Details

Time bar (total: 6.4s)

sample46.0ms

Algorithm
intervals
Results
10.0ms37×body1280valid
8.0ms33×body2560valid
7.0ms178×body80valid
3.0ms22×body640valid
3.0ms79×body80nan
1.0ms3×body5120valid
1.0ms7×body320valid
0.0ms6×body160valid

simplify84.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12917
26417
311917
414117
514717
615017
done15017

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite73.0ms

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:
40.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
6.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series300.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
51.0ms
(- (* b b) (* 4.0 (* a c)))
81.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify620.0ms

Counts
169 → 169
Iterations

Useful iterations: done (613.0ms)

IterNodesCost
02436690
15784705
218083760
done50013759

prune376.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune27.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.4b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite53.0ms

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:
25.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series381.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
50.0ms
(- (* b b) (* 4.0 (* a c)))
81.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify625.0ms

Counts
168 → 168
Iterations

Useful iterations: 2 (182.0ms)

IterNodesCost
02336633
15344640
216963700
done50003700

prune344.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 2.0 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a))
0.4b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
168×*-un-lft-identity
159×times-frac
116×add-cube-cbrt
61×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
26×distribute-lft-out-- difference-of-squares
25×associate-/r*
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv flip3-- diff-log div-exp flip-- associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r/
Counts
4 → 243
Calls
4 calls:
27.0ms
(/ 2.0 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series315.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ 2.0 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a))
45.0ms
(- (* b b) (* 4.0 (* a c)))
81.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify992.0ms

Counts
255 → 255
Iterations

Useful iterations: done (979.0ms)

IterNodesCost
03649535
18397412
227916450
done50006449

prune511.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.9b

regimes292.0ms

Accuracy

86.4% (4.6b remaining)

Error of 10.4b against oracle of 5.7b and baseline of 39.7b

bsearch90.0ms

Steps
ItersRangePoint
8
1.5276508475467709e+44
4.1560730947117816e+46
4.1199128263687574e+46
5
-1.2023865605984147e-79
-5.347575839305805e-80
-8.364554704106616e-80

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03247
13847
done3847

end0.0ms

sample1.1s

Algorithm
intervals
Results
246.0ms1073×body2560valid
228.0ms5862×body80valid
178.0ms902×body1280valid
108.0ms2862×body80nan
71.0ms459×body640valid
32.0ms114×body5120valid
23.0ms213×body320valid
9.0ms116×body160valid