Details

Time bar (total: 19.2s)

sample106.0ms

Algorithm
intervals
Results
38.0ms190×body80valid
22.0ms43×body2560valid
10.0ms24×body1280valid
7.0ms85×body80nan
4.0ms12×body640valid
3.0ms12×body320valid
1.0ms1×body5120valid
1.0ms3×body160valid

simplify147.0ms

Counts
1 → 1
Iterations
IterNodes
done142
7142
6140
5135
4130
3110
263
129
014

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.9b

localize30.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
0.8b
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
22.0b
(sqrt (fma (* -4 a) c (* b b)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
77×*-un-lft-identity
60×prod-diff
57×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
10×fma-neg distribute-lft-out-- difference-of-squares
7×neg-mul-1 associate-/l* add-log-exp
5×add-cbrt-cube add-exp-log
4×pow1
3×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u
2×flip3-- diff-log flip-- associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log div-inv
Counts
3 → 156
Calls
3 calls:
49.0ms
(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
17.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
6.0ms
(sqrt (fma (* -4 a) c (* b b)))

series326.0ms

Counts
3 → 9
Calls
3 calls:
110.0ms
(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
104.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
112.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify2.4s

Counts
165 → 165
Iterations
IterNodes
done5042
33375
21124
1479
0211

prune795.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.7b

localize42.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ (- 0 (+ b (sqrt (fma (* -4 a) c (* b b))))) a)
0.8b
(+ b (sqrt (fma (* -4 a) c (* b b))))
22.0b
(sqrt (fma (* -4 a) c (* b b)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
25×add-sqr-sqrt
18×times-frac
16×add-cube-cbrt
8×distribute-lft-out--
6×associate-/l*
5×add-cbrt-cube add-exp-log distribute-lft-out add-log-exp
4×pow1 difference-of-squares
3×expm1-log1p-u associate-/r* fma-def sqrt-prod insert-posit16 log1p-expm1-u
2×associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 flip3-+ flip3-- pow1/2 div-sub div-exp distribute-frac-neg flip-+ div-inv flip-- sub0-neg
Counts
3 → 80
Calls
3 calls:
100.0ms
(/ (- 0 (+ b (sqrt (fma (* -4 a) c (* b b))))) a)
9.0ms
(+ b (sqrt (fma (* -4 a) c (* b b))))
3.0ms
(sqrt (fma (* -4 a) c (* b b)))

series266.0ms

Counts
3 → 9
Calls
3 calls:
97.0ms
(/ (- 0 (+ b (sqrt (fma (* -4 a) c (* b b))))) a)
80.0ms
(+ b (sqrt (fma (* -4 a) c (* b b))))
89.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify2.0s

Counts
89 → 89
Iterations
IterNodes
done5003
32796
2849
1338
0143

prune525.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.7b

localize47.0ms

Local error

Found 3 expressions with local error:

0.4b
(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
0.8b
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
22.0b
(sqrt (fma (* -4 a) c (* b b)))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
69×add-sqr-sqrt
62×*-un-lft-identity
60×prod-diff
53×add-cube-cbrt
35×sqrt-prod
23×distribute-rgt-neg-in
21×distribute-lft-neg-in
13×associate-*r*
12×add-exp-log
11×times-frac
10×fma-neg
8×add-cbrt-cube
7×neg-mul-1 associate-*l* add-log-exp
6×pow1
4×prod-exp distribute-lft-out-- difference-of-squares
3×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip-- unswap-sqr
2×frac-times diff-log div-exp associate-*l/ cbrt-unprod
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square rec-exp sub-neg sqrt-pow1 pow1/2 1-exp pow-prod-down neg-log associate-*r/ un-div-inv *-commutative div-inv
Counts
3 → 154
Calls
3 calls:
97.0ms
(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
43.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
4.0ms
(sqrt (fma (* -4 a) c (* b b)))

series415.0ms

Counts
3 → 9
Calls
3 calls:
158.0ms
(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
129.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
128.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify3.3s

Counts
163 → 163
Iterations
IterNodes
done5002
33442
21322
1541
0230

prune586.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.7b

localize61.0ms

Local error

Found 4 expressions with local error:

0.8b
(+ b (sqrt (fma (* -4 a) c (* b b))))
0.8b
(+ b (sqrt (fma (* -4 a) c (* b b))))
22.0b
(sqrt (fma (* -4 a) c (* b b)))
22.0b
(sqrt (fma (* -4 a) c (* b b)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
10×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×pow1 fma-def sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ pow1/2 flip-+ distribute-lft-out
Counts
4 → 68
Calls
4 calls:
13.0ms
(+ b (sqrt (fma (* -4 a) c (* b b))))
7.0ms
(+ b (sqrt (fma (* -4 a) c (* b b))))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))
2.0ms
(sqrt (fma (* -4 a) c (* b b)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(+ b (sqrt (fma (* -4 a) c (* b b))))
121.0ms
(+ b (sqrt (fma (* -4 a) c (* b b))))
112.0ms
(sqrt (fma (* -4 a) c (* b b)))
113.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify3.1s

Counts
80 → 80
Iterations
IterNodes
done5002
42511
3872
2354
1141
061

prune642.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.7b

regimes559.0ms

Accuracy

82.3% (5.0b remaining)

Error of 10.4b against oracle of 5.4b and baseline of 33.7b

bsearch165.0ms

Steps
ItersRangePoint
8
4.664337482673326e-05
0.17679972651571432
0.17389787404847717
7
-2.1239343788780832e-66
-2.400891841159577e-68
-1.264659490877098e-67

simplify5.0ms

Iterations
IterNodes
done35
135
029

end0.0ms

sample3.0s

Algorithm
intervals
Results
701.0ms877×body1280valid
668.0ms5823×body80valid
654.0ms1103×body2560valid
286.0ms2975×body80nan
160.0ms440×body640valid
102.0ms125×body5120valid
91.0ms249×body320valid
18.0ms121×body160valid