Details

Time bar (total: 8.7s)

sample40.0ms

Algorithm
intervals
Results
8.0ms201×body80valid
7.0ms35×body1280valid
6.0ms27×body2560valid
3.0ms87×body80nan
2.0ms12×body640valid
1.0ms7×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify96.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12917
26417
311917
414117
514717
615017
done15017

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
46.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
17.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series296.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify746.0ms

Counts
169 → 169
Iterations

Useful iterations: done (739.0ms)

IterNodesCost
02436690
15784705
217913760
done50003759

prune380.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
60×add-sqr-sqrt
57×*-un-lft-identity
49×add-cube-cbrt
35×sqrt-prod
23×add-exp-log distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-cbrt-cube
11×fma-neg
10×prod-exp add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-*l*
5×flip3-- flip--
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 165
Calls
4 calls:
58.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify969.0ms

Counts
177 → 177
Iterations

Useful iterations: done (962.0ms)

IterNodesCost
02696947
16424848
219843851
done50003850

prune354.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))) (* 2.0 a))
0.3b
(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
1.3b
(fma b b (- (* (* a c) 4.0)))
20.5b
(sqrt (fma b b (- (* (* a c) 4.0))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
60×*-un-lft-identity prod-diff
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv flip3-- diff-log div-exp flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod fma-udef div-inv
Counts
4 → 149
Calls
4 calls:
32.0ms
(/ (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))) (* 2.0 a))
12.0ms
(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
0.0ms
(fma b b (- (* (* a c) 4.0)))
1.0ms
(sqrt (fma b b (- (* (* a c) 4.0))))

series333.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))) (* 2.0 a))
88.0ms
(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
51.0ms
(fma b b (- (* (* a c) 4.0)))
83.0ms
(sqrt (fma b b (- (* (* a c) 4.0))))

simplify671.0ms

Counts
161 → 161
Iterations

Useful iterations: done (665.0ms)

IterNodesCost
02226500
15064536
214153612
done50003603

prune327.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

localize19.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
2.7b
(/ (/ (+ (* (* a c) 4.0) (* b (- b b))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.3b
(/ (+ (* (* a c) 4.0) (* b (- b b))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
20.5b
(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
78×times-frac
72×*-un-lft-identity
50×add-cube-cbrt
27×associate-/l*
26×sqrt-prod
22×difference-of-squares
18×add-exp-log prod-diff add-cbrt-cube
11×distribute-lft-out--
7×cbrt-undiv div-exp associate-/r*
6×fma-neg associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 173
Calls
4 calls:
47.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
79.0ms
(/ (/ (+ (* (* a c) 4.0) (* b (- b b))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (* 2.0 a))
52.0ms
(/ (+ (* (* a c) 4.0) (* b (- b b))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
14.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

series532.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
168.0ms
(/ (/ (+ (* (* a c) 4.0) (* b (- b b))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (* 2.0 a))
206.0ms
(/ (+ (* (* a c) 4.0) (* b (- b b))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
75.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify1.1s

Counts
185 → 185
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02906139
17285272
224494386
done50004384

prune509.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

regimes217.0ms

Accuracy

81.6% (4.8b remaining)

Error of 10.6b against oracle of 5.8b and baseline of 31.9b

bsearch101.0ms

Steps
ItersRangePoint
8
2.1878188410446244e+107
3.8616146939177386e+111
3.6627135292415903e+111
8
-4.854151311909829e-126
-9.294658666337375e-130
-4.7828589349284326e-126

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02737
13537
done3537

end0.0ms

sample1.2s

Algorithm
intervals
Results
260.0ms1110×body2560valid
230.0ms5789×body80valid
166.0ms885×body1280valid
117.0ms2998×body80nan
69.0ms448×body640valid
29.0ms101×body5120valid
28.0ms253×body320valid
12.0ms126×body160valid