Details

Time bar (total: 19.8s)

sample76.0ms

Algorithm
intervals
Results
31.0ms282×body80valid
14.0ms81×body80nan

simplify248.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
02038
13838
27837
313537
415537
516537
616937
done16937

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.6b

localize127.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
12×*-un-lft-identity
10×add-log-exp
8×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip-- difference-of-squares
3×diff-log distribute-lft-out--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 63
Calls
4 calls:
58.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
56.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series477.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
101.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
135.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
115.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.0s

Counts
75 → 75
Iterations

Useful iterations: done (3.0s)

IterNodesCost
01061330
12411181
27481110
326691090
done50011085

prune485.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.3b

localize137.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.4b
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
6.8b
(/ (* a c) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite703.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
17×*-un-lft-identity
14×add-exp-log 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-- difference-of-squares
3×flip3-- flip--
2×frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l*
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 neg-log
Counts
4 → 81
Calls
4 calls:
51.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
615.0ms
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
19.0ms
(/ (* a c) b)
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
131.0ms
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
36.0ms
(/ (* a c) b)
118.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
93 → 93
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01831490
14411392
216101238
done50001227

prune534.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.7b

localize162.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.5b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.4b
(/ (* 2.0 c) (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
33×times-frac
30×add-exp-log *-un-lft-identity
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-- difference-of-squares
3×flip3-- flip-- div-inv
2×sqrt-div diff-log associate-/r/
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 119
Calls
4 calls:
35.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
93.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
915.0ms
(/ (* 2.0 c) (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
124.0ms
(/ (* 2.0 c) (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts
131 → 131
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02672588
17172457
227541963
done50001770

prune844.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.5b

localize184.0ms

Local error

Found 4 expressions with local error:

6.2b
(cbrt (/ a (* (cbrt b) (cbrt b))))
6.2b
(cbrt (/ a (* (cbrt b) (cbrt b))))
6.2b
(cbrt (/ a (* (cbrt b) (cbrt b))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×times-frac
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 63
Calls
4 calls:
7.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
8.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
13.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series762.0ms

Counts
4 → 12
Calls
4 calls:
226.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
216.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
233.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
87.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
75 → 75
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0981008
1199966
2537892
31806880
done5000870

prune682.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.5b

regimes493.0ms

Accuracy

89.7% (1.5b remaining)

Error of 8.1b against oracle of 6.6b and baseline of 20.9b

bsearch346.0ms

Steps
ItersRangePoint
8
1.538525478595148e+72
6.402915924844171e+74
1.3910222191204909e+74
8
-1.173014798652874e+100
-8.67642318333193e+96
-1.1200838301149146e+100

simplify12.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
051144
160142
done60142

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.6s8755×body80valid
292.0ms2933×body80nan