Details

Time bar (total: 16.4s)

sample105.0ms

Algorithm
intervals
Results
22.0ms37×body2560valid
18.0ms182×body80valid
15.0ms31×body1280valid
8.0ms22×body640valid
8.0ms89×body80nan
3.0ms9×body320valid
1.0ms3×body160valid
1.0ms1×body5120valid

simplify159.0ms

Counts
1 → 1
Iterations
IterNodes
done164
6164
5160
4153
3121
264
129
014

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite159.0ms

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-cbrt-cube add-exp-log
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- log1p-expm1-u flip--
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
80.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
43.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series407.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
101.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
56.0ms
(- (* b b) (* 4.0 (* a c)))
99.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.3s

Counts
169 → 169
Iterations
IterNodes
done5001
22466
1610
0241

prune874.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
1.4b
(- (* b b) (* 4.0 (* a c)))
6.1b
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
204×times-frac
141×prod-diff
101×*-un-lft-identity
98×add-sqr-sqrt
95×add-cube-cbrt
51×sqrt-prod
34×distribute-rgt-neg-in
33×distribute-lft-neg-in
28×div-inv
15×fma-neg
11×neg-mul-1
9×add-cbrt-cube add-exp-log
8×add-log-exp
6×associate-/l*
5×pow1
4×expm1-log1p-u flip3-- sqrt-div log1p-expm1-u flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 div-sub prod-exp frac-sub cbrt-unprod sub-div difference-of-squares
Counts
4 → 240
Calls
4 calls:
18.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
14.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series557.0ms

Counts
4 → 12
Calls
4 calls:
204.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
63.0ms
(- (* b b) (* 4.0 (* a c)))
183.0ms
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
107.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.5s

Counts
252 → 252
Iterations
IterNodes
done5000
23027
1863
0354

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize98.0ms

Local error

Found 4 expressions with local error:

16.5b
(- (- b) (* (* (cbrt (sqrt (- (* b b) (* 4.0 (* a c))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
10×fma-neg prod-diff
9×sqrt-prod
8×add-log-exp
7×pow1
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-div
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log log1p-expm1-u flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg neg-log
Counts
4 → 87
Calls
4 calls:
25.0ms
(- (- b) (* (* (cbrt (sqrt (- (* b b) (* 4.0 (* a c))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
17.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series477.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(- (- b) (* (* (cbrt (sqrt (- (* b b) (* 4.0 (* a c))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
105.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
113.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
117.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts
99 → 99
Iterations
IterNodes
done5000
21298
1297
0114

prune769.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.2b

localize5.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune1.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.2b

regimes583.0ms

Accuracy

84.8% (4.3b remaining)

Error of 10.5b against oracle of 6.2b and baseline of 34.5b

bsearch211.0ms

Steps
ItersRangePoint
5
2.6243927093659187e+107
5.901159163981397e+107
3.038903409991338e+107
9
-1.0952546209266604e-55
-7.034794544076098e-65
-9.332433396832084e-58

simplify11.0ms

Iterations
IterNodes
done35
135
028

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.2s5891×body80valid
885.0ms1016×body2560valid
426.0ms892×body1280valid
269.0ms2883×body80nan
171.0ms461×body640valid
51.0ms98×body5120valid
49.0ms220×body320valid
17.0ms118×body160valid