Details

Time bar (total: 6.4s)

sample45.0ms

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

simplify90.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12917
26417
312017
414417
515017
615317
done15317

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))))

rewrite74.0ms

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:
44.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series285.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify771.0ms

Counts
169 → 169
Iterations

Useful iterations: done (765.0ms)

IterNodesCost
02436690
16074755
219903760
done50003759

prune355.0ms

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

prune20.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize12.0ms

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))))

rewrite55.0ms

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:
22.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
19.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series369.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify957.0ms

Counts
168 → 168
Iterations

Useful iterations: 2 (182.0ms)

IterNodesCost
02336633
15674690
219263700
done50013700

prune343.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.1b

localize14.0ms

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))))

rewrite75.0ms

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:
45.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series281.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify777.0ms

Counts
169 → 169
Iterations

Useful iterations: done (770.0ms)

IterNodesCost
02436690
16074755
219903760
done50003759

prune314.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 6.1b

regimes302.0ms

Accuracy

87.2% (4.3b remaining)

Error of 10.2b against oracle of 5.8b and baseline of 39.8b

bsearch85.0ms

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
03043
13743
done3743

end0.0ms

sample1.1s

Algorithm
intervals
Results
250.0ms1073×body2560valid
221.0ms5862×body80valid
176.0ms902×body1280valid
102.0ms2862×body80nan
73.0ms459×body640valid
31.0ms114×body5120valid
23.0ms213×body320valid
9.0ms116×body160valid