Details

Time bar (total: 5.4s)

sample36.0ms

Algorithm
intervals
Results
13.0ms281×body80valid
4.0ms77×body80nan

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03618
16718
212318
316018
417518
517718
617718
done17718

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.3b

localize88.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 151
Calls
4 calls:
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify66.0ms

Counts
163 → 163
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04183056
114712008
250011917
done50011917

prune439.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.4b

localize90.0ms

Local error

Found 4 expressions with local error:

4.3b
(expm1 (log1p (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.7b
(- (- b) (expm1 (log1p (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt *-un-lft-identity
30×prod-diff
28×add-cube-cbrt
13×distribute-rgt-neg-in
12×distribute-lft-neg-in
10×fma-neg
8×add-log-exp
6×pow1 sqrt-prod
4×add-exp-log expm1-log1p-u neg-mul-1 sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out-- expm1-udef
1×associate--l- neg-sub0 sub-neg expm1-log1p neg-log associate--r- difference-of-squares
Counts
4 → 105
Calls
4 calls:
0.0ms
(expm1 (log1p (sqrt (- (* b b) (* (* 4.0 a) c)))))
16.0ms
(- (- b) (expm1 (log1p (sqrt (- (* b b) (* (* 4.0 a) c))))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series334.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(expm1 (log1p (sqrt (- (* b b) (* (* 4.0 a) c)))))
69.0ms
(- (- b) (expm1 (log1p (sqrt (- (* b b) (* (* 4.0 a) c))))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify53.0ms

Counts
117 → 117
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03782190
112291213
250011163
done50011163

prune393.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.9b

localize89.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.9b
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
6.2b
(/ (* a c) b)
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
55×add-sqr-sqrt
54×*-un-lft-identity
50×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×add-exp-log add-cbrt-cube
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×times-frac
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp associate-/r* log1p-expm1-u associate-/l*
3×flip3-- flip--
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod div-inv associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 div-sub neg-log
Counts
4 → 156
Calls
4 calls:
32.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
15.0ms
(/ (* a c) b)
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series257.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
20.0ms
(/ (* a c) b)
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify131.0ms

Counts
168 → 168
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06513103
127072019
250021941
done50021941

prune463.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize87.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite102.0ms

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:
46.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify71.0ms

Counts
168 → 168
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05453278
121142181
250022098
done50022098

prune383.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

regimes205.0ms

Accuracy

96% (0.6b remaining)

Error of 6.8b against oracle of 6.2b and baseline of 21.6b

bsearch196.0ms

Steps
ItersRangePoint
5
3.355600980676121e+98
1.2784432988208537e+99
5.2633913525772375e+98
8
-2.2416054230608577e-248
-1.872794966336752e-252
-6.7247162669225565e-252
6
-1.0975144697592171e+114
-1.919867654883946e+113
-8.414325781162306e+113

simplify16.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08098
18898
29098
311998
415398
516698
619198
720898
822098
922998
1023398
1124098
1225398
1326398
1427798
1531398
1632398
1733998
1835698
1938498
2039198
2139198
done39198

end0.0ms

sample912.0ms

Algorithm
intervals
Results
427.0ms8707×body80valid
134.0ms2850×body80nan