Details

Time bar (total: 8.9s)

sample36.0ms

Algorithm
intervals
Results
14.0ms281×body80valid
4.0ms77×body80nan

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03818
17918
213618
316118
417318
517718
617718
done17718

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.6b

localize90.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 63
Calls
4 calls:
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series329.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
89.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
78.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify117.0ms

Counts
75 → 75
Iterations

Useful iterations: 3 (106.0ms)

IterNodesCost
0246646
1890606
23702588
35001584
done5001584

prune289.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.4b

localize95.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
6.2b
(/ (* a c) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt
8×times-frac associate-/r* add-log-exp
5×pow1
4×cbrt-undiv div-exp sqrt-prod distribute-lft-out
3×distribute-rgt-neg-in
2×flip3-- frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ flip-- cbrt-unprod div-inv associate-/l* distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 81
Calls
4 calls:
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
88.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
10.0ms
(/ (* a c) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series373.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
187.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
21.0ms
(/ (* a c) b)
78.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0440738
12043649
25001646
done5001646

prune339.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.9b

localize98.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.8b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.0b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite515.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×*-un-lft-identity
33×times-frac
30×add-exp-log
23×add-cbrt-cube
22×add-cube-cbrt associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
8×add-log-exp
7×pow1 associate-*l*
6×unswap-sqr
5×associate-/r*
4×sqrt-prod distribute-lft-out
3×distribute-rgt-neg-in div-inv
2×flip3-- sqrt-div diff-log associate-/r/ flip-- distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 119
Calls
4 calls:
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
435.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
224.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify82.0ms

Counts
131 → 131
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
07361436
136021249
250021207
done50021207

prune593.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize107.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.6b
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt 1)))
3.0b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt 1))) (/ (cbrt c) (cbrt b)))) b)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite2.5s

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
31×add-sqr-sqrt
27×add-cbrt-cube
26×*-un-lft-identity
24×times-frac
16×prod-exp cbrt-unprod
14×cbrt-undiv div-exp
12×add-cube-cbrt
10×associate-*r*
8×add-log-exp unswap-sqr
7×pow1 cbrt-prod associate-*l*
5×associate-/r*
4×sqrt-prod distribute-lft-out
3×distribute-rgt-neg-in div-inv
2×flip3-- sqrt-div diff-log associate-/r/ flip-- distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 115
Calls
4 calls:
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt 1)))
2.4s
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt 1))) (/ (cbrt c) (cbrt b)))) b)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series464.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
94.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt 1)))
203.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt 1))) (/ (cbrt c) (cbrt b)))) b)))
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify86.0ms

Counts
127 → 127
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07901859
135921580
250011551
done50011551

prune739.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

regimes269.0ms

Accuracy

93.6% (1.0b remaining)

Error of 7.9b against oracle of 7.0b and baseline of 21.9b

bsearch120.0ms

Steps
ItersRangePoint
5
3.355600980676121e+98
1.2784432988208537e+99
1.1125484838729303e+99
6
-4.2638646006519825e+105
-4.3760586339396263e+104
-4.2041496511092447e+105

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06671
16671
done6671

end0.0ms

sample948.0ms

Algorithm
intervals
Results
456.0ms8756×body80valid
130.0ms2874×body80nan