Details

Time bar (total: 5.1s)

sample42.0ms

Algorithm
intervals
Results
9.0ms178×body80valid
8.0ms41×body2560valid
4.0ms26×body1280valid
3.0ms75×body80nan
2.0ms14×body640valid
1.0ms7×body320valid
0.0ms3×body160valid

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649
done1649

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite133.0ms

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-/l*
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-/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 → 157
Calls
4 calls:
76.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms
(- (* b b) (* 4.0 (* a c)))
31.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify70.0ms

Counts
169 → 169
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05903305
121012212
250022128
done50022128

prune534.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
1.0b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
61×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
7×neg-mul-1 associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 171
Calls
4 calls:
75.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
9.0ms
(- (* b b) (* 4.0 (* a c)))
29.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series287.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
47.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify72.0ms

Counts
183 → 183
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05663514
119662446
250012361
done50012361

prune345.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.0b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
171×add-sqr-sqrt
170×*-un-lft-identity
165×times-frac
118×add-cube-cbrt
61×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
27×associate-/r*
26×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
15×add-exp-log
11×fma-neg
10×add-log-exp
9×associate-/r/ add-cbrt-cube
7×neg-mul-1 flip3-- div-exp flip--
6×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv diff-log associate-/l*
2×sub-neg rec-exp sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num inv-pow
Counts
4 → 257
Calls
4 calls:
47.0ms
(/ 1 (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
31.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series306.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ 1 (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
46.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify108.0ms

Counts
269 → 269
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
07825140
133273846
250023657
done50023657

prune420.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.4b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* 4.0 (* a c)))
5.5b
(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
21.9b
(- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
24.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
91×prod-diff
75×add-sqr-sqrt
72×*-un-lft-identity
68×add-cube-cbrt log-prod exp-sum
37×sqrt-prod
31×distribute-rgt-neg-in
30×distribute-lft-neg-in
11×fma-neg
10×neg-mul-1 add-log-exp
7×pow1
6×exp-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
3×diff-log log-pow difference-of-squares
2×sub-neg log-div sqrt-pow1 pow1/2 exp-diff distribute-lft-out--
1×associate--l- neg-sub0 rem-sqrt-square neg-log rem-exp-log
Counts
4 → 178
Calls
4 calls:
9.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
39.0ms
(- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series274.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
81.0ms
(- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify72.0ms

Counts
190 → 190
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05475051
115862594
250022469
done50022469

prune305.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

regimes188.0ms

Accuracy

83.5% (4.5b remaining)

Error of 10.0b against oracle of 5.5b and baseline of 32.8b

bsearch100.0ms

Steps
ItersRangePoint
9
5.30600492772346e+88
5.894388948599132e+93
2.5429514865802255e+93
7
-1.9051551317192057e-67
-2.58855871570434e-69
-2.6444093768085776e-69

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03917
14117
24117
done4117

end0.0ms

sample1.2s

Algorithm
intervals
Results
227.0ms1061×body2560valid
218.0ms5877×body80valid
152.0ms852×body1280valid
102.0ms2982×body80nan
63.0ms473×body640valid
29.0ms112×body5120valid
25.0ms243×body320valid
8.0ms123×body160valid