Details

Time bar (total: 13.7s)

sample119.0ms

Algorithm
intervals
Results
32.0ms39×body2560valid
18.0ms36×body1280valid
16.0ms166×body80valid
8.0ms90×body80nan
7.0ms18×body640valid
3.0ms10×body320valid
3.0ms4×body5120valid
0.0ms2×body160valid

simplify240.0ms

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: 36.1b

localize31.0ms

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))))

rewrite250.0ms

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:
139.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
56.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.0ms
(- (* b b) (* 4.0 (* a c)))
23.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series431.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
98.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(- (* b b) (* 4.0 (* a c)))
111.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
169 → 169
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02436690
16164729
224663764
done50013675

prune582.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.5b

localize4.0ms

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

prune52.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.5b

localize33.0ms

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))))

rewrite198.0ms

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:
137.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
33.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series409.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
102.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
57.0ms
(- (* b b) (* 4.0 (* a c)))
108.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.1s

Counts
177 → 177
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02696947
16904918
230473859
done50013766

prune518.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))) (* 2.0 a))
0.8b
(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
1.5b
(fma b b (- (* (* a c) 4.0)))
22.5b
(sqrt (fma b b (- (* (* a c) 4.0))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
60×*-un-lft-identity prod-diff
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv flip3-- diff-log div-exp flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod fma-udef div-inv
Counts
4 → 149
Calls
4 calls:
62.0ms
(/ (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))) (* 2.0 a))
20.0ms
(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
0.0ms
(fma b b (- (* (* a c) 4.0)))
2.0ms
(sqrt (fma b b (- (* (* a c) 4.0))))

series490.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(/ (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))) (* 2.0 a))
138.0ms
(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
86.0ms
(fma b b (- (* (* a c) 4.0)))
111.0ms
(sqrt (fma b b (- (* (* a c) 4.0))))

simplify1.9s

Counts
161 → 161
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02226500
15324556
220453616
done50012969

prune423.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.3b

regimes304.0ms

Accuracy

85% (4.1b remaining)

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

bsearch264.0ms

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

simplify15.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
04171
15369
25669
done5669

end0.0ms

sample3.5s

Algorithm
intervals
Results
635.0ms1014×body2560valid
560.0ms5936×body80valid
513.0ms100×body5120valid
501.0ms2934×body80nan
412.0ms912×body1280valid
137.0ms439×body640valid
91.0ms232×body320valid
19.0ms122×body160valid