Details

Time bar (total: 13.1s)

sample44.0ms

Algorithm
intervals
Results
8.0ms37×body2560valid
6.0ms175×body80valid
5.0ms32×body1280valid
4.0ms104×body80nan
2.0ms17×body640valid
1.0ms3×body5120valid
1.0ms6×body320valid
0.0ms4×body160valid

simplify119.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12917
26417
312017
414517
515217
615617
done15617

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite144.0ms

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:
82.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
31.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(- (* b b) (* 4.0 (* a c)))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series317.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
87.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
53.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify998.0ms

Counts
169 → 169
Iterations

Useful iterations: done (992.0ms)

IterNodesCost
02436690
15874705
217513760
done50003113

prune366.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize19.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
6.9b
(/ (/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (* 2.0 a))
11.2b
(/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
23.4b
(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite331.0ms

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:
85.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
132.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (* 2.0 a))
88.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
18.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

series592.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
214.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (* 2.0 a))
212.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
80.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify1.2s

Counts
185 → 185
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02895475
17064741
227034291
done50024223

prune540.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize20.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
6.6b
(/ (* 2.0 a) (/ (* c (* 4.0 a)) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)))
11.2b
(/ (* c (* 4.0 a)) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
23.4b
(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite279.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
45×add-exp-log add-cbrt-cube
35×*-un-lft-identity
30×times-frac
25×add-cube-cbrt
20×sqrt-prod
18×prod-diff associate-/r*
17×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
10×difference-of-squares
7×associate-/r/
6×fma-neg add-log-exp
5×pow1 flip3-- flip-- distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u div-inv
2×frac-2neg sqrt-div clear-num associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 145
Calls
4 calls:
84.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
87.0ms
(/ (* 2.0 a) (/ (* c (* 4.0 a)) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)))
84.0ms
(/ (* c (* 4.0 a)) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
18.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

series471.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
94.0ms
(/ (* 2.0 a) (/ (* c (* 4.0 a)) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)))
209.0ms
(/ (* c (* 4.0 a)) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
80.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify1.4s

Counts
157 → 157
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02624190
16943781
230363086
done50003019

prune410.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 4 expressions with local error:

6.9b
(/ (/ (/ (* c (* 4.0 a)) (sqrt (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))) (sqrt (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))) (* 2.0 a))
7.2b
(/ (* c (* 4.0 a)) (sqrt (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)))
23.4b
(sqrt (- (pow b 2) (* 4.0 (* a c))))
23.4b
(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite415.0ms

Algorithm
rewrite-expression-head
Rules
582×times-frac
356×sqrt-prod
328×add-sqr-sqrt
226×*-un-lft-identity
142×associate-/l*
126×add-cube-cbrt
100×difference-of-squares
58×add-exp-log add-cbrt-cube
50×distribute-lft-out--
46×sqrt-div
42×associate-/r/
27×cbrt-undiv div-exp
23×flip3-- flip--
22×div-inv
14×prod-exp cbrt-unprod
10×associate-/r*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 389
Calls
4 calls:
254.0ms
(/ (/ (/ (* c (* 4.0 a)) (sqrt (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))) (sqrt (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))) (* 2.0 a))
85.0ms
(/ (* c (* 4.0 a)) (sqrt (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)))
19.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))
20.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

series885.0ms

Counts
4 → 12
Calls
4 calls:
205.0ms
(/ (/ (/ (* c (* 4.0 a)) (sqrt (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))) (sqrt (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))) (* 2.0 a))
529.0ms
(/ (* c (* 4.0 a)) (sqrt (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)))
77.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))
73.0ms
(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify2.0s

Counts
401 → 401
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
055819027
1140616533
2496715355
done500015355

prune975.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 5.4b

regimes277.0ms

Accuracy

80.3% (5.3b remaining)

Error of 10.6b against oracle of 5.3b and baseline of 32.4b

bsearch96.0ms

Steps
ItersRangePoint
6
2.0335150395734557e+19
1.0746392320557105e+20
4.652262621973548e+19
9
-2.2937511015552136e-106
-2.1895844909113535e-111
-6.151530580746178e-108

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02941
13641
done3641

end0.0ms

sample1.2s

Algorithm
intervals
Results
230.0ms1077×body2560valid
214.0ms5761×body80valid
163.0ms912×body1280valid
97.0ms2832×body80nan
64.0ms463×body640valid
27.0ms105×body5120valid
25.0ms249×body320valid
11.0ms118×body160valid