Details

Time bar (total: 9.2s)

sample58.0ms

Algorithm
intervals
Results
15.0ms159×body160valid
9.0ms504×pre80true
9.0ms248×body80nan
5.0ms46×body320valid
2.0ms51×body80valid

simplify44.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01417
12417
24416
37816
49016
59816
done9816

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
38.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-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 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(- (* b b) (* (* 4.0 a) c))
34.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series302.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
45.0ms
(- (* b b) (* (* 4.0 a) c))
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify504.0ms

Counts
82 → 82
Iterations

Useful iterations: done (501.0ms)

IterNodesCost
01541565
14061461
213801245
done50011235

prune196.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 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 → 151
Calls
4 calls:
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
38.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
51.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series452.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
181.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
148.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify849.0ms

Counts
163 → 163
Iterations

Useful iterations: done (843.0ms)

IterNodesCost
02505760
16535251
224644487
done50014467

prune454.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (* 2.0 (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×*-un-lft-identity
15×add-exp-log add-cbrt-cube
10×add-log-exp
8×add-cube-cbrt
7×associate-*r*
6×pow1 associate-*r/
4×sub-neg flip3-- prod-exp flip-- cbrt-unprod distribute-lft-out-- difference-of-squares
3×cbrt-undiv times-frac diff-log div-exp associate-*l* associate-/l*
2×distribute-rgt-in distribute-rgt-neg-in distribute-lft-in sqrt-prod associate-/r/ associate-/l/
1×associate--l- neg-sub0 frac-2neg flip3-+ pow-prod-down neg-log clear-num associate-/r* *-commutative flip-+ div-inv unswap-sqr
Counts
4 → 85
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
43.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
53.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (* 2.0 (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))

series377.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
109.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
147.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (* 2.0 (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))

simplify754.0ms

Counts
97 → 97
Iterations

Useful iterations: done (751.0ms)

IterNodesCost
01862332
15172166
221651761
done50001742

prune275.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.3b
(* (/ (- (* 4.0 (* a c)) 0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
332×times-frac
260×add-sqr-sqrt
234×*-un-lft-identity
144×add-cube-cbrt
85×associate-*r*
48×add-exp-log
44×distribute-lft-out-- difference-of-squares
30×add-cbrt-cube
27×associate-/l*
23×div-exp
22×distribute-rgt-neg-in sqrt-prod
14×associate-/r/
13×associate-*l*
12×cbrt-undiv
10×prod-exp div-inv add-log-exp
9×flip3-- flip--
8×unswap-sqr
6×pow1 cbrt-unprod
3×rec-exp diff-log 1-exp associate-/r*
2×sub-neg
1×associate--l- neg-sub0 frac-times frac-2neg associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 292
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
38.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
99.0ms
(* (/ (- (* 4.0 (* a c)) 0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series402.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
121.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
152.0ms
(* (/ (- (* 4.0 (* a c)) 0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify1.7s

Counts
304 → 304
Iterations

Useful iterations: 2 (706.0ms)

IterNodesCost
04179274
112288104
244977455
done50007455

prune650.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes135.0ms

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
02029
12829
done2829

end0.0ms

sample1.5s

Algorithm
intervals
Results
353.0ms4829×body160valid
301.0ms16283×pre80true
284.0ms8283×body80nan
152.0ms1358×body320valid
70.0ms1813×body80valid