Details

Time bar (total: 18.5s)

sample200.0ms

Algorithm
intervals
Results
70.0ms151×body160valid
39.0ms281×body80nan
33.0ms537×pre80true
19.0ms41×body320valid
9.0ms64×body80valid

simplify102.0ms

Counts
1 → 1
Iterations
IterNodes
898
798
697
595
487
370
243
124
014

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* c a) 4)))
0.2b
(- (* b b) (* (* c a) 4))
0.2b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
37.9b
(- (sqrt (- (* b b) (* (* c a) 4))) b)

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
sqrt-prod add-log-exp
add-cbrt-cube add-exp-log associate-/l*
pow1 distribute-lft-out--
flip3-- flip--
associate-/r*
sub-neg sqrt-div diff-log associate-/l/
cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 84
Calls
4 calls:
8.0ms
(sqrt (- (* b b) (* (* c a) 4)))
7.0ms
(- (* b b) (* (* c a) 4))
76.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
49.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)

series432.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(sqrt (- (* b b) (* (* c a) 4)))
62.0ms
(- (* b b) (* (* c a) 4))
141.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
121.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)

simplify1.9s

Counts
96 → 96
Iterations
IterNodes
33755
21153
1395
0157

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.2b

localize12.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
10
00

prune50.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.2b

localize20.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (* -2 (/ (* a c) b)) a)
0.3b
(/ (* a c) b)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
21×add-cbrt-cube add-exp-log
cbrt-undiv div-exp
add-sqr-sqrt associate-/r* *-un-lft-identity times-frac add-cube-cbrt
prod-exp cbrt-unprod
pow1 clear-num frac-2neg div-inv associate-/l* add-log-exp
associate-*r/ associate-/l/
Counts
2 → 47
Calls
2 calls:
14.0ms
(/ (* -2 (/ (* a c) b)) a)
8.0ms
(/ (* a c) b)

series58.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(/ (* -2 (/ (* a c) b)) a)
31.0ms
(/ (* a c) b)

simplify2.8s

Counts
53 → 53
Iterations
IterNodes
37181
21093
1261
097

prune508.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 5.2b

localize28.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (/ (/ 1 c) -2) b)
0.3b
(/ 1 (* (/ (/ 1 c) -2) b))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
71×add-exp-log
52×add-sqr-sqrt
43×associate-*l*
41×*-un-lft-identity
40×add-cube-cbrt
36×div-exp
25×add-cbrt-cube
20×prod-exp
10×cbrt-undiv rec-exp 1-exp
pow1
cbrt-unprod
div-inv
unswap-sqr
associate-*r* associate-/l*
pow-prod-down associate-*l/ pow-flip add-log-exp
clear-num associate-/r* frac-2neg associate-/r/ *-commutative inv-pow
Counts
2 → 111
Calls
2 calls:
21.0ms
(* (/ (/ 1 c) -2) b)
16.0ms
(/ 1 (* (/ (/ 1 c) -2) b))

series48.0ms

Counts
2 → 6
Calls
2 calls:
25.0ms
(* (/ (/ 1 c) -2) b)
22.0ms
(/ 1 (* (/ (/ 1 c) -2) b))

simplify3.7s

Counts
117 → 117
Iterations
IterNodes
33283
21105
1478
0196

prune781.0ms

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 5.2b

regimes420.0ms

Accuracy

11.3% (6.1b remaining)

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

bsearch30.0ms

Steps
ItersRangePoint
2
0.014039008561512432
0.015746105955969297
0.014244826613571458

simplify6.0ms

Iterations
IterNodes
235
135
026

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.3s4818×body160valid
1.2s8344×body80nan
999.0ms16344×pre80true
712.0ms1357×body320valid
332.0ms1825×body80valid