Details

Time bar (total: 18.1s)

sample82.0ms

Algorithm
intervals
Results
34.0ms273×body80valid
12.0ms103×body80nan

simplify211.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
02038
13938
27937
314337
417937
518937
619337
done19337

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize168.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
78×prod-diff
71×add-sqr-sqrt
67×*-un-lft-identity
61×add-cube-cbrt
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×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 log1p-expm1-u flip-- difference-of-squares
3×diff-log distribute-lft-out--
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
75.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
51.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series483.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
108.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
126.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
177 → 177
Iterations

Useful iterations: 2 (444.0ms)

IterNodesCost
02086992
15084619
227253570
done50013570

prune720.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.9b

localize174.0ms

Local error

Found 4 expressions with local error:

22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

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 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 → 62
Calls
4 calls:
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series511.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
112.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
145.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
156.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
74 → 74
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
0941258
12241190
27671076
342671058
done50001058

prune729.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.9b

localize162.0ms

Local error

Found 4 expressions with local error:

23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt cbrt-div *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 flip3-- add-cbrt-cube pow1/3 add-exp-log log1p-expm1-u flip-- add-log-exp
Counts
4 → 60
Calls
4 calls:
5.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series601.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
147.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
191.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
126.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
72 → 72
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
0671268
11691224
26211100
336431076
done50001076

prune957.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.9b

localize134.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.5b
(/ (fma (/ (* a c) b) 2.0 (* b -2)) (* 2.0 a))
6.0b
(/ (* a c) b)
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
25×*-un-lft-identity
23×add-cube-cbrt
18×prod-diff
16×sqrt-prod
14×add-cbrt-cube add-exp-log
6×times-frac fma-neg add-log-exp
5×pow1
4×expm1-log1p-u cbrt-undiv associate-/r* div-exp log1p-expm1-u associate-/l*
2×clear-num frac-2neg flip3-- sqrt-div prod-exp cbrt-unprod div-inv flip-- difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 104
Calls
4 calls:
61.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
6.0ms
(/ (fma (/ (* a c) b) 2.0 (* b -2)) (* 2.0 a))
7.0ms
(/ (* a c) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series382.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
117.0ms
(/ (fma (/ (* a c) b) 2.0 (* b -2)) (* 2.0 a))
38.0ms
(/ (* a c) b)
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
116 → 116
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02022129
15241846
227121552
done50021485

prune842.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.8b

regimes381.0ms

Accuracy

90.3% (1.4b remaining)

Error of 7.9b against oracle of 6.5b and baseline of 21.3b

bsearch651.0ms

Steps
ItersRangePoint
9
6.258218916731328e+93
1.8883840965187804e+99
1.51853191339641e+99
9
-7.261872368850313e+67
-2.967245708633018e+62
-4.677090600991111e+67

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
049155
157155
done57155

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.2s8730×body80valid
357.0ms2931×body80nan