Details

Time bar (total: 18.2s)

sample95.0ms

Algorithm
intervals
Results
18.0ms146×body160valid
18.0ms302×body80nan
15.0ms558×pre80true
7.0ms110×body80valid

simplify111.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize26.0ms

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))
28.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite165.0ms

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:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(- (* b b) (* (* 4.0 a) c))
99.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
41.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series414.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
57.0ms
(- (* b b) (* (* 4.0 a) c))
158.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
123.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify969.0ms

Counts
82 → 82
Iterations

Useful iterations: done (966.0ms)

IterNodesCost
01541565
14191461
219261245
done50011239

prune218.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(- (- 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))
0.4b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite190.0ms

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:
8.0ms
(- (* b b) (* (* 4.0 a) c))
24.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
86.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
66.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series558.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (* b b) (* (* 4.0 a) c))
93.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
191.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
203.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.0s

Counts
163 → 163
Iterations

Useful iterations: 2 (632.0ms)

IterNodesCost
02475048
16594512
238214174
done50014174

prune480.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite232.0ms

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:
94.0ms
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms
(- (* b b) (* (* 4.0 a) c))
35.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
89.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series535.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
74.0ms
(- (* b b) (* (* 4.0 a) c))
118.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
209.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify2.7s

Counts
97 → 97
Iterations

Useful iterations: 2 (727.0ms)

IterNodesCost
01762262
15432068
243271766
done50001766

prune465.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(+ (* (* a 2.0) (- b)) (* (* a 2.0) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b
(* (* a 2.0) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (+ (* (* a 2.0) (- b)) (* (* a 2.0) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-*r*
12×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
8×add-log-exp
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
5×distribute-rgt-neg-out distribute-lft-out
4×associate-/r*
3×flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+ associate-/l*
2×flip3-- sqrt-div associate-*r/ associate-/r/ flip-- associate-/l/ distribute-neg-frac
1×cbrt-undiv +-commutative neg-mul-1 sub-neg distribute-neg-out frac-2neg diff-log div-exp associate-*l* unsub-neg clear-num sum-log *-commutative div-inv
Counts
4 → 96
Calls
4 calls:
17.0ms
(- (* b b) (* (* 4.0 a) c))
41.0ms
(+ (* (* a 2.0) (- b)) (* (* a 2.0) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
94.0ms
(* (* a 2.0) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
73.0ms
(/ (+ 0 (* (* 4.0 a) c)) (+ (* (* a 2.0) (- b)) (* (* a 2.0) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))

series778.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(- (* b b) (* (* 4.0 a) c))
196.0ms
(+ (* (* a 2.0) (- b)) (* (* a 2.0) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
150.0ms
(* (* a 2.0) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
366.0ms
(/ (+ 0 (* (* 4.0 a) c)) (+ (* (* a 2.0) (- b)) (* (* a 2.0) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))

simplify3.0s

Counts
108 → 108
Iterations

Useful iterations: done (3.0s)

IterNodesCost
02062948
16092425
239522182
done50002178

prune513.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes221.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify22.0ms

Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
02533
13831
25030
35830
done5830

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.6s8805×body80nan
777.0ms4436×body160valid
704.0ms16805×pre80true
366.0ms3564×body80valid