Details

Time bar (total: 6.1s)

sample50.0ms

Algorithm
intervals
Results
11.0ms171×body160valid
9.0ms517×pre80true
8.0ms261×body80nan
3.0ms33×body320valid
2.0ms52×body80valid

simplify55.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01217
12217
24216
38216
410016
510816
done10816

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 3.0 a) c))
0.3b
(* (* 3.0 a) c)
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
38.6b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-cube-cbrt fma-def add-log-exp
9×pow1
6×distribute-rgt-neg-in distribute-lft-out
5×times-frac associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u
3×distribute-lft-neg-in associate-*r* pow-prod-down
2×cbrt-undiv neg-sub0 associate-+l- flip3-+ div-exp sum-log flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg flip3-- frac-2neg fma-neg diff-log div-sub associate-*l* prod-diff neg-log clear-num associate-/r* *-commutative flip-- div-inv
Counts
4 → 93
Calls
4 calls:
3.0ms
(- (* b b) (* (* 3.0 a) c))
7.0ms
(* (* 3.0 a) c)
37.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
16.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series256.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 3.0 a) c))
23.0ms
(* (* 3.0 a) c)
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify956.0ms

Counts
105 → 105
Iterations

Useful iterations: done (954.0ms)

IterNodesCost
01671559
14461478
217471247
done50011246

prune268.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.6b

localize6.0ms

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

prune32.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.3b
(* -1.5 (/ (* a c) b))
0.3b
(/ (* a c) b)
0.4b
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log add-cbrt-cube
17×prod-exp cbrt-unprod
16×cbrt-undiv div-exp
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×times-frac associate-*r*
5×pow1
4×associate-/r*
3×expm1-log1p-u associate-*l* log1p-expm1-u div-inv add-log-exp
2×frac-2neg associate-*r/ clear-num associate-/l*
1×pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
3 → 84
Calls
3 calls:
8.0ms
(* -1.5 (/ (* a c) b))
3.0ms
(/ (* a c) b)
9.0ms
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series72.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(* -1.5 (/ (* a c) b))
20.0ms
(/ (* a c) b)
24.0ms
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify987.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (191.0ms)

IterNodesCost
01291138
13831097
21927813
done5001813

prune195.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 5.5b

localize7.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ -1.5 (* a (/ 3.0 (/ (* a c) b))))
0.3b
(/ 3.0 (/ (* a c) b))
0.3b
(/ (* a c) b)
0.3b
(* a (/ 3.0 (/ (* a c) b)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
70×times-frac
52×add-exp-log add-cbrt-cube
44×add-sqr-sqrt
39×add-cube-cbrt *-un-lft-identity
26×associate-*r*
22×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
11×associate-/r* div-inv
7×associate-/l*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*l* clear-num associate-/r/
2×associate-*r/ unswap-sqr
1×pow-prod-down *-commutative
Counts
4 → 154
Calls
4 calls:
10.0ms
(/ -1.5 (* a (/ 3.0 (/ (* a c) b))))
5.0ms
(/ 3.0 (/ (* a c) b))
3.0ms
(/ (* a c) b)
17.0ms
(* a (/ 3.0 (/ (* a c) b)))

series93.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ -1.5 (* a (/ 3.0 (/ (* a c) b))))
28.0ms
(/ 3.0 (/ (* a c) b))
19.0ms
(/ (* a c) b)
24.0ms
(* a (/ 3.0 (/ (* a c) b)))

simplify852.0ms

Counts
166 → 166
Iterations

Useful iterations: done (848.0ms)

IterNodesCost
02202041
15601955
220481511
done50011509

prune290.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 5.5b

regimes364.0ms

Accuracy

6.9% (6.3b remaining)

Error of 11.4b against oracle of 5.1b and baseline of 11.9b

bsearch26.0ms

Steps
ItersRangePoint
4
0.1123162942048503
0.21462860711519482
0.11411310699712364

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01826
12626
23426
done3426

end0.0ms

sample1.4s

Algorithm
intervals
Results
323.0ms4861×body160valid
305.0ms16375×pre80true
252.0ms8375×body80nan
129.0ms1380×body320valid
58.0ms1759×body80valid