Details

Time bar (total: 14.2s)

sample65.0ms

Algorithm
intervals
Results
31.0ms273×body80valid
9.0ms92×body80nan

simplify203.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
02038
13538
26637
311637
415037
516437
616637
done16637

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.0b

localize145.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite186.0ms

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:
91.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
48.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series536.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
145.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
117.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
134.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify763.0ms

Counts
75 → 75
Iterations

Useful iterations: done (759.0ms)

IterNodesCost
01061330
12501189
210981110
done50011100

prune520.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.4b

localize143.0ms

Local error

Found 4 expressions with local error:

7.0b
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))
24.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×pow1
4×add-exp-log cbrt-div flip3-- add-cbrt-cube flip--
3×sqrt-prod
2×pow1/3 sqrt-div diff-log
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 55
Calls
4 calls:
21.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series560.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
94.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
168.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
151.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
67 → 67
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01491566
13791475
216261275
done50001259

prune594.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.4b

localize142.0ms

Local error

Found 4 expressions with local error:

23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))
24.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))
24.6b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log flip3-- add-cbrt-cube flip-- add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
121.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
127.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
129.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
66 → 66
Iterations

Useful iterations: done (2.6s)

IterNodesCost
0901170
12111110
27001000
33606985
done5001953

prune586.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.4b

localize149.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×*-un-lft-identity
10×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt
6×sqrt-div
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg distribute-rgt-neg-in neg-log
Counts
4 → 63
Calls
4 calls:
42.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series490.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
126.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify728.0ms

Counts
75 → 75
Iterations

Useful iterations: done (724.0ms)

IterNodesCost
0871276
12161122
28961056
done50001048

prune553.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.4b

regimes405.0ms

Accuracy

85.2% (1.8b remaining)

Error of 9.4b against oracle of 7.6b and baseline of 20.0b

bsearch351.0ms

Steps
ItersRangePoint
10
1.3113650301339767e-12
0.01077406869848718
0.010648423176581222
8
-7.015537041391403e+155
-3.156875883067517e+151
-1.376637749254643e+154

simplify12.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
050167
160167
done60167

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.2s8732×body80valid
909.0ms3047×body80nan