Details

Time bar (total: 9.2s)

sample68.0ms

Algorithm
intervals
Results
18.0ms120×body320valid
10.0ms238×body80nan
10.0ms494×pre80true
8.0ms97×body160valid
3.0ms17×body640valid
1.0ms22×body80valid

simplify51.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12417
24416
37816
49016
59816
done9816

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(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))
27.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite59.0ms

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)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
39.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series300.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify853.0ms

Counts
82 → 82
Iterations

Useful iterations: done (850.0ms)

IterNodesCost
01541565
14061461
213611245
done50001235

prune188.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

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

rewrite114.0ms

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))
36.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
54.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series419.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
166.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
130.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify917.0ms

Counts
163 → 163
Iterations

Useful iterations: done (907.0ms)

IterNodesCost
02545790
16705273
223874513
done50004511

prune431.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
0.3b
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
0.6b
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
0.7b
(pow (- (* b b) (* (* 4.0 a) c)) 3)

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
166×add-sqr-sqrt
138×times-frac
96×*-un-lft-identity
60×difference-of-squares
56×add-cube-cbrt
52×cbrt-prod
50×sqrt-prod
42×associate-/l*
20×distribute-lft-out--
19×add-exp-log add-cbrt-cube
16×unpow-prod-down cube-prod
12×associate-/r* sqr-pow
10×distribute-rgt-neg-in
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×cube-div div-inv add-log-exp
3×pow-unpow associate-/l/
2×cube-mult cbrt-div frac-2neg unpow3 prod-exp clear-num cbrt-unprod
1×pow-to-exp pow-pow flip3-+ pow1/3 pow-exp rem-cbrt-cube flip-+ rem-cube-cbrt
Counts
4 → 209
Calls
4 calls:
63.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
98.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
5.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
5.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

series427.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
127.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
45.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
92.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

simplify1.1s

Counts
221 → 221
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03558874
19017419
232486489
done50006487

prune656.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (pow b 2) (* 4.0 (* a c)))))
0.1b
(- (pow b 2) (* 4.0 (* a c)))
0.1b
(* a (- (- b) (sqrt (- (pow b 2) (* 4.0 (* a c))))))
0.4b
(/ (+ 0 (* 4.0 (* a c))) (* a (- (- b) (sqrt (- (pow b 2) (* 4.0 (* a c)))))))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×*-un-lft-identity
11×add-exp-log add-cbrt-cube
10×add-log-exp
8×add-cube-cbrt
7×associate-*r*
6×pow1
4×sub-neg flip3-- associate-*r/ flip-- distribute-lft-out-- difference-of-squares
3×times-frac diff-log associate-*l* associate-/l*
2×cbrt-undiv distribute-rgt-in distribute-rgt-neg-in distribute-lft-in div-exp prod-exp sqrt-prod associate-/r/ cbrt-unprod 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 → 83
Calls
4 calls:
19.0ms
(- (- b) (sqrt (- (pow b 2) (* 4.0 (* a c)))))
8.0ms
(- (pow b 2) (* 4.0 (* a c)))
74.0ms
(* a (- (- b) (sqrt (- (pow b 2) (* 4.0 (* a c))))))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (* a (- (- b) (sqrt (- (pow b 2) (* 4.0 (* a c)))))))

series376.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (pow b 2) (* 4.0 (* a c)))))
46.0ms
(- (pow b 2) (* 4.0 (* a c)))
104.0ms
(* a (- (- b) (sqrt (- (pow b 2) (* 4.0 (* a c))))))
148.0ms
(/ (+ 0 (* 4.0 (* a c))) (* a (- (- b) (sqrt (- (pow b 2) (* 4.0 (* a c)))))))

simplify647.0ms

Counts
95 → 95
Iterations

Useful iterations: done (644.0ms)

IterNodesCost
01642004
14261822
217221606
done50001605

prune251.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes92.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 2 (3.0ms)

IterNodesCost
02230
13428
24327
34527
done4527

end0.0ms

sample1.8s

Algorithm
intervals
Results
458.0ms3615×body320valid
329.0ms8135×body80nan
318.0ms16135×pre80true
252.0ms2978×body160valid
84.0ms495×body640valid
40.0ms912×body80valid