Details

Time bar (total: 17.5s)

sample94.0ms

Algorithm
intervals
Results
52.0ms282×body80valid
10.0ms92×body80nan

simplify194.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
02038
13638
26637
312237
416137
517437
617637
done17637

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.5b

localize175.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
25.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(- (* b b) (* (* 4.0 a) c))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
27.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series349.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- (* b b) (* (* 4.0 a) c))
61.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
120.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
78 → 78
Iterations

Useful iterations: 2 (156.0ms)

IterNodesCost
0711146
11851058
2843952
done5000952

prune590.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.4b

localize142.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.7b
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
5.5b
(/ (* a c) b)
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×add-cube-cbrt
8×times-frac
6×associate-/l* add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp associate-/r* log1p-expm1-u distribute-lft-out
3×sqrt-prod
2×flip3-- distribute-rgt-neg-in frac-2neg sqrt-div div-sub prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l/
1×neg-sub0 associate-+l- associate-+r- sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 87
Calls
4 calls:
17.0ms
(- (* b b) (* (* 4.0 a) c))
203.0ms
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
10.0ms
(/ (* a c) b)
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (* b b) (* (* 4.0 a) c))
94.0ms
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
37.0ms
(/ (* a c) b)
92.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
99 → 99
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01771501
14831388
225311222
done50011218

prune711.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

localize134.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/r*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 156
Calls
4 calls:
75.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
45.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series549.0ms

Counts
4 → 12
Calls
4 calls:
284.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
112.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms
(- (* b b) (* (* 4.0 a) c))
101.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts
168 → 168
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02356633
15814663
228403705
done50003619

prune613.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize162.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.5b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
2.7b
(/ (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)) (* 2.0 a))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
33×times-frac
30×add-exp-log *-un-lft-identity
23×add-cbrt-cube
22×add-cube-cbrt associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
7×pow1 associate-*l*
6×add-log-exp unswap-sqr
5×associate-/l*
4×expm1-log1p-u log1p-expm1-u distribute-lft-out
3×sqrt-prod div-inv
2×flip3-- distribute-rgt-neg-in sqrt-div div-sub flip-- associate-/l/
1×neg-sub0 frac-times associate-+l- associate-+r- sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num associate-/r* *-commutative flip-+
Counts
4 → 125
Calls
4 calls:
17.0ms
(- (* b b) (* (* 4.0 a) c))
46.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
1.1s
(/ (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)) (* 2.0 a))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- (* b b) (* (* 4.0 a) c))
89.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
119.0ms
(/ (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)) (* 2.0 a))
115.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
137 → 137
Iterations

Useful iterations: 2 (812.0ms)

IterNodesCost
02622641
17872492
246021964
done50001964

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.9b

regimes332.0ms

Accuracy

84.6% (2.3b remaining)

Error of 8.7b against oracle of 6.3b and baseline of 21.5b

bsearch211.0ms

Steps
ItersRangePoint
8
6412590.878131424
2116652649.122401
2098947641.3561494
9
-2.364746502264313e+125
-7.44056492395588e+118
-1.3675682634777099e+124

simplify37.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
045114
155114
done55114

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.1s8674×body80valid
331.0ms2912×body80nan