Details

Time bar (total: 9.0s)

sample44.0ms

Algorithm
intervals
Results
9.0ms27×body2560valid
8.0ms201×body80valid
7.0ms35×body1280valid
3.0ms87×body80nan
2.0ms12×body640valid
1.0ms7×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify79.0ms

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: 32.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite79.0ms

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:
47.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
18.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series303.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
82.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify689.0ms

Counts
169 → 169
Iterations

Useful iterations: done (683.0ms)

IterNodesCost
02436690
16074755
219653760
done50003759

prune385.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite92.0ms

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:
61.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
17.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series300.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify969.0ms

Counts
177 → 177
Iterations

Useful iterations: done (963.0ms)

IterNodesCost
02696947
16774904
224303851
done50003850

prune339.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* 4.0 (* a c)))
12.2b
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×fma-neg prod-diff
10×add-log-exp
6×pow1 distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
3×diff-log
2×neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 neg-log difference-of-squares
Counts
4 → 87
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series280.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* b b) (* 4.0 (* a c)))
83.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify438.0ms

Counts
99 → 99
Iterations

Useful iterations: done (435.0ms)

IterNodesCost
01302598
13181642
210871548
done50001513

prune337.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.7b
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.3b
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
20.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite110.0ms

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 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 173
Calls
4 calls:
23.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
48.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
27.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series556.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
179.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
215.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
77.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts
185 → 185
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02885475
17354743
234834271
done50004269

prune467.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

regimes214.0ms

Accuracy

81.6% (4.8b remaining)

Error of 10.6b against oracle of 5.8b and baseline of 32.0b

bsearch107.0ms

Steps
ItersRangePoint
8
2.1878188410446244e+107
3.8616146939177386e+111
3.6627135292415903e+111
8
-4.854151311909829e-126
-9.294658666337375e-130
-4.7828589349284326e-126

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02839
13639
done3639

end0.0ms

sample1.2s

Algorithm
intervals
Results
268.0ms1110×body2560valid
238.0ms5789×body80valid
172.0ms885×body1280valid
118.0ms2998×body80nan
68.0ms448×body640valid
31.0ms253×body320valid
29.0ms101×body5120valid
10.0ms126×body160valid