Details

Time bar (total: 7.7s)

sample57.0ms

Algorithm
intervals
Results
10.0ms314×body80nan
10.0ms570×pre80true
10.0ms137×body160valid
7.0ms119×body80valid

simplify51.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12517
24516
38716
410516
511316
done11316

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
27.3b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite78.0ms

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:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
39.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
22.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series308.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
50.0ms
(- (* b b) (* (* 4.0 a) c))
109.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify984.0ms

Counts
195 → 195
Iterations

Useful iterations: done (977.0ms)

IterNodesCost
03214967
17514592
226044265
done50004264

prune546.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 9.8b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune78.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 9.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
0.2b
(/ (* a c) b)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-exp-log add-cbrt-cube
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×cbrt-undiv div-exp
8×associate-/l*
6×associate-/r* div-inv
5×prod-exp cbrt-unprod
2×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
1×associate-/l/
Counts
2 → 77
Calls
2 calls:
10.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
3.0ms
(/ (* a c) b)

series45.0ms

Counts
2 → 6
Calls
2 calls:
25.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
20.0ms
(/ (* a c) b)

simplify586.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (187.0ms)

IterNodesCost
01711200
14441154
21950992
done5000992

prune255.0ms

Pruning

37 alts after pruning (36 fresh and 1 done)

Merged error: 9.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (* a c) b)
0.3b
(/ (/ (/ (* -2.0 (/ (* a c) b)) 2.0) (sqrt a)) (sqrt a))
0.3b
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) (sqrt a))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
762×times-frac
318×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
312×sqrt-prod
59×div-inv
55×add-exp-log add-cbrt-cube
54×associate-/l*
30×cbrt-undiv div-exp
15×associate-/r*
9×prod-exp cbrt-unprod
3×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×associate-/l/
Counts
3 → 454
Calls
3 calls:
4.0ms
(/ (* a c) b)
25.0ms
(/ (/ (/ (* -2.0 (/ (* a c) b)) 2.0) (sqrt a)) (sqrt a))
15.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) (sqrt a))

series147.0ms

Counts
3 → 9
Calls
3 calls:
19.0ms
(/ (* a c) b)
51.0ms
(/ (/ (/ (* -2.0 (/ (* a c) b)) 2.0) (sqrt a)) (sqrt a))
76.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) (sqrt a))

simplify1.8s

Counts
463 → 463
Iterations

Useful iterations: 2 (911.0ms)

IterNodesCost
060012162
1146410973
2497510230
done500010230

prune654.0ms

Pruning

40 alts after pruning (39 fresh and 1 done)

Merged error: 9.6b

regimes550.0ms

Accuracy

46.8% (7.3b remaining)

Error of 16.4b against oracle of 9.0b and baseline of 22.8b

bsearch4.0ms

Steps
ItersRangePoint
0
3187.1734153117472
3187.188536646724
3187.1809759792354

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02238
12638
done2638

end0.0ms

sample1.4s

Algorithm
intervals
Results
308.0ms4461×body160valid
299.0ms16802×pre80true
292.0ms8802×body80nan
122.0ms3538×body80valid
0.0ms1×body320valid