Details

Time bar (total: 9.4s)

sample42.0ms

Algorithm
intervals
Results
7.0ms186×body80valid
6.0ms85×body80nan
6.0ms31×body1280valid
6.0ms27×body2560valid
2.0ms16×body640valid
1.0ms3×body5120valid
0.0ms4×body320valid
0.0ms2×body160valid

simplify118.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12917
26417
312017
414517
515217
615617
done15617

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite130.0ms

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:
74.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms
(- (* b b) (* 4.0 (* a c)))
30.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series312.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms
(- (* b b) (* 4.0 (* a c)))
84.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
77.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts
169 → 169
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02436690
15874705
217533760
done50003113

prune355.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize16.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
2.1b
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
8.6b
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
25.0b
(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
78×times-frac
72×*-un-lft-identity
50×add-cube-cbrt
27×associate-/l*
26×sqrt-prod
22×difference-of-squares
18×add-exp-log prod-diff add-cbrt-cube
11×distribute-lft-out--
7×cbrt-undiv div-exp associate-/r*
6×fma-neg associate-/r/ add-log-exp
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 171
Calls
4 calls:
12.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
47.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
35.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
2.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

series817.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
412.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
222.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
90.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify966.0ms

Counts
183 → 183
Iterations

Useful iterations: done (955.0ms)

IterNodesCost
02755401
16554711
222914237
done50014169

prune462.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize16.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
2.1b
(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
8.6b
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
25.0b
(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
80×add-sqr-sqrt
58×*-un-lft-identity
51×add-exp-log
42×add-cube-cbrt
40×times-frac
27×add-cbrt-cube
24×associate-*l*
23×sqrt-prod
20×prod-exp
18×prod-diff
16×div-exp difference-of-squares
8×cbrt-undiv cbrt-unprod distribute-lft-out--
7×pow1 associate-*r*
6×fma-neg associate-/r* add-log-exp
4×expm1-log1p-u rec-exp 1-exp associate-/r/ log1p-expm1-u
3×flip3-- flip-- div-inv associate-/l*
2×associate-/l/ unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 169
Calls
4 calls:
11.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
70.0ms
(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
32.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
2.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

series565.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
174.0ms
(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
210.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
87.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.1s

Counts
181 → 181
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02805119
17144377
225023764
done50003696

prune448.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b
(fma b b (- (* 4.0 (* a c))))
1.4b
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
11.8b
(/ (* (* a c) 4.0) (* 2.0 a))
25.0b
(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
24×add-sqr-sqrt
21×*-un-lft-identity
19×add-cube-cbrt
18×prod-diff
16×sqrt-prod
9×prod-exp cbrt-unprod
6×cbrt-undiv fma-neg div-exp add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×difference-of-squares
1×sub-neg rem-sqrt-square flip3-- frac-2neg sqrt-pow1 times-frac pow1/2 diff-log clear-num associate-/r* flip-- fma-udef div-inv associate-/l* distribute-lft-out--
Counts
4 → 93
Calls
4 calls:
0.0ms
(fma b b (- (* 4.0 (* a c))))
13.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
22.0ms
(/ (* (* a c) 4.0) (* 2.0 a))
2.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

series248.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(fma b b (- (* 4.0 (* a c))))
95.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
14.0ms
(/ (* (* a c) 4.0) (* 2.0 a))
82.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify713.0ms

Counts
105 → 105
Iterations

Useful iterations: done (709.0ms)

IterNodesCost
01681926
14131650
218051333
done50001266

prune227.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

regimes180.0ms

Accuracy

96.1% (0.9b remaining)

Error of 7.0b against oracle of 6.0b and baseline of 29.9b

bsearch166.0ms

Steps
ItersRangePoint
9
8.777746745010686e+110
1.2290467223415774e+117
1.1912031425131646e+117
9
-5.951265309377375e-290
-1.5896185090842948e-298
-2.695863739873929e-295
7
-1.6239005782062206e+154
-7.680972122048022e+152
-1.457738542065717e+153

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03657
14857
25657
done5657

end0.0ms

sample1.2s

Algorithm
intervals
Results
234.0ms1106×body2560valid
221.0ms5897×body80valid
154.0ms886×body1280valid
101.0ms2958×body80nan
65.0ms445×body640valid
35.0ms110×body5120valid
23.0ms231×body320valid
7.0ms106×body160valid