Details

Time bar (total: 10.4s)

sample41.0ms

Algorithm
intervals
Results
7.0ms186×body80valid
6.0ms27×body2560valid
6.0ms31×body1280valid
3.0ms85×body80nan
2.0ms16×body640valid
1.0ms3×body5120valid
0.0ms4×body320valid
0.0ms2×body160valid

simplify106.0ms

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: 35.1b

localize12.0ms

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)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite102.0ms

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:
60.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms
(- (* b b) (* 4.0 (* a c)))
23.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.1s

Counts
89 → 89
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
01571750
14021650
213171474
349661459
done50001459

prune220.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.1b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
8.6b
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
25.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite208.0ms

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 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
59.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series524.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
165.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
203.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify990.0ms

Counts
153 → 153
Iterations

Useful iterations: 2 (383.0ms)

IterNodesCost
02534579
16194057
224603753
done50003753

prune411.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.9b

localize17.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.1b
(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
8.6b
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
25.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite244.0ms

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:
39.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
130.0ms
(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
60.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series534.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
170.0ms
(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
207.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts
151 → 151
Iterations

Useful iterations: 2 (413.0ms)

IterNodesCost
02584293
16783713
226683279
done50003279

prune383.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.9b

localize15.0ms

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
(/ (* (* 4.0 a) c) (* 2.0 a))
25.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite82.0ms

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:
8.0ms
(- (* b b) (* 4.0 (* a c)))
39.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.0ms
(/ (* (* 4.0 a) c) (* 2.0 a))
8.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series217.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* 4.0 (* a c)))
83.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
11.0ms
(/ (* (* 4.0 a) c) (* 2.0 a))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts
79 → 79
Iterations

Useful iterations: 2 (241.0ms)

IterNodesCost
01501246
13931128
21989964
done5000964

prune170.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

regimes172.0ms

Accuracy

96.1% (0.9b remaining)

Error of 7.0b against oracle of 6.0b and baseline of 29.9b

bsearch166.0ms

Steps
ItersRangePoint
9
8.777746745010686e+110
1.2290467223415774e+117
1.1912031425131646e+117
9
-5.951265309377375e-290
-1.5896185090842948e-298
-2.695863739873929e-295
7
-1.6239005782062206e+154
-7.680972122048022e+152
-1.457738542065717e+153

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03357
14157
done4157

end0.0ms

sample1.2s

Algorithm
intervals
Results
250.0ms1106×body2560valid
222.0ms5897×body80valid
166.0ms886×body1280valid
110.0ms2958×body80nan
67.0ms445×body640valid
30.0ms110×body5120valid
25.0ms231×body320valid
8.0ms106×body160valid