Details

Time bar (total: 54.9s)

sample61.0ms

Algorithm
intervals
Results
36.0ms277×body80valid
9.0ms77×body80nan

simplify187.0ms

Counts
1 → 1
Iterations
IterNodes
8160
7160
6159
5152
4140
3108
263
136
020

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize190.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×expm1-log1p-u flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u flip--
3×diff-log
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 neg-log
Counts
4 → 144
Calls
4 calls:
16.0ms
(- (* b b) (* (* 4 a) c))
38.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
19.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (* b b) (* (* 4 a) c))
121.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
109.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
125.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.9s

Counts
156 → 156
Iterations
IterNodes
33463
21118
1426
0183

prune2.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize170.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4 a) c))
2.1b
(* c (/ a b))
4.3b
(/ (* 2 c) (* (- (* c (/ a b)) b) 2))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
21×add-cbrt-cube add-exp-log
19×add-sqr-sqrt
13×*-un-lft-identity associate-*r* add-cube-cbrt
11×times-frac
7×pow1
6×prod-exp cbrt-unprod add-log-exp
5×cbrt-undiv div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×flip3-- associate-*l* sqrt-prod flip--
2×sqrt-div associate-*l/ associate-/r/ div-inv unswap-sqr
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down associate-*r/ *-commutative associate-/l*
Counts
4 → 96
Calls
4 calls:
16.0ms
(- (* b b) (* (* 4 a) c))
18.0ms
(* c (/ a b))
42.0ms
(/ (* 2 c) (* (- (* c (/ a b)) b) 2))
20.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(- (* b b) (* (* 4 a) c))
37.0ms
(* c (/ a b))
90.0ms
(/ (* 2 c) (* (- (* c (/ a b)) b) 2))
85.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.4s

Counts
108 → 108
Iterations
IterNodes
22171
1523
0193

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize201.0ms

Local error

Found 4 expressions with local error:

4.3b
(/ (* 2 c) (* (- (* c (/ a b)) b) 2))
12.6b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube add-exp-log
11×add-sqr-sqrt
10×fma-def
9×*-un-lft-identity add-cube-cbrt
8×add-log-exp
6×pow1 sqrt-prod
4×expm1-log1p-u cbrt-undiv sqrt-div div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in distribute-rgt-neg-in flip3-- flip--
2×rem-sqrt-square sum-log sqrt-pow1 pow1/2 associate-*l/ associate-/r/
1×neg-sub0 +-commutative clear-num associate-/r* neg-mul-1 frac-2neg flip3-+ times-frac neg-log associate-+l- flip-+ div-inv associate-/l*
Counts
4 → 88
Calls
4 calls:
22.0ms
(/ (* 2 c) (* (- (* c (/ a b)) b) 2))
12.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
17.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
21.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (* 2 c) (* (- (* c (/ a b)) b) 2))
109.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
101.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
107.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify35.8s

Counts
100 → 100
Iterations
IterNodes
39413
21864
1445
0152

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize198.0ms

Local error

Found 4 expressions with local error:

23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.9b
(cbrt (- (* b b) (* (* 4 a) c)))
23.9b
(cbrt (- (* b b) (* (* 4 a) c)))
23.9b
(cbrt (- (* b b) (* (* 4 a) c)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip-- add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 66
Calls
4 calls:
10.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
8.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
136.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
120.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
115.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

simplify652.0ms

Counts
78 → 78
Iterations
IterNodes
32005
2612
1213
093

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.4b

regimes449.0ms

Accuracy

93% (1.1b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 21.0b

bsearch329.0ms

Steps
ItersRangePoint
7
1.602087361235081e+82
9.448026055101687e+83
4.866803345215698e+83
8
-5.520406447692031e+155
-8.116303404487084e+152
-4.82289647433212e+153

simplify72.0ms

Iterations
IterNodes
382
282
180
062

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.1s8706×body80valid
529.0ms2907×body80nan