Details

Time bar (total: 5.3s)

sample42.0ms

Algorithm
intervals
Results
9.0ms41×body2560valid
7.0ms178×body80valid
5.0ms26×body1280valid
3.0ms75×body80nan
2.0ms14×body640valid
1.0ms7×body320valid
0.0ms3×body160valid

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489
done1489

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite110.0ms

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:
65.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms
(- (* b b) (* 4.0 (* a c)))
26.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Counts
89 → 89
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0404890
11481801
25001796
done5001796

prune248.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
1.0b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 91
Calls
4 calls:
63.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
9.0ms
(- (* b b) (* 4.0 (* a c)))
23.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series303.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
46.0ms
(- (* b b) (* 4.0 (* a c)))
84.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify51.0ms

Counts
103 → 103
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03811101
113431035
250011026
done50011026

prune266.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.4b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* 4.0 (* a c)))
3.1b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
11.1b
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
146×add-sqr-sqrt
113×*-un-lft-identity
81×add-cube-cbrt
32×difference-of-squares
27×associate-/l*
19×sqrt-prod
16×distribute-lft-out--
11×add-exp-log add-cbrt-cube
10×associate-/r/
9×associate-/r*
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 184
Calls
4 calls:
9.0ms
(- (* b b) (* 4.0 (* a c)))
97.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
64.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series514.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* 4.0 (* a c)))
174.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
215.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
77.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify116.0ms

Counts
196 → 196
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
07323440
133893258
250013235
done50013235

prune569.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.3b

localize24.0ms

Local error

Found 4 expressions with local error:

15.5b
(cbrt (+ 0 (* 4.0 (* a c))))
15.5b
(cbrt (+ 0 (* 4.0 (* a c))))
24.6b
(sqrt (- (* b b) (* 4.0 (* a c))))
24.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log cbrt-div sqrt-div add-cbrt-cube add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 pow1/3 flip-- flip-+
Counts
4 → 56
Calls
4 calls:
3.0ms
(cbrt (+ 0 (* 4.0 (* a c))))
6.0ms
(cbrt (+ 0 (* 4.0 (* a c))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series356.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(cbrt (+ 0 (* 4.0 (* a c))))
105.0ms
(cbrt (+ 0 (* 4.0 (* a c))))
77.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Counts
68 → 68
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0239534
1912500
25001480
done5001480

prune346.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.3b

regimes213.0ms

Accuracy

83.5% (4.5b remaining)

Error of 10.0b against oracle of 5.5b and baseline of 32.8b

bsearch108.0ms

Steps
ItersRangePoint
9
5.30600492772346e+88
5.894388948599132e+93
2.5429514865802255e+93
7
-1.9051551317192057e-67
-2.58855871570434e-69
-2.6444093768085776e-69

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03818
13818
done3818

end0.0ms

sample1.2s

Algorithm
intervals
Results
241.0ms1061×body2560valid
224.0ms5877×body80valid
155.0ms852×body1280valid
112.0ms2982×body80nan
66.0ms473×body640valid
30.0ms112×body5120valid
26.0ms243×body320valid
9.0ms123×body160valid