Details

Time bar (total: 16.3s)

sample78.0ms

Algorithm
intervals
Results
13.0ms32×body2560valid
13.0ms185×body80valid
11.0ms31×body1280valid
7.0ms108×body80nan
3.0ms6×body5120valid
3.0ms11×body640valid
2.0ms7×body320valid
1.0ms6×body160valid

simplify520.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12817
26417
311417
414117
515117
615517
done15517

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize20.0ms

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)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite210.0ms

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:
137.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
27.0ms
(- (* b b) (* 4.0 (* a c)))
30.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series496.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
71.0ms
(- (* b b) (* 4.0 (* a c)))
136.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
117.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify900.0ms

Counts
89 → 89
Iterations

Useful iterations: done (891.0ms)

IterNodesCost
01571750
14181650
216441474
done50001466

prune316.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.8b

localize32.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.7b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
7.9b
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite312.0ms

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:
60.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
144.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
82.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
15.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series771.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
235.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
297.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
94.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.3s

Counts
153 → 153
Iterations

Useful iterations: 2 (693.0ms)

IterNodesCost
02504579
16494063
236203761
done50013761

prune620.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.8b

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.7b
(/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
7.9b
(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite227.0ms

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:
51.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
82.0ms
(/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
71.0ms
(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series676.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
132.0ms
(/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
346.0ms
(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
97.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.2s

Counts
125 → 125
Iterations

Useful iterations: 2 (570.0ms)

IterNodesCost
02233302
16693102
243492566
done50012566

prune566.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
11.8b
(/ (* 2.0 a) (* 4.0 (* a c)))
23.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×add-log-exp
7×*-un-lft-identity
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 clear-num associate-/r* div-inv associate-/l* distribute-lft-out--
Counts
4 → 67
Calls
4 calls:
9.0ms
(- (* b b) (* 4.0 (* a c)))
82.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
26.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
19.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series317.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- (* b b) (* 4.0 (* a c)))
134.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
17.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
102.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts
79 → 79
Iterations

Useful iterations: 2 (317.0ms)

IterNodesCost
01471248
14121138
22268920
done5000920

prune260.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.8b

regimes442.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.4b against oracle of 5.3b and baseline of 29.5b

bsearch298.0ms

Steps
ItersRangePoint
6
1.9101351599902807e+102
2.525038855038462e+103
5.81008349881366e+102
8
1.0408663060912465e-291
3.4349488111407062e-289
1.4736206571352836e-291
9
-2.501158360438979e+160
-5.198860796817705e+153
-5.562666016748883e+153

simplify18.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
03765
14663
24963
35163
done5163

end0.0ms

sample3.4s

Algorithm
intervals
Results
678.0ms5808×body80valid
649.0ms465×body640valid
620.0ms1050×body2560valid
372.0ms936×body1280valid
289.0ms2896×body80nan
96.0ms111×body5120valid
61.0ms105×body160valid
52.0ms234×body320valid