Details

Time bar (total: 15.1s)

sample64.0ms

Algorithm
intervals
Results
18.0ms188×body80valid
11.0ms36×body2560valid
6.0ms24×body1280valid
5.0ms108×body80nan
3.0ms17×body640valid
2.0ms5×body5120valid
1.0ms6×body320valid
0.0ms5×body160valid

simplify135.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01417
12517
24616
38616
411916
512816
done12816

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.4b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
82.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
13.0ms
(- (* b b) (* 4.0 (* a c)))
54.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series442.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
65.0ms
(- (* b b) (* 4.0 (* a c)))
110.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
112.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.3s

Counts
102 → 102
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01651697
14481588
218601361
done50001352

prune461.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize26.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
2.0b
(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
8.0b
(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite331.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 232
Calls
4 calls:
49.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
129.0ms
(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
107.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
19.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series740.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
266.0ms
(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
286.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
87.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify583.0ms

Counts
244 → 244
Iterations

Useful iterations: done (573.0ms)

IterNodesCost
033710067
18567629
done50006649

prune820.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.0b

localize45.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
2.0b
(* (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
8.0b
(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite372.0ms

Algorithm
rewrite-expression-head
Rules
109×add-sqr-sqrt
103×*-un-lft-identity
71×add-cube-cbrt
60×prod-diff
51×add-exp-log
46×times-frac
41×sqrt-prod
29×distribute-rgt-neg-in
27×associate-*l* add-cbrt-cube
21×distribute-lft-neg-in
20×prod-exp
16×div-exp distribute-lft-out-- difference-of-squares
10×fma-neg
8×cbrt-undiv cbrt-unprod add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-/r*
4×expm1-log1p-u rec-exp flip3-- 1-exp associate-/r/ flip-- log1p-expm1-u
3×div-inv associate-/l*
2×sqrt-div diff-log associate-/l/ unswap-sqr
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 227
Calls
4 calls:
42.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
175.0ms
(* (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
97.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
31.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series714.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
253.0ms
(* (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
257.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
103.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify702.0ms

Counts
239 → 239
Iterations

Useful iterations: done (690.0ms)

IterNodesCost
03429661
19627185
done50016075

prune886.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* 4.0 (* a c)))
1.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.4b
(/ (* (* 4.0 c) a) (* 2.0 a))
22.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
51×add-sqr-sqrt
50×*-un-lft-identity
46×add-cube-cbrt
34×sqrt-prod
25×add-exp-log add-cbrt-cube
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×prod-exp cbrt-unprod
7×neg-mul-1
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 150
Calls
4 calls:
20.0ms
(- (* b b) (* 4.0 (* a c)))
64.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
36.0ms
(/ (* (* 4.0 c) a) (* 2.0 a))
29.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series294.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (* b b) (* 4.0 (* a c)))
103.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(/ (* (* 4.0 c) a) (* 2.0 a))
106.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.1s

Counts
162 → 162
Iterations

Useful iterations: 2 (576.0ms)

IterNodesCost
02426252
16404235
237973241
done50003241

prune674.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.0b

regimes210.0ms

Accuracy

94.4% (1.4b remaining)

Error of 6.6b against oracle of 5.3b and baseline of 29.5b

bsearch274.0ms

Steps
ItersRangePoint
6
1.9101351599902807e+102
2.525038855038462e+103
1.4066822953018111e+103
5
-1.7140185252229956e-250
-6.426569281983545e-251
-8.441935351115962e-251
10
-2.8734245235493903e+48
-2.602501271628617e+37
-2.8472042802820317e+48

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03867
14763
24863
done4863

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.1s1074×body2560valid
705.0ms5856×body80valid
349.0ms903×body1280valid
308.0ms2902×body80nan
224.0ms451×body640valid
63.0ms112×body5120valid
54.0ms223×body320valid
16.0ms111×body160valid