Details

Time bar (total: 6.3s)

sample58.0ms

Algorithm
intervals
Results
10.0ms145×body160valid
9.0ms293×body80nan
9.0ms549×pre80true
5.0ms47×body320valid
2.0ms64×body80valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219
done1219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
35.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms
(- (* b b) (* (* 4.0 a) c))
23.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series333.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
115.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
52.0ms
(- (* b b) (* (* 4.0 a) c))
86.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify50.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0438854
11702750
25001735
done5001735

prune264.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt *-un-lft-identity
90×times-frac
79×add-cube-cbrt
61×prod-diff
41×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 expm1-log1p-u log1p-expm1-u div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 231
Calls
4 calls:
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
88.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
61.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series498.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
164.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
200.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify155.0ms

Counts
243 → 243
Iterations

Useful iterations: 2 (117.0ms)

IterNodesCost
08325099
139673830
250013828
done50013828

prune557.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.4b
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
181×prod-diff
132×add-sqr-sqrt *-un-lft-identity
124×add-cube-cbrt
92×sqrt-prod
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
19×neg-mul-1
18×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
9×pow1
7×associate-*r*
6×prod-exp cbrt-unprod
4×expm1-log1p-u sub-neg flip3-- associate-*r/ flip-- log1p-expm1-u distribute-lft-out-- difference-of-squares
3×cbrt-undiv times-frac diff-log div-exp pow-prod-down associate-/l*
2×associate-/r/ associate-/l/
1×associate--l- neg-sub0 frac-2neg flip3-+ associate-*l* neg-log clear-num associate-/r* *-commutative flip-+ div-inv
Counts
4 → 285
Calls
4 calls:
91.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
58.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series407.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
84.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
161.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify85.0ms

Counts
297 → 297
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010108635
150015618
done50015618

prune453.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (pow (* b b) 3) (pow (* (* 4.0 a) c) 3)) (fma (* 4.0 (* a c)) (fma b b (* (* 4.0 a) c)) (* (* b b) (* b b))))
0.5b
(* (* b b) (* b b))
0.7b
(pow (* b b) 3)
0.7b
(pow (* (* 4.0 a) c) 3)

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
129×pow1
48×add-sqr-sqrt
39×times-frac
37×pow-prod-up
32×*-un-lft-identity difference-of-squares
27×add-exp-log pow-prod-down add-cbrt-cube
26×sqr-pow
24×add-cube-cbrt
23×pow-sqr
19×pow-plus
14×pow2
13×associate-/l*
12×prod-exp cbrt-unprod
10×unpow-prod-down cube-prod
9×pow-pow
6×pow-unpow
5×pow-exp rem-cube-cbrt
4×difference-cubes expm1-log1p-u log1p-expm1-u distribute-lft-out-- add-log-exp
3×associate-/r*
2×cube-mult pow-to-exp unpow3 associate-/l/
1×cbrt-undiv flip3-- frac-2neg div-sub swap-sqr div-exp associate-*r* associate-*l* clear-num *-commutative flip-- div-inv unswap-sqr
Counts
4 → 192
Calls
4 calls:
48.0ms
(/ (- (pow (* b b) 3) (pow (* (* 4.0 a) c) 3)) (fma (* 4.0 (* a c)) (fma b b (* (* 4.0 a) c)) (* (* b b) (* b b))))
30.0ms
(* (* b b) (* b b))
6.0ms
(pow (* b b) 3)
17.0ms
(pow (* (* 4.0 a) c) 3)

series280.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (- (pow (* b b) 3) (pow (* (* 4.0 a) c) 3)) (fma (* 4.0 (* a c)) (fma b b (* (* 4.0 a) c)) (* (* b b) (* b b))))
33.0ms
(* (* b b) (* b b))
49.0ms
(pow (* b b) 3)
59.0ms
(pow (* (* 4.0 a) c) 3)

simplify99.0ms

Counts
204 → 204
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
05672218
124432095
250022089
done50022089

prune672.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes109.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03325
13525
23525
done3525

end0.0ms

sample1.5s

Algorithm
intervals
Results
323.0ms4779×body160valid
276.0ms8549×body80nan
275.0ms16549×pre80true
142.0ms1363×body320valid
65.0ms1858×body80valid