Details

Time bar (total: 20.8s)

sample98.0ms

Algorithm
intervals
Results
33.0ms538×pre80true
16.0ms282×body80nan
15.0ms147×body160valid
7.0ms45×body320valid
3.0ms64×body80valid

simplify542.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize22.0ms

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))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
39.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite183.0ms

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:
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(- (* b b) (* (* 4.0 a) c))
121.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
32.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series464.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms
(- (* b b) (* (* 4.0 a) c))
178.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
119.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.2s

Counts
82 → 82
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01541565
14011461
213421245
done50011233

prune268.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize29.0ms

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))
0.2b
(/ (/ (+ 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)))))

rewrite221.0ms

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:
26.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
104.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
74.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series694.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(- (* b b) (* (* 4.0 a) c))
233.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
262.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.3s

Counts
163 → 163
Iterations

Useful iterations: 2 (563.0ms)

IterNodesCost
02475048
16124510
224984166
done50014166

prune537.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite405.0ms

Algorithm
rewrite-expression-head
Rules
338×times-frac
263×add-sqr-sqrt
252×*-un-lft-identity
151×add-cube-cbrt
107×add-exp-log
85×associate-*r*
65×add-cbrt-cube
50×distribute-lft-out-- difference-of-squares
47×div-exp
35×prod-exp
30×associate-/l*
25×cbrt-undiv distribute-rgt-neg-in sqrt-prod
21×cbrt-unprod
16×associate-/r/
11×div-inv
10×associate-/r*
9×flip3-- flip--
7×pow1 associate-*l*
6×rec-exp 1-exp add-log-exp
4×unswap-sqr
2×frac-2neg clear-num
1×frac-times sub-neg pow-flip diff-log associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/ inv-pow
Counts
4 → 329
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
67.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
102.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
182.0ms
(* (/ (* (* a c) 4.0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series662.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (* b b) (* (* 4.0 a) c))
148.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
177.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
255.0ms
(* (/ (* (* a c) 4.0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify2.6s

Counts
341 → 341
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
043510074
112189067
242018096
done50008096

prune969.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c))))))))
0.4b
(* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c)))
0.7b
(pow (* (* a c) 4.0) 3)

rewrite495.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
58×*-un-lft-identity times-frac
36×difference-of-squares
34×add-cube-cbrt
23×add-exp-log add-cbrt-cube
21×sqr-pow
19×pow1
13×associate-/l*
12×distribute-lft-out--
11×associate-/r*
9×unpow-prod-down pow-prod-down prod-exp cbrt-unprod
8×sqrt-prod
4×distribute-rgt-neg-in associate-/r/ associate-/l/ add-log-exp
3×pow-unpow pow-pow flip3-+ associate-*r* pow-exp flip-+ rem-cube-cbrt
2×cbrt-undiv flip3-- frac-2neg associate-*r/ div-exp clear-num flip-- div-inv
1×distribute-rgt-in cube-mult pow-to-exp distribute-lft-in unpow3 div-sub cube-prod associate-*l* *-commutative
Counts
4 → 161
Calls
4 calls:
80.0ms
(/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c)))))
253.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c))))))))
108.0ms
(* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c)))
45.0ms
(pow (* (* a c) 4.0) 3)

series795.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c)))))
410.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* a c) 4.0) 3)) (+ (pow b 4) (* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c))))))))
119.0ms
(* (* (* a c) 4.0) (+ (* b b) (* (* 4.0 a) c)))
79.0ms
(pow (* (* a c) 4.0) 3)

simplify3.5s

Counts
173 → 173
Iterations

Useful iterations: 2 (1.3s)

IterNodesCost
03377440
18336981
244076599
done50016599

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes174.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01925
12625
done2625

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.5s4786×body160valid
862.0ms16502×pre80true
678.0ms8502×body80nan
397.0ms1349×body320valid
181.0ms1865×body80valid