Details

Time bar (total: 19.5s)

sample90.0ms

Algorithm
intervals
Results
19.0ms37×body2560valid
17.0ms191×body80valid
10.0ms23×body1280valid
7.0ms90×body80nan
5.0ms15×body640valid
1.0ms5×body160valid
1.0ms1×body5120valid
1.0ms3×body320valid

simplify232.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12917
26417
312117
415317
516017
616417
done16417

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite258.0ms

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:
145.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
17.0ms
(- (* b b) (* 4.0 (* a c)))
56.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
27.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series476.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
75.0ms
(- (* b b) (* 4.0 (* a c)))
126.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
116.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.1s

Counts
169 → 169
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02436690
16164729
224823764
done50023675

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite334.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
60×add-sqr-sqrt
57×*-un-lft-identity
49×add-cube-cbrt
35×sqrt-prod
23×add-exp-log distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-cbrt-cube
11×fma-neg
10×prod-exp add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-*l*
5×flip3-- flip--
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 165
Calls
4 calls:
207.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
26.0ms
(- (* b b) (* 4.0 (* a c)))
62.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
26.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series565.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
94.0ms
(- (* b b) (* 4.0 (* a c)))
142.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
140.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.1s

Counts
177 → 177
Iterations

Useful iterations: done (3.1s)

IterNodesCost
02696947
16894918
230513859
done50003766

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
88×*-un-lft-identity
68×add-cube-cbrt
67×times-frac
61×prod-diff
38×sqrt-prod
26×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
13×associate-/r* add-cbrt-cube
12×div-exp
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
7×neg-mul-1 flip3-- flip--
6×pow1
5×cbrt-undiv div-inv
4×expm1-log1p-u log1p-expm1-u
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 205
Calls
4 calls:
109.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
20.0ms
(- (* b b) (* 4.0 (* a c)))
66.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series598.0ms

Counts
4 → 12
Calls
4 calls:
216.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
94.0ms
(- (* b b) (* 4.0 (* a c)))
152.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
135.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.1s

Counts
217 → 217
Iterations

Useful iterations: done (3.0s)

IterNodesCost
03118365
17816147
232945142
done50015052

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.8b

localize11.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune1.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 7.8b

regimes481.0ms

Accuracy

84.4% (4.4b remaining)

Error of 9.9b against oracle of 5.5b and baseline of 33.9b

bsearch239.0ms

Steps
ItersRangePoint
10
9.08791783933159e+82
5.750161104817302e+93
9.623020473898683e+86
5
-1.2210963557284012e-33
-3.582918381276583e-34
-3.8424248185280593e-34

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02737
13537
done3537

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.4s5910×body80valid
917.0ms1110×body2560valid
510.0ms3015×body80nan
483.0ms901×body1280valid
164.0ms436×body640valid
74.0ms104×body5120valid
60.0ms217×body320valid
21.0ms111×body160valid