Details

Time bar (total: 9.2s)

sample35.0ms

Algorithm
intervals
Results
15.0ms267×body80valid
4.0ms87×body80nan

simplify87.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
02038
13538
26537
311437
413637
514837
614937
done14937

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.4b

localize114.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×*-un-lft-identity add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log difference-of-squares
1×distribute-lft-out--
Counts
4 → 57
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
19.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series282.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* b b) (* (* 4.0 a) c))
85.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
69 → 69
Iterations

Useful iterations: 3 (380.0ms)

IterNodesCost
0911129
12091001
2684935
32433930
done5000930

prune283.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.2b

localize122.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.2b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
6.5b
(/ (* a c) b)
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
18×add-sqr-sqrt
14×add-exp-log add-cbrt-cube
9×add-cube-cbrt times-frac associate-/r*
6×add-log-exp
5×pow1 distribute-lft-out--
4×cbrt-undiv div-exp sqrt-prod difference-of-squares
3×flip3-- flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 80
Calls
4 calls:
18.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
3.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
184.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
20.0ms
(/ (* a c) b)
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify684.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (149.0ms)

IterNodesCost
01781468
14351368
216641212
done50001212

prune351.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.3b

localize129.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.2b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
3.6b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
34×times-frac
32×*-un-lft-identity
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
7×pow1 associate-*l*
6×associate-/r* add-log-exp unswap-sqr
5×distribute-lft-out--
4×sqrt-prod difference-of-squares
3×flip3-- flip-- div-inv
2×distribute-rgt-neg-in sqrt-div associate-/r/
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 118
Calls
4 calls:
21.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
24.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
220.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
56.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify998.0ms

Counts
130 → 130
Iterations

Useful iterations: done (993.0ms)

IterNodesCost
02622573
17332440
228981940
done50001934

prune721.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize128.0ms

Local error

Found 4 expressions with local error:

3.6b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
13.3b
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
28×times-frac
25×add-exp-log
22×associate-*r*
21×add-cube-cbrt *-un-lft-identity
18×add-cbrt-cube
11×cbrt-prod
8×pow1 prod-exp cbrt-unprod
7×cbrt-undiv div-exp associate-*l*
6×sqrt-prod add-log-exp unswap-sqr
4×sqrt-div
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 div-inv
1×frac-times sub-neg diff-log associate-*r/ pow-prod-down associate-*l/ *-commutative difference-of-squares
Counts
4 → 102
Calls
4 calls:
23.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
19.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
79.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify806.0ms

Counts
114 → 114
Iterations

Useful iterations: done (799.0ms)

IterNodesCost
02052121
15851726
222571488
done50001482

prune554.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.3b

regimes197.0ms

Accuracy

91.2% (1.3b remaining)

Error of 7.9b against oracle of 6.6b and baseline of 21.5b

bsearch196.0ms

Steps
ItersRangePoint
8
2.1878188410446244e+107
3.8616146939177386e+111
3.264911199889295e+111
10
-2.699314103090194e+180
-2.227381996671495e+165
-2.272454186637281e+165

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
056151
166151
done66151

end0.0ms

sample899.0ms

Algorithm
intervals
Results
475.0ms8700×body80valid
147.0ms2997×body80nan