Details

Time bar (total: 13.7s)

sample132.0ms

Algorithm
intervals
Results
36.0ms304×body80nan
34.0ms156×body160valid
28.0ms560×pre80true
11.0ms100×body80valid

simplify120.0ms

Counts
1 → 1
Iterations
IterNodes
done105
7105
6104
5102
494
377
244
125
014

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma b b (* (* a -4) c))
0.1b
(sqrt (fma b b (* (* a -4) c)))
0.3b
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
30.7b
(- (sqrt (fma b b (* (* a -4) c))) b)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 114
Calls
4 calls:
0.0ms
(fma b b (* (* a -4) c))
2.0ms
(sqrt (fma b b (* (* a -4) c)))
26.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
12.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

series421.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(fma b b (* (* a -4) c))
99.0ms
(sqrt (fma b b (* (* a -4) c)))
142.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
110.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

simplify1.0s

Counts
126 → 126
Iterations
IterNodes
done2000
32000
21008
1423
0180

prune600.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 8.9b

localize16.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune78.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 8.9b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
21×add-cbrt-cube add-exp-log
8×cbrt-undiv div-exp
6×add-sqr-sqrt associate-/r* *-un-lft-identity times-frac add-cube-cbrt
5×prod-exp cbrt-unprod
2×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Counts
2 → 53
Calls
2 calls:
9.0ms
(/ (* a c) b)
19.0ms
(/ (* -2 (/ (* a c) b)) a)

series46.0ms

Counts
2 → 6
Calls
2 calls:
23.0ms
(/ (* a c) b)
22.0ms
(/ (* -2 (/ (* a c) b)) a)

simplify1.1s

Counts
59 → 59
Iterations
IterNodes
done2014
32014
21285
1282
0103

prune320.0ms

Pruning

31 alts after pruning (30 fresh and 1 done)

Merged error: 8.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* a c) b)
0.3b
(/ -2 (sqrt a))
0.4b
(* (/ -2 (sqrt a)) (/ (/ (* a c) b) (sqrt a)))
0.4b
(/ (/ (* a c) b) (sqrt a))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
121×add-sqr-sqrt
91×*-un-lft-identity add-cube-cbrt
72×sqrt-prod
52×add-cbrt-cube add-exp-log
46×associate-*r*
22×cbrt-undiv div-exp associate-*l*
18×div-inv
15×associate-/r*
12×prod-exp cbrt-unprod
11×associate-/l*
9×unswap-sqr
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 249
Calls
4 calls:
19.0ms
(/ (* a c) b)
5.0ms
(/ -2 (sqrt a))
27.0ms
(* (/ -2 (sqrt a)) (/ (/ (* a c) b) (sqrt a)))
17.0ms
(/ (/ (* a c) b) (sqrt a))

series249.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(/ (* a c) b)
60.0ms
(/ -2 (sqrt a))
65.0ms
(* (/ -2 (sqrt a)) (/ (/ (* a c) b) (sqrt a)))
101.0ms
(/ (/ (* a c) b) (sqrt a))

simplify1.2s

Counts
261 → 261
Iterations
IterNodes
done2000
22000
11052
0345

prune1.3s

Pruning

39 alts after pruning (38 fresh and 1 done)

Merged error: 8.7b

regimes1.1s

Accuracy

41.4% (8.1b remaining)

Error of 17.2b against oracle of 9.1b and baseline of 22.9b

bsearch40.0ms

Steps
ItersRangePoint
2
82.56954229495332
91.66372883969355
83.70631561304585

simplify5.0ms

Iterations
IterNodes
done29
129
024

end0.0ms

sample5.7s

Algorithm
intervals
Results
1.8s16641×pre80true
1.4s8641×body80nan
1.4s4445×body160valid
616.0ms3555×body80valid