Details

Time bar (total: 15.2s)

sample72.0ms

Algorithm
intervals
Results
14.0ms299×body80nan
14.0ms142×body160valid
12.0ms555×pre80true
6.0ms114×body80valid

simplify83.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite162.0ms

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:
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms
(- (* b b) (* (* 4.0 a) c))
113.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series454.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms
(- (* b b) (* (* 4.0 a) c))
152.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
103.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.3s

Counts
82 → 82
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01541565
14011461
213421245
done50011233

prune260.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

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)))))

rewrite215.0ms

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:
24.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
109.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
68.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series604.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
60.0ms
(- (* b b) (* (* 4.0 a) c))
182.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
264.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.2s

Counts
163 → 163
Iterations

Useful iterations: 2 (464.0ms)

IterNodesCost
02475048
16124510
224984166
done50014166

prune663.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(* (* 2.0 a) (- (- 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
18×add-exp-log add-cbrt-cube
15×add-sqr-sqrt *-un-lft-identity
10×add-log-exp
9×pow1
7×add-cube-cbrt associate-*r*
6×prod-exp cbrt-unprod
4×sub-neg flip3-- associate-*r/ flip-- distribute-lft-out-- difference-of-squares
3×cbrt-undiv times-frac diff-log div-exp pow-prod-down 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-+ associate-*l* neg-log clear-num associate-/r* *-commutative flip-+ div-inv
Counts
4 → 85
Calls
4 calls:
32.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
86.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms
(- (* b b) (* (* 4.0 a) c))
68.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series626.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
170.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
63.0ms
(- (* b b) (* (* 4.0 a) c))
273.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify1.4s

Counts
97 → 97
Iterations

Useful iterations: 2 (497.0ms)

IterNodesCost
01762262
14932066
225611750
done50021750

prune406.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
47×*-un-lft-identity
43×times-frac
33×add-exp-log add-cbrt-cube
19×add-cube-cbrt
14×distribute-lft-out-- difference-of-squares
13×cbrt-undiv div-exp
10×sqrt-prod add-log-exp
9×prod-exp cbrt-unprod div-inv
7×distribute-rgt-neg-in associate-/r*
5×pow1 associate-/l*
4×flip3-- flip--
3×diff-log
2×sub-neg sqrt-div associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 119
Calls
4 calls:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
87.0ms
(/ (/ (* 4.0 (* a c)) (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
44.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.0ms
(- (* b b) (* (* 4.0 a) c))

series428.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
160.0ms
(/ (/ (* 4.0 (* a c)) (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
95.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms
(- (* b b) (* (* 4.0 a) c))

simplify2.1s

Counts
131 → 131
Iterations

Useful iterations: 2 (810.0ms)

IterNodesCost
02373765
16333592
233263170
done50013170

prune494.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes221.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01723
12223
done2223

end0.0ms

sample4.0s

Algorithm
intervals
Results
888.0ms4493×body160valid
853.0ms3507×body80valid
729.0ms8495×body80nan
686.0ms16495×pre80true