Details

Time bar (total: 6.5s)

sample55.0ms

Algorithm
intervals
Results
10.0ms314×body80nan
10.0ms570×pre80true
9.0ms137×body160valid
7.0ms119×body80valid

simplify47.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01417
12517
24516
38716
410616
511416
done11416

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize10.0ms

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)

rewrite76.0ms

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))
38.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
22.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series295.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms
(- (* b b) (* (* 4.0 a) c))
103.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
80.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify976.0ms

Counts
195 → 195
Iterations

Useful iterations: done (970.0ms)

IterNodesCost
03214967
17804592
230174265
done50014264

prune522.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 9.8b

localize4.0ms

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

prune79.0ms

Pruning

27 alts after pruning (26 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)

rewrite19.0ms

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:
13.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
3.0ms
(/ (* a c) b)

series39.0ms

Counts
2 → 6
Calls
2 calls:
20.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
19.0ms
(/ (* a c) b)

simplify741.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (152.0ms)

IterNodesCost
01711200
14591154
22303992
done5001992

prune251.0ms

Pruning

38 alts after pruning (37 fresh and 1 done)

Merged error: 9.7b

localize10.0ms

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))

rewrite72.0ms

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:
6.0ms
(/ (* a c) b)
25.0ms
(/ (/ (/ (* -2.0 (/ (* a c) b)) 2.0) (sqrt a)) (sqrt a))
11.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) (sqrt a))

series148.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(/ (* a c) b)
47.0ms
(/ (/ (/ (* -2.0 (/ (* a c) b)) 2.0) (sqrt a)) (sqrt a))
76.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) (sqrt a))

simplify449.0ms

Counts
463 → 463
Iterations

Useful iterations: done (432.0ms)

IterNodesCost
060012162
1148511167
done500110959

prune723.0ms

Pruning

43 alts after pruning (42 fresh and 1 done)

Merged error: 9.6b

regimes602.0ms

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
315.0ms4461×body160valid
313.0ms16802×pre80true
288.0ms8802×body80nan
122.0ms3538×body80valid
0.0ms1×body320valid