Details

Time bar (total: 41.4s)

sample74.0ms

Algorithm
intervals
Results
30.0ms277×body80valid
8.0ms82×body80nan

simplify835.0ms

Counts
1 → 1
Iterations
IterNodes
done170
7170
6168
5164
4157
3134
275
139
020

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize311.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log sqrt-pow1 pow1/2 diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×associate--l- +-commutative sub-neg flip3-+ associate-+l- flip-+
Counts
4 → 155
Calls
4 calls:
60.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
101.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
39.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series611.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
147.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
129.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
156.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify9.5s

Counts
167 → 167
Iterations
IterNodes
done5000
34467
21211
1434
0182

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize408.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.9b
(* (/ a b) (* c 2.0))
4.8b
(/ (fma b -2 (* (/ a b) (* c 2.0))) (* 2.0 a))
21.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity add-cbrt-cube add-exp-log
18×add-sqr-sqrt
17×add-cube-cbrt
13×associate-*l*
12×times-frac
10×pow1 fma-def
8×add-log-exp
7×prod-exp cbrt-unprod
4×expm1-log1p-u cbrt-undiv distribute-rgt-neg-in div-exp insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in pow-prod-down sqrt-prod associate-/l*
2×sum-log sqrt-div div-inv distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 frac-2neg sqrt-pow1 flip3-+ flip3-- pow1/2 associate-*r* neg-log associate-*l/ *-commutative associate-+l- flip-+ flip--
Counts
4 → 106
Calls
4 calls:
73.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
63.0ms
(* (/ a b) (* c 2.0))
38.0ms
(/ (fma b -2 (* (/ a b) (* c 2.0))) (* 2.0 a))
39.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series449.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(* (/ a b) (* c 2.0))
113.0ms
(/ (fma b -2 (* (/ a b) (* c 2.0))) (* 2.0 a))
142.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.3s

Counts
118 → 118
Iterations
IterNodes
done5003
21801
1537
0207

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize314.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.4b
(- (* b b) (* (* 4.0 a) c))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite279.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-cube-cbrt add-log-exp
9×add-cbrt-cube add-exp-log
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 associate-/r* times-frac
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-/r/ flip-+ flip--
1×neg-sub0 +-commutative rem-sqrt-square clear-num neg-mul-1 sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff neg-log prod-exp associate-+l- cbrt-unprod div-inv associate-/l*
Counts
4 → 93
Calls
4 calls:
162.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.0ms
(- (* b b) (* (* 4.0 a) c))
55.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
28.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series880.0ms

Counts
4 → 12
Calls
4 calls:
458.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
78.0ms
(- (* b b) (* (* 4.0 a) c))
166.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
176.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.9s

Counts
105 → 105
Iterations
IterNodes
done5006
21373
1417
0161

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize301.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* a (* 4.0 c)))
0.5b
(/ 2.0 (/ (- (sqrt (- (* b b) (* a (* 4.0 c)))) b) c))
0.9b
(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
21.8b
(sqrt (- (* b b) (* a (* 4.0 c))))

rewrite435.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/r*
19×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv flip3-- div-exp flip-- associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/r/
Counts
4 → 186
Calls
4 calls:
24.0ms
(- (* b b) (* a (* 4.0 c)))
138.0ms
(/ 2.0 (/ (- (sqrt (- (* b b) (* a (* 4.0 c)))) b) c))
204.0ms
(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
29.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

series597.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (* b b) (* a (* 4.0 c)))
265.0ms
(/ 2.0 (/ (- (sqrt (- (* b b) (* a (* 4.0 c)))) b) c))
120.0ms
(- (sqrt (- (* b b) (* a (* 4.0 c)))) b)
137.0ms
(sqrt (- (* b b) (* a (* 4.0 c))))

simplify5.4s

Counts
198 → 198
Iterations
IterNodes
done5001
22511
1845
0319

prune2.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

regimes962.0ms

Accuracy

94.3% (0.9b remaining)

Error of 6.3b against oracle of 5.4b and baseline of 20.7b

bsearch507.0ms

Steps
ItersRangePoint
10
1.0955696400612189e+91
1.0202913897586463e+104
4.237649019836543e+103
8
3.681474241313154e-261
4.412586208951887e-257
3.7351193763925545e-261
9
-2.0274263258127503e+155
-2.0044150779320932e+149
-3.3646042166231086e+152

simplify31.0ms

Iterations
IterNodes
done61
161
051

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.6s8759×body80valid
365.0ms2919×body80nan