/ 1 (* (/ (+ b (sqrt (fma c (* 4.0 (- a)) (* b b)))) (- (* 4.0 a))) (/ a c)))
0.4b
(* (/ (+ b (sqrt (fma c (* 4.0 (- a)) (* b b)))) (- (* 4.0 a))) (/ a c))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
64×times-frac
62×*-un-lft-identity add-exp-log
48×add-sqr-sqrt
36×add-cbrt-cube add-cube-cbrt
28×associate-*l*
27×div-exp
16×prod-exp
14×cbrt-undiv
13×associate-*r* distribute-lft-out
9×distribute-lft-neg-in pow1 neg-mul-1 distribute-rgt-neg-in
8×cbrt-unprod
7×associate-/r* associate-/l*
5×rec-exp 1-exp
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp unswap-sqr
3×associate-/r/
2×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ pow-flip associate-/l/
1×flip3-+ *-commutative flip-+ fma-udef inv-pow
Counts
4 → 172
Calls
4 calls:
18.0ms
(/ (+ b (sqrt (fma c (* 4.0 (- a)) (* b b)))) (- (* 4.0 a)))
0.0ms
(fma c (* 4.0 (- a)) (* b b))
28.0ms
(/ 1 (* (/ (+ b (sqrt (fma c (* 4.0 (- a)) (* b b)))) (- (* 4.0 a))) (/ a c)))
67.0ms
(* (/ (+ b (sqrt (fma c (* 4.0 (- a)) (* b b)))) (- (* 4.0 a))) (/ a c))

series541.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ (+ b (sqrt (fma c (* 4.0 (- a)) (* b b)))) (- (* 4.0 a)))
86.0ms
(fma c (* 4.0 (- a)) (* b b))
191.0ms
(/ 1 (* (/ (+ b (sqrt (fma c (* 4.0 (- a)) (* b b)))) (- (* 4.0 a))) (/ a c)))
136.0ms
(* (/ (+ b (sqrt (fma c (* 4.0 (- a)) (* b b)))) (- (* 4.0 a))) (/ a c))

simplify2.0s

Counts
184 → 184
Iterations
IterNodes
done5000
24497
1849
0288

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes294.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.2s

Iterations
IterNodes
done5000
122668
111482
10872
9550
8372
7266
6193
5128
480
361
249
135
021

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.1s16517×pre80true
905.0ms4827×body160valid
762.0ms8517×body80nan
681.0ms1361×body320valid
239.0ms1812×body80valid