Details

Time bar (total: 10.5s)

sample36.0ms

Algorithm
intervals
Results
14.0ms269×body80valid
4.0ms85×body80nan

simplify147.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
02038
13938
27937
314237
417137
518137
618537
done18537

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.4b

localize85.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
25.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite113.0ms

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×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
32.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
80.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
177 → 177
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02086992
14584570
212263570
done50002949

prune402.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.0b

localize88.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.1b
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
4.3b
(/ (* a c) b)
25.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
32×add-sqr-sqrt
23×add-cube-cbrt
18×prod-diff
16×sqrt-prod
14×add-exp-log add-cbrt-cube
9×times-frac
7×associate-/l*
6×fma-neg add-log-exp
5×pow1 distribute-lft-out--
4×cbrt-undiv expm1-log1p-u div-exp associate-/r* log1p-expm1-u difference-of-squares
3×flip3-- flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num cbrt-unprod div-inv associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-sub
Counts
4 → 113
Calls
4 calls:
51.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
59.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
10.0ms
(/ (* a c) b)
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
62.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
20.0ms
(/ (* a c) b)
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
125 → 125
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02172386
15442081
219591775
done50011679

prune408.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
25.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/r* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/r/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 105
Calls
4 calls:
49.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
8.0ms
(- (* b b) (* (* 4.0 a) c))
52.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
46.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify950.0ms

Counts
117 → 117
Iterations

Useful iterations: done (946.0ms)

IterNodesCost
01862435
14392125
213421819
done50001750

prune364.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize100.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.9b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.1b
(/ (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))) (* 2.0 a))
25.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
46×*-un-lft-identity
36×add-cube-cbrt
34×times-frac
30×add-exp-log
23×add-cbrt-cube
22×associate-*r*
18×prod-diff
16×sqrt-prod
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
7×pow1 associate-*l*
6×fma-neg associate-/l* add-log-exp unswap-sqr
5×distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u difference-of-squares
3×flip3-- flip-- div-inv
2×distribute-rgt-neg-in sqrt-div associate-/l/
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r* *-commutative
Counts
4 → 151
Calls
4 calls:
49.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
43.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
57.0ms
(/ (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))) (* 2.0 a))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
48.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
86.0ms
(/ (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))) (* 2.0 a))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
163 → 163
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03023540
18203175
230662336
done50002222

prune616.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

regimes200.0ms

Accuracy

93.2% (1.0b remaining)

Error of 7.8b against oracle of 6.8b and baseline of 21.3b

bsearch261.0ms

Steps
ItersRangePoint
9
8.777746745010686e+110
1.2290467223415774e+117
1.1912031425131646e+117
9
1.1467953016179043e-293
9.802722462678435e-287
1.160883915256953e-293
7
-1.6239005782062206e+154
-7.680972122048022e+152
-1.3333004218627638e+154

simplify13.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
051180
160178
done60178

end0.0ms

sample962.0ms

Algorithm
intervals
Results
459.0ms8781×body80valid
142.0ms2958×body80nan