Details

Time bar (total: 19.4s)

sample58.0ms

Algorithm
intervals
Results
30.0ms283×body80valid
7.0ms106×body80nan

simplify161.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
02038
13538
26637
311637
413937
515137
615337
done15337

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize129.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite161.0ms

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:
40.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
78.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series517.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
127.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
132.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
146.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
75 → 75
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01061330
12411181
27481110
326611090
done50001085

prune394.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.2b

localize117.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.8b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.8b
(/ (* a c) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt add-cbrt-cube
11×*-un-lft-identity
9×add-cube-cbrt
6×times-frac associate-/r* add-log-exp
5×pow1
4×cbrt-undiv div-exp sqrt-prod
3×flip3-- flip--
2×frac-2neg sqrt-div prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l* difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 74
Calls
4 calls:
73.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
66.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
28.0ms
(/ (* a c) b)
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
126.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
37.0ms
(/ (* a c) b)
133.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
86 → 86
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01701340
14301248
216001098
done50001096

prune558.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize157.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.7b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.8b
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite392.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
31×times-frac
30×add-exp-log
24×*-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
7×pow1 associate-*l*
6×add-log-exp unswap-sqr
4×sqrt-prod
3×flip3-- associate-/r* flip-- div-inv
2×sqrt-div associate-/r/ difference-of-squares
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* distribute-lft-out--
Counts
4 → 112
Calls
4 calls:
73.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
65.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
231.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series477.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
85.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
146.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
92.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts
124 → 124
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02542410
17062285
227941811
done50011639

prune807.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.3b

localize198.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b))))
1.2b
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b)))) (/ (cbrt c) (cbrt (sqrt b))))) (* 2 b)))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
34×add-sqr-sqrt
27×add-cbrt-cube
25×times-frac
16×prod-exp cbrt-unprod
15×*-un-lft-identity
14×cbrt-undiv div-exp
13×add-cube-cbrt associate-*r*
10×cbrt-prod
9×sqrt-prod
8×unswap-sqr
7×pow1 associate-*l*
6×add-log-exp
3×flip3-- associate-/r* flip-- div-inv
2×sqrt-div associate-/r/ difference-of-squares
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* distribute-lft-out--
Counts
4 → 111
Calls
4 calls:
96.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b))))
1.4s
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b)))) (/ (cbrt c) (cbrt (sqrt b))))) (* 2 b)))
68.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series784.0ms

Counts
4 → 12
Calls
4 calls:
225.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b))))
357.0ms
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b)))) (/ (cbrt c) (cbrt (sqrt b))))) (* 2 b)))
107.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
94.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
123 → 123
Iterations

Useful iterations: done (2.6s)

IterNodesCost
03153314
18623187
232802723
done50012666

prune990.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.3b

regimes421.0ms

Accuracy

91.1% (1.3b remaining)

Error of 8.3b against oracle of 7.0b and baseline of 21.5b

bsearch308.0ms

Steps
ItersRangePoint
9
1.7084993271036838e+35
8.915315724770326e+40
1.7754385347718217e+40
8
-4.810799056667626e+157
-8.81647488783933e+153
-1.367002129773412e+154

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
051143
161143
done61143

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.1s8744×body80valid
417.0ms3010×body80nan