Details

Time bar (total: 8.9s)

sample43.0ms

Algorithm
intervals
Results
11.0ms40×body2560valid
7.0ms187×body80valid
4.0ms23×body1280valid
3.0ms86×body80nan
2.0ms16×body640valid
1.0ms9×body320valid
1.0ms2×body5120valid
0.0ms5×body160valid

simplify51.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12517
24516
38716
410616
511416
done11416

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
0.8b
(- (* b b) (* 4.0 (* a c)))
1.3b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite74.0ms

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-/l*
19×prod-diff
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 183
Calls
4 calls:
37.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
3.0ms
(- (* b b) (* 4.0 (* a c)))
21.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series303.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) a)
43.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify993.0ms

Counts
195 → 195
Iterations

Useful iterations: done (986.0ms)

IterNodesCost
03194967
17794592
229844265
done50014264

prune514.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) (/ 1 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.3b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
46×*-un-lft-identity
36×add-cube-cbrt
34×times-frac
26×add-exp-log
22×associate-*l*
19×prod-diff sqrt-prod
16×add-cbrt-cube
13×associate-*r*
8×div-exp prod-exp add-log-exp difference-of-squares
7×pow1 fma-neg
6×unswap-sqr
4×cbrt-undiv expm1-log1p-u cbrt-unprod log1p-expm1-u distribute-lft-out--
3×flip3-- flip--
2×sub-neg rec-exp sqrt-div diff-log 1-exp div-inv
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ un-div-inv *-commutative
Counts
4 → 142
Calls
4 calls:
53.0ms
(* (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) (/ 1 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
21.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0) (/ 1 a))
48.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
66.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts
154 → 154
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02613349
17412948
227742479
done50002478

prune354.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a)
0.8b
(- (* b b) (* 4.0 (* a c)))
1.3b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-exp-log add-cbrt-cube associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num div-inv
Counts
4 → 118
Calls
4 calls:
39.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a)
3.0ms
(- (* b b) (* 4.0 (* a c)))
22.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series294.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a)
48.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify646.0ms

Counts
130 → 130
Iterations

Useful iterations: done (642.0ms)

IterNodesCost
01972768
14852451
216922164
done50002163

prune325.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.3b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
137×add-sqr-sqrt
110×*-un-lft-identity
84×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
24×associate-/r*
19×prod-diff
15×add-exp-log
13×distribute-lft-out--
9×associate-/r/ add-cbrt-cube
8×add-log-exp
7×flip3-- fma-neg div-exp flip--
6×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv associate-/l*
2×sub-neg rec-exp sqrt-div diff-log 1-exp
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num inv-pow
Counts
4 → 196
Calls
4 calls:
28.0ms
(/ 1 (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
21.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series331.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ 1 (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
48.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts
208 → 208
Iterations

Useful iterations: 2 (256.0ms)

IterNodesCost
03015378
16944728
226484177
done50004177

prune390.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.3b

regimes211.0ms

Accuracy

83.3% (4.7b remaining)

Error of 10.1b against oracle of 5.4b and baseline of 33.8b

bsearch99.0ms

Steps
ItersRangePoint
8
1.3679096689958957e-81
5.608239720335765e-77
3.84613441880261e-81
7
-3.550313394724354e+57
-2.3888623512096697e+55
-3.124283374205192e+57

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03249
14145
24545
done4545

end0.0ms

sample1.2s

Algorithm
intervals
Results
254.0ms1074×body2560valid
232.0ms5844×body80valid
169.0ms907×body1280valid
106.0ms2890×body80nan
73.0ms452×body640valid
34.0ms102×body5120valid
26.0ms234×body320valid
9.0ms119×body160valid