Details

Time bar (total: 6.7s)

sample34.0ms

Algorithm
intervals
Results
13.0ms281×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

localize85.0ms

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)))

rewrite67.0ms

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))))
20.0ms
(+ (- 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)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
85.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify113.0ms

Counts
75 → 75
Iterations

Useful iterations: 3 (107.0ms)

IterNodesCost
0246646
1890606
23702588
35001584
done5001584

prune274.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.4b

localize90.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
6.2b
(/ (* a c) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt add-cbrt-cube
13×*-un-lft-identity
9×add-cube-cbrt
8×add-log-exp
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv div-exp sqrt-prod
3×flip3-- flip--
2×frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l* distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 neg-log
Counts
4 → 77
Calls
4 calls:
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
35.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
9.0ms
(/ (* a c) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
20.0ms
(/ (* a c) b)
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify60.0ms

Counts
89 → 89
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0450688
12176609
25001607
done5001607

prune318.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.9b

localize93.0ms

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) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
31×times-frac
30×add-exp-log
26×*-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
4×sqrt-prod
3×flip3-- associate-/r* flip-- div-inv
2×sqrt-div diff-log associate-/r/ distribute-lft-out-- difference-of-squares
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 → 115
Calls
4 calls:
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
41.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
152.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
53.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
106.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify87.0ms

Counts
127 → 127
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07461377
137511199
250011149
done50011149

prune523.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize106.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.5b
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
3.0b
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))) (* 2 b)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
78×add-exp-log
44×add-cbrt-cube
33×prod-exp cbrt-unprod
24×cbrt-undiv div-exp
21×add-sqr-sqrt
14×*-un-lft-identity
11×times-frac
10×add-cube-cbrt
8×add-log-exp
7×pow1 associate-*l*
5×associate-*r*
4×sqrt-prod unswap-sqr
3×flip3-- associate-/r* flip-- div-inv
2×sqrt-div diff-log associate-/r/ distribute-lft-out-- difference-of-squares
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 → 114
Calls
4 calls:
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
1.1s
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))) (* 2 b)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series516.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
222.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
103.0ms
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))) (* 2 b)))
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify119.0ms

Counts
126 → 126
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
08512334
144201840
250021769
done50021769

prune531.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

regimes246.0ms

Accuracy

93.6% (1.0b remaining)

Error of 7.9b against oracle of 7.0b and baseline of 22.0b

bsearch124.0ms

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
07281
17281
done7281

end0.0ms

sample899.0ms

Algorithm
intervals
Results
434.0ms8756×body80valid
123.0ms2874×body80nan