Details

Time bar (total: 19.7s)

sample243.0ms

Algorithm
intervals
Results
68.0ms106×body160valid
24.0ms109×body320valid
23.0ms265×body80nan
18.0ms521×pre80true
4.0ms12×body640valid
2.0ms29×body80valid

simplify95.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.0b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite198.0ms

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:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(- (* b b) (* (* 4.0 a) c))
113.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
60.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series445.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms
(- (* b b) (* (* 4.0 a) c))
148.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
132.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.2s

Counts
82 → 82
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01541565
14191461
219261245
done50011239

prune313.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* b b) (* (* 4.0 a) c))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

rewrite244.0ms

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:
12.0ms
(- (* b b) (* (* 4.0 a) c))
36.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
114.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series618.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* b b) (* (* 4.0 a) c))
103.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
249.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
203.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify2.5s

Counts
163 → 163
Iterations

Useful iterations: 2 (739.0ms)

IterNodesCost
02475048
16584512
237894174
done50024174

prune598.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* b b) (* (* 4.0 a) c))
0.1b
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.4b
(/ (+ 0 (* (* 4.0 a) c)) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

rewrite359.0ms

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
4×sub-neg flip3-- associate-*r/ 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 associate-*l/ 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:
17.0ms
(- (* b b) (* (* 4.0 a) c))
129.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
26.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
182.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

series570.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(- (* b b) (* (* 4.0 a) c))
148.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
119.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
217.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

simplify2.3s

Counts
97 → 97
Iterations

Useful iterations: 2 (642.0ms)

IterNodesCost
01832186
15431993
235021725
done50001725

prune367.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* b b) (* (* 4.0 a) c))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.4b
(* (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

rewrite279.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
61×*-un-lft-identity
51×add-exp-log
46×times-frac
29×add-cube-cbrt
27×associate-*l* add-cbrt-cube
20×prod-exp
16×div-exp distribute-lft-out-- difference-of-squares
10×add-log-exp
8×cbrt-undiv distribute-rgt-neg-in sqrt-prod cbrt-unprod
7×associate-*r* associate-/r*
6×pow1
4×rec-exp flip3-- 1-exp associate-/r/ flip--
3×diff-log div-inv associate-/l*
2×sub-neg associate-/l/ unswap-sqr
1×associate--l- neg-sub0 frac-times frac-2neg flip3-+ associate-*r/ pow-prod-down neg-log associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 146
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
95.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
146.0ms
(* (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

series743.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (* b b) (* (* 4.0 a) c))
136.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
304.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
235.0ms
(* (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

simplify3.1s

Counts
158 → 158
Iterations

Useful iterations: 2 (871.0ms)

IterNodesCost
02534638
17564068
248283604
done50013604

prune689.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes172.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01725
12223
22323
done2323

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.3s3551×body320valid
1.1s16336×pre80true
656.0ms8336×body80nan
600.0ms3003×body160valid
140.0ms484×body640valid
113.0ms962×body80valid