Details

Time bar (total: 6.5s)

sample60.0ms

Algorithm
intervals
Results
12.0ms263×body80nan
12.0ms164×body160valid
9.0ms519×pre80true
4.0ms41×body320valid
2.0ms51×body80valid

simplify73.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
41.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
add-exp-log add-cbrt-cube
add-log-exp
fma-neg
times-frac associate-/l* difference-of-squares
pow1
expm1-log1p-u flip3-- flip-- log1p-expm1-u
distribute-lft-out--
cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 106
Calls
4 calls:
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(- (* b b) (* (* 4.0 a) c))
95.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
54.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series318.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms
(- (* b b) (* (* 4.0 a) c))
111.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
84.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify943.0ms

Counts
118 → 118
Iterations

Useful iterations: done (939.0ms)

IterNodesCost
01952476
14802169
214441861
done50011789

prune279.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.7b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune33.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.7b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log add-cbrt-cube
14×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac associate-/r*
pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u div-inv associate-/l* add-log-exp
associate-*r/ associate-/l/
Counts
2 → 55
Calls
2 calls:
23.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
12.0ms
(/ (* a c) b)

series43.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
21.0ms
(/ (* a c) b)

simplify656.0ms

Counts
61 → 61
Iterations

Useful iterations: 2 (205.0ms)

IterNodesCost
0111818
1314787
21661559
done5001559

prune137.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 4.6b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
37×add-exp-log add-cbrt-cube
18×prod-exp cbrt-unprod
cbrt-undiv div-exp
pow1 add-sqr-sqrt expm1-log1p-u add-cube-cbrt frac-2neg *-un-lft-identity times-frac clear-num associate-/r* log1p-expm1-u div-inv associate-/l* add-log-exp
Counts
1 → 33
Calls
1 calls:
33.0ms
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

series25.0ms

Counts
1 → 3
Calls
1 calls:
25.0ms
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

simplify1.8s

Counts
36 → 36
Iterations

Useful iterations: 2 (241.0ms)

IterNodesCost
088667
1280640
22036420
done5000420

prune39.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 4.6b

regimes261.0ms

Accuracy

11.6% (6.2b remaining)

Error of 11.2b against oracle of 5.1b and baseline of 12.0b

bsearch10.0ms

Steps
ItersRangePoint
1
0.0009123898704921593
0.0009468676847004557
0.0009210093240442334

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02438
13138
done3138

end0.0ms

sample1.6s

Algorithm
intervals
Results
348.0ms4882×body160valid
279.0ms8217×body80nan
272.0ms16217×pre80true
143.0ms1310×body320valid
66.0ms1808×body80valid