Details

Time bar (total: 19.9s)

sample119.0ms

Algorithm
intervals
Results
32.0ms40×body2560valid
19.0ms181×body80valid
13.0ms26×body1280valid
10.0ms92×body80nan
6.0ms14×body640valid
5.0ms7×body5120valid
1.0ms5×body320valid
1.0ms3×body160valid

simplify219.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12817
26417
311417
413017
513717
614117
done14117

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite190.0ms

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:
113.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
26.0ms
(- (* b b) (* 4.0 (* a c)))
39.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series434.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
73.0ms
(- (* b b) (* 4.0 (* a c)))
124.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
111.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.7s

Counts
89 → 89
Iterations

Useful iterations: 3 (1.7s)

IterNodesCost
01571750
14021650
213171474
349661459
done50001459

prune326.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

localize33.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.8b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
8.4b
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite321.0ms

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:
51.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
154.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
94.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
16.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series801.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
278.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
299.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
93.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
153 → 153
Iterations

Useful iterations: 2 (606.0ms)

IterNodesCost
02534579
16194057
224603753
done50003753

prune637.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize22.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.9b
(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
8.4b
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite429.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
51×add-exp-log
44×*-un-lft-identity
40×times-frac
28×add-cube-cbrt
27×add-cbrt-cube
24×associate-*l*
20×prod-exp
16×div-exp difference-of-squares
11×sqrt-prod
8×cbrt-undiv cbrt-unprod distribute-lft-out--
7×pow1 associate-*r*
6×associate-/r* add-log-exp
4×rec-exp flip3-- 1-exp associate-/r/ flip--
3×div-inv associate-/l*
2×sqrt-div associate-/l/ unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 139
Calls
4 calls:
78.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
220.0ms
(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
107.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series813.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
272.0ms
(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
297.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
116.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
151 → 151
Iterations

Useful iterations: 2 (650.0ms)

IterNodesCost
02584293
16783713
226683279
done50003279

prune596.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.3b

localize36.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (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)))
8.4b
(/ (* (* 4.0 a) c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite306.0ms

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:
84.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
117.0ms
(/ (* 2.0 a) (/ (* (* 4.0 a) c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
79.0ms
(/ (* (* 4.0 a) c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
17.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series712.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
139.0ms
(/ (* 2.0 a) (/ (* (* 4.0 a) c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
325.0ms
(/ (* (* 4.0 a) c) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
128.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.8s

Counts
125 → 125
Iterations

Useful iterations: 2 (641.0ms)

IterNodesCost
02263312
16063108
228612560
done50012560

prune488.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

regimes326.0ms

Accuracy

95.7% (1.1b remaining)

Error of 6.3b against oracle of 5.3b and baseline of 29.6b

bsearch419.0ms

Steps
ItersRangePoint
10
4.61796087672408e+142
1.3206820209921783e+153
3.1607591925776442e+143
10
-8.239971213717205e-281
-2.1361244948559116e-295
-2.182382645844659e-295
8
-1.769171722317776e+149
-1.7344183351890289e+146
-5.263290697710818e+146

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03767
14567
done4567

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.2s1095×body2560valid
654.0ms956×body1280valid
625.0ms5729×body80valid
304.0ms457×body640valid
247.0ms2914×body80nan
80.0ms119×body5120valid
62.0ms241×body320valid
20.0ms115×body160valid