Details

Time bar (total: 12.5s)

sample43.0ms

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

simplify116.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12817
26417
311417
413017
513717
614117
done14117

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize12.0ms

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))))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in 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 → 77
Calls
4 calls:
62.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
24.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(- (* b b) (* 4.0 (* a c)))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series302.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.3s

Counts
89 → 89
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
01571750
14021650
213221474
349551459
done50001459

prune234.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite210.0ms

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt
78×times-frac
58×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
22×difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-lft-out--
7×cbrt-undiv div-exp associate-/r*
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×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 → 141
Calls
4 calls:
40.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
94.0ms
(/ (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
60.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series575.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
215.0ms
(/ (/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
206.0ms
(/ (+ 0 (* (* 4.0 c) a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts
153 → 153
Iterations

Useful iterations: 2 (467.0ms)

IterNodesCost
02534579
16224057
225713753
done50003753

prune413.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log add-cbrt-cube
32×add-sqr-sqrt
30×times-frac
21×*-un-lft-identity
18×associate-/r*
17×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
11×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod
7×associate-/r/
6×add-log-exp
5×pow1 flip3-- flip-- distribute-lft-out--
4×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 → 113
Calls
4 calls:
42.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
65.0ms
(/ (* 2.0 a) (/ (* (* 4.0 c) a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
59.0ms
(/ (* (* 4.0 c) a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series469.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
95.0ms
(/ (* 2.0 a) (/ (* (* 4.0 c) a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
207.0ms
(/ (* (* 4.0 c) a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
77.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts
125 → 125
Iterations

Useful iterations: 2 (459.0ms)

IterNodesCost
02263312
16123108
229272426
done50022426

prune336.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (/ 1 1) (/ 2.0 (/ (* 4.0 c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
1.0b
(- (* b b) (* 4.0 (* a c)))
1.2b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
1667×times-frac
738×add-sqr-sqrt
651×*-un-lft-identity
565×add-cube-cbrt
99×associate-/r/ div-inv
98×add-exp-log
86×difference-of-squares
79×div-exp
46×sqrt-prod
45×flip3-- flip--
43×distribute-lft-out--
41×associate-/r*
36×add-cbrt-cube
22×cbrt-undiv
20×1-exp
13×associate-/l*
8×rec-exp add-log-exp
7×prod-exp
5×pow1
2×sub-neg sqrt-div diff-log cbrt-unprod
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 677
Calls
4 calls:
76.0ms
(/ (/ 1 1) (/ 2.0 (/ (* 4.0 c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
8.0ms
(- (* b b) (* 4.0 (* a c)))
43.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series422.0ms

Counts
4 → 12
Calls
4 calls:
205.0ms
(/ (/ 1 1) (/ 2.0 (/ (* 4.0 c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
47.0ms
(- (* b b) (* 4.0 (* a c)))
87.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
82.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.2s

Counts
689 → 689
Iterations

Useful iterations: 2 (1.5s)

IterNodesCost
0108630023
1274923510
2477322102
done500122102

prune438.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.4b

regimes220.0ms

Accuracy

76.7% (5.6b remaining)

Error of 10.9b against oracle of 5.3b and baseline of 29.3b

bsearch174.0ms

Steps
ItersRangePoint
3
1.0157310028094029e-63
1.3160112691565966e-63
1.031355438277998e-63
6
3.6410892437809104e-110
3.0960233903298005e-109
3.7052502960789305e-110
8
1.0691773024250323e-170
5.5548132533506025e-168
5.330769455174493e-168
9
-1.4924982923623064e+60
-5.817343306680769e+54
-3.203999247190538e+59

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04897
15993
done5993

end0.0ms

sample1.2s

Algorithm
intervals
Results
241.0ms1077×body2560valid
201.0ms5761×body80valid
154.0ms912×body1280valid
95.0ms2832×body80nan
64.0ms463×body640valid
31.0ms105×body5120valid
27.0ms249×body320valid
8.0ms118×body160valid