Details

Time bar (total: 13.1s)

sample100.0ms

Algorithm
intervals
Results
20.0ms39×body2560valid
19.0ms166×body80valid
15.0ms36×body1280valid
8.0ms90×body80nan
6.0ms18×body640valid
3.0ms4×body5120valid
2.0ms10×body320valid
0.0ms2×body160valid

simplify489.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12917
26417
312117
415317
516017
616417
done16417

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite179.0ms

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:
99.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
37.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms
(- (* b b) (* 4.0 (* a c)))
21.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series370.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
111.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
68.0ms
(- (* b b) (* 4.0 (* a c)))
86.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts
169 → 169
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02436690
16164729
224663764
done50013675

prune636.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.5b

localize7.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune42.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.5b

localize29.0ms

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) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite197.0ms

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:
112.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
48.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series342.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
84.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
52.0ms
(- (* b b) (* 4.0 (* a c)))
99.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.8s

Counts
177 → 177
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02696947
16904918
230473859
done50013766

prune565.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (+ b (sqrt (- (* b b) (* (* a c) 4.0))))) (* 2.0 a))
0.8b
(+ b (sqrt (- (* b b) (* (* a c) 4.0))))
1.2b
(- (* b b) (* (* a c) 4.0))
22.5b
(sqrt (- (* b b) (* (* a c) 4.0)))

rewrite247.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
13×add-sqr-sqrt
12×add-cube-cbrt times-frac associate-/l*
9×add-exp-log add-cbrt-cube
8×distribute-lft-neg-in distribute-rgt-neg-in add-log-exp
5×pow1 distribute-lft-out
4×expm1-log1p-u log1p-expm1-u
3×fma-def sqrt-prod
2×cbrt-undiv neg-mul-1 flip3-- flip3-+ sqrt-div div-exp flip-- flip-+ associate-/l/ distribute-neg-frac
1×+-commutative neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub distribute-frac-neg prod-diff prod-exp clear-num associate-/r* sum-log cbrt-unprod div-inv
Counts
4 → 95
Calls
4 calls:
168.0ms
(/ (- (+ b (sqrt (- (* b b) (* (* a c) 4.0))))) (* 2.0 a))
28.0ms
(+ b (sqrt (- (* b b) (* (* a c) 4.0))))
24.0ms
(- (* b b) (* (* a c) 4.0))
22.0ms
(sqrt (- (* b b) (* (* a c) 4.0)))

series471.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(/ (- (+ b (sqrt (- (* b b) (* (* a c) 4.0))))) (* 2.0 a))
120.0ms
(+ b (sqrt (- (* b b) (* (* a c) 4.0))))
68.0ms
(- (* b b) (* (* a c) 4.0))
115.0ms
(sqrt (- (* b b) (* (* a c) 4.0)))

simplify1.4s

Counts
107 → 107
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01821968
14721857
219701686
done50001677

prune447.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.3b

regimes463.0ms

Accuracy

84.9% (4.1b remaining)

Error of 9.9b against oracle of 5.8b and baseline of 32.9b

bsearch349.0ms

Steps
ItersRangePoint
11
8.182113676652236e-12
2116652649.122401
2098867031.9345784
9
-2.2616674886517874e-265
-3.8719083319631725e-273
-6.982634002611897e-268
4
-2.14594256023029e+80
-1.5018560828312564e+80
-1.6830054045997346e+80

simplify31.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
04172
16066
27366
38166
done8166

end0.0ms

sample3.3s

Algorithm
intervals
Results
905.0ms912×body1280valid
701.0ms5936×body80valid
558.0ms1014×body2560valid
247.0ms2934×body80nan
128.0ms439×body640valid
87.0ms232×body320valid
55.0ms100×body5120valid
18.0ms122×body160valid