Details

Time bar (total: 29.5s)

sample100.0ms

Algorithm
intervals
Results
18.0ms32×body2560valid
16.0ms171×body80valid
16.0ms34×body1280valid
9.0ms105×body80nan
5.0ms13×body640valid
2.0ms3×body5120valid
2.0ms10×body160valid
1.0ms5×body320valid

simplify308.0ms

Counts
1 → 1
Iterations
IterNodes
done139
7139
6137
5134
4131
3113
262
129
014

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b
(- (* b b) (* 4.0 (* a c)))
2.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite288.0ms

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:
155.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
20.0ms
(- (* b b) (* 4.0 (* a c)))
71.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series674.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
90.0ms
(- (* b b) (* 4.0 (* a c)))
272.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
127.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.3s

Counts
169 → 169
Iterations
IterNodes
done5001
21843
1607
0243

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (fma b b (- (* 4.0 (* a c)))))) (* 2.0 a))
1.3b
(fma b b (- (* 4.0 (* a c))))
2.4b
(- (- b) (sqrt (fma b b (- (* 4.0 (* a c))))))
22.3b
(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
60×*-un-lft-identity prod-diff
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv flip3-- diff-log div-exp flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod fma-udef div-inv
Counts
4 → 149
Calls
4 calls:
92.0ms
(/ (- (- b) (sqrt (fma b b (- (* 4.0 (* a c)))))) (* 2.0 a))
1.0ms
(fma b b (- (* 4.0 (* a c))))
38.0ms
(- (- b) (sqrt (fma b b (- (* 4.0 (* a c))))))
4.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

series615.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(/ (- (- b) (sqrt (fma b b (- (* 4.0 (* a c)))))) (* 2.0 a))
100.0ms
(fma b b (- (* 4.0 (* a c))))
162.0ms
(- (- b) (sqrt (fma b b (- (* 4.0 (* a c))))))
161.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify3.2s

Counts
161 → 161
Iterations
IterNodes
done5001
21468
1527
0221

prune1.6s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b
(- (* b b) (* 4.0 (* a c)))
2.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite329.0ms

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:
204.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
20.0ms
(- (* b b) (* 4.0 (* a c)))
61.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
31.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series570.0ms

Counts
4 → 12
Calls
4 calls:
205.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
80.0ms
(- (* b b) (* 4.0 (* a c)))
145.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
140.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify4.2s

Counts
177 → 177
Iterations
IterNodes
done5000
21987
1670
0269

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.9b

localize63.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* 4.0 (* a c)))
11.4b
(/ (/ (+ (- (* b b) (* b b)) (* (* c a) 4.0)) 2.0) a)
18.3b
(- (* b b) (* b b))
22.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite247.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
48×add-sqr-sqrt
47×add-cube-cbrt *-un-lft-identity
13×associate-/l*
9×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-/r* sqrt-prod flip--
2×sub-neg fma-neg sqrt-div diff-log div-sub prod-diff
1×associate-+l- rem-sqrt-square distribute-rgt-out-- frac-2neg sqrt-pow1 pow1/2 +-inverses clear-num associate-/l/ distribute-lft-out-- difference-of-squares
Counts
4 → 126
Calls
4 calls:
18.0ms
(- (* b b) (* 4.0 (* a c)))
161.0ms
(/ (/ (+ (- (* b b) (* b b)) (* (* c a) 4.0)) 2.0) a)
39.0ms
(- (* b b) (* b b))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(- (* b b) (* 4.0 (* a c)))
19.0ms
(/ (/ (+ (- (* b b) (* b b)) (* (* c a) 4.0)) 2.0) a)
2.0ms
(- (* b b) (* b b))
188.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.6s

Counts
138 → 138
Iterations
IterNodes
done5001
21652
1583
0248

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.8b

regimes493.0ms

Accuracy

95.6% (1.1b remaining)

Error of 6.5b against oracle of 5.4b and baseline of 30.2b

bsearch366.0ms

Steps
ItersRangePoint
7
6.896997489231346e+142
2.39218470372122e+144
6.994525771494005e+142
9
1.431611294151488e-203
4.1417548827777133e-196
1.5861830220858986e-203
6
-4.525167845450207e+100
-9.36795079059543e+99
-1.6507168034351889e+100

simplify25.0ms

Iterations
IterNodes
done55
255
147
036

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.3s5836×body80valid
1.1s230×body320valid
1.0s1056×body2560valid
606.0ms909×body1280valid
325.0ms2825×body80nan
188.0ms449×body640valid
146.0ms103×body5120valid
24.0ms127×body160valid