Details

Time bar (total: 13.2s)

sample34.0ms

Algorithm
intervals
Results
15.0ms286×body80valid
4.0ms79×body80nan

simplify110.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
02038
13938
27937
314337
417037
517937
618237
done18237

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.5b

localize113.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 neg-log
Counts
4 → 140
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series259.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify618.0ms

Counts
152 → 152
Iterations

Useful iterations: done (613.0ms)

IterNodesCost
01816137
14224178
213133279
done50003272

prune429.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize114.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.6b
(/ (* a c) b)
4.9b
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
59×add-sqr-sqrt
58×*-un-lft-identity
50×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×add-exp-log add-cbrt-cube
10×fma-neg
8×times-frac associate-/r* add-log-exp
7×neg-mul-1
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u distribute-lft-out-- difference-of-squares
3×flip3-- flip--
2×frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l*
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 159
Calls
4 calls:
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(/ (* a c) b)
47.0ms
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series229.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(/ (* a c) b)
66.0ms
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify849.0ms

Counts
171 → 171
Iterations

Useful iterations: 2 (208.0ms)

IterNodesCost
02616392
16354465
223983464
done50003464

prune485.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.2b

localize119.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.5b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.9b
(/ (* 2.0 c) (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite362.0ms

Algorithm
rewrite-expression-head
Rules
88×add-sqr-sqrt
71×*-un-lft-identity
63×add-cube-cbrt
60×prod-diff
34×sqrt-prod
33×times-frac
30×add-exp-log
23×add-cbrt-cube
22×distribute-rgt-neg-in associate-*r*
21×distribute-lft-neg-in
11×cbrt-prod
10×fma-neg
9×cbrt-undiv div-exp prod-exp cbrt-unprod
8×add-log-exp
7×pow1 neg-mul-1 associate-*l*
6×unswap-sqr
5×associate-/r*
4×expm1-log1p-u log1p-expm1-u distribute-lft-out-- difference-of-squares
3×flip3-- flip-- div-inv
2×sqrt-div diff-log associate-/r/
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 197
Calls
4 calls:
18.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
309.0ms
(/ (* 2.0 c) (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
99.0ms
(/ (* 2.0 c) (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
209 → 209
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03457518
19315564
238044153
done50004149

prune730.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize129.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.9b
(/ (* 2.0 c) (- (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))) b) b))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite2.7s

Algorithm
rewrite-expression-head
Rules
78×add-exp-log
66×add-sqr-sqrt
60×prod-diff
59×*-un-lft-identity
51×add-cube-cbrt
44×add-cbrt-cube
34×sqrt-prod
33×prod-exp cbrt-unprod
24×cbrt-undiv div-exp
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
13×times-frac
10×fma-neg
8×add-log-exp
7×pow1 neg-mul-1 associate-*l*
5×associate-*r* associate-/r*
4×expm1-log1p-u log1p-expm1-u distribute-lft-out-- difference-of-squares unswap-sqr
3×flip3-- flip-- div-inv
2×sqrt-div diff-log associate-/r/
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 196
Calls
4 calls:
36.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.7s
(/ (* 2.0 c) (- (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))) b) b))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
217.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms
(/ (* 2.0 c) (- (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))) b) b))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
208 → 208
Iterations

Useful iterations: 2 (400.0ms)

IterNodesCost
03628978
110356987
245075329
done50005329

prune807.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.9b

regimes316.0ms

Accuracy

90.5% (1.4b remaining)

Error of 7.9b against oracle of 6.5b and baseline of 21.4b

bsearch185.0ms

Steps
ItersRangePoint
8
1.5276508475467709e+44
4.1560730947117816e+46
4.1199128263687574e+46
9
-3.226264717511912e+140
-2.187052964502477e+134
-3.505198499083171e+136

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
055154
170154
272154
done72154

end0.0ms

sample825.0ms

Algorithm
intervals
Results
449.0ms8739×body80valid
137.0ms2862×body80nan