Details

Time bar (total: 10.9s)

sample335.0ms

Algorithm
intervals
Results
8.0ms187×body80valid
7.0ms36×body2560valid
4.0ms26×body1280valid
2.0ms73×body80nan
2.0ms19×body640valid
0.0ms5×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify13.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1237
2307
3327
4347
5347
done347

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b
(- (* b_2 b_2) (* a c))
21.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
19×add-sqr-sqrt
18×add-cube-cbrt
15×times-frac
10×fma-def distribute-lft-out add-log-exp
8×distribute-rgt-neg-in
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub div-exp prod-diff neg-log clear-num div-inv
Counts
4 → 100
Calls
4 calls:
71.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
24.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(- (* b_2 b_2) (* a c))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series281.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
76.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0389850
11366779
25001753
done5001753

prune296.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.2b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
7.9b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
199×add-sqr-sqrt
198×*-un-lft-identity
186×times-frac
130×add-cube-cbrt
60×prod-diff
50×sqrt-prod
38×distribute-rgt-neg-in
34×distribute-lft-out-- difference-of-squares
30×associate-/l*
21×distribute-lft-neg-in
11×add-exp-log add-cbrt-cube
10×fma-neg associate-/r* associate-/r/
8×add-log-exp
7×neg-mul-1 flip3-- flip--
6×div-inv
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 284
Calls
4 calls:
31.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
82.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
57.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series461.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
148.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
174.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify134.0ms

Counts
296 → 296
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
09195579
139184508
250014505
done50014505

prune574.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.2b
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
21.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
951×times-frac
630×add-sqr-sqrt
629×*-un-lft-identity
433×add-cube-cbrt
98×distribute-lft-out-- difference-of-squares
83×associate-/l*
82×sqrt-prod
70×distribute-rgt-neg-in
60×prod-diff
28×associate-/r*
22×div-inv
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
9×cbrt-undiv div-exp
8×add-log-exp
7×neg-mul-1
5×pow1 associate-/r/
4×expm1-log1p-u log1p-expm1-u
2×flip3-- frac-2neg sqrt-div diff-log clear-num flip--
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 569
Calls
4 calls:
32.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
46.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
85.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series492.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
190.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
162.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify111.0ms

Counts
581 → 581
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0175510832
150029428
done50029428

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.6b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(/ (/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
1.4b
(/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
21.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite368.0ms

Algorithm
rewrite-expression-head
Rules
3159×times-frac
1899×add-sqr-sqrt
1898×*-un-lft-identity
1306×add-cube-cbrt
1071×cbrt-prod
296×distribute-lft-out-- difference-of-squares
181×sqrt-prod
169×distribute-rgt-neg-in
161×associate-/l*
60×prod-diff
58×div-inv
31×associate-/r*
21×distribute-lft-neg-in
18×add-exp-log
11×add-cbrt-cube
10×fma-neg
9×cbrt-undiv div-exp
8×associate-/r/ add-log-exp
7×neg-mul-1
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×flip3-- frac-2neg sqrt-div diff-log clear-num flip--
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 1415
Calls
4 calls:
30.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
113.0ms
(/ (/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
49.0ms
(/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series653.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
160.0ms
(/ (/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
358.0ms
(/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify284.0ms

Counts
1427 → 1427
Iterations

Useful iterations: 1 (54.0ms)

IterNodesCost
0320733621
1500132782
done500132782

prune3.8s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.6b

regimes198.0ms

Accuracy

94.2% (1.4b remaining)

Error of 6.9b against oracle of 5.5b and baseline of 29.9b

bsearch120.0ms

Steps
ItersRangePoint
6
1.4800420954007604e+99
6.083502279918113e+99
1.5670766344383297e+99
8
-3.113339068412751e-239
-3.8269450675186263e-243
-3.8863905932895883e-243
10
-4.9909276054097234e+78
-4.785667473127655e+65
-3.974595954042362e+78

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04527
14727
24727
done4727

end0.0ms

sample1.1s

Algorithm
intervals
Results
196.0ms1108×body2560valid
186.0ms5758×body80valid
136.0ms916×body1280valid
84.0ms2868×body80nan
54.0ms489×body640valid
23.0ms105×body5120valid
19.0ms224×body320valid
6.0ms103×body160valid