Details

Time bar (total: 17.1s)

sample73.0ms

Algorithm
intervals
Results
18.0ms36×body2560valid
16.0ms187×body80valid
10.0ms25×body1280valid
7.0ms86×body80nan
5.0ms17×body640valid
2.0ms8×body320valid
1.0ms4×body160valid

simplify139.0ms

Counts
1 → 1
Iterations
IterNodes
done93
793
692
590
482
366
240
121
012

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3 a) c)
0.8b
(- (* b b) (* (* 3 a) c))
0.9b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
23.5b
(sqrt (- (* b b) (* (* 3 a) c)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod insert-posit16
3×flip3-- associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
14.0ms
(* (* 3 a) c)
13.0ms
(- (* b b) (* (* 3 a) c))
40.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
8.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (* 3 a) c)
57.0ms
(- (* b b) (* (* 3 a) c))
106.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
99.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.3s

Counts
76 → 76
Iterations
IterNodes
done2002
32002
2910
1297
0123

prune884.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 3 (* a c))
0.8b
(- (* b b) (* 3 (* a c)))
0.9b
(- (sqrt (- (* b b) (* 3 (* a c)))) b)
23.5b
(sqrt (- (* b b) (* 3 (* a c))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod insert-posit16
3×flip3-- associate-*l* pow-prod-down prod-exp cbrt-unprod flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
13.0ms
(* 3 (* a c))
10.0ms
(- (* b b) (* 3 (* a c)))
49.0ms
(- (sqrt (- (* b b) (* 3 (* a c)))) b)
15.0ms
(sqrt (- (* b b) (* 3 (* a c))))

series270.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* 3 (* a c))
51.0ms
(- (* b b) (* 3 (* a c)))
104.0ms
(- (sqrt (- (* b b) (* 3 (* a c)))) b)
90.0ms
(sqrt (- (* b b) (* 3 (* a c))))

simplify1.1s

Counts
76 → 76
Iterations
IterNodes
done2007
32007
2780
1281
0120

prune903.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 3 a) c))
11.4b
(- (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))) b)
23.5b
(sqrt (- (* b b) (* (* 3 a) c)))
23.5b
(sqrt (- (* b b) (* (* 3 a) c)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip--
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
1×difference-of-squares
Counts
4 → 59
Calls
4 calls:
7.0ms
(- (* b b) (* (* 3 a) c))
45.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))) b)
7.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 3 a) c))
97.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))) b)
80.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
110.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.2s

Counts
71 → 71
Iterations
IterNodes
done2009
32009
2723
1232
096

prune1.2s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 13.6b

localize87.0ms

Local error

Found 4 expressions with local error:

23.5b
(sqrt (* (* (cbrt (- (* b b) (* (* 3 a) c))) (cbrt (- (* b b) (* (* 3 a) c)))) (cbrt (- (* b b) (* (* 3 a) c)))))
24.3b
(cbrt (- (* b b) (* (* 3 a) c)))
24.3b
(cbrt (- (* b b) (* (* 3 a) c)))
24.3b
(cbrt (- (* b b) (* (* 3 a) c)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
30×flip3-- flip--
28×frac-times
26×sqrt-div
24×pow1
15×sqrt-pow1
14×associate-*l/
12×pow1/3
9×cbrt-prod pow-prod-up
8×associate-*r/
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow-plus
5×pow-prod-down
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 93
Calls
4 calls:
73.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 3 a) c))) (cbrt (- (* b b) (* (* 3 a) c)))) (cbrt (- (* b b) (* (* 3 a) c)))))
5.0ms
(cbrt (- (* b b) (* (* 3 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 3 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 3 a) c)))

series557.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 3 a) c))) (cbrt (- (* b b) (* (* 3 a) c)))) (cbrt (- (* b b) (* (* 3 a) c)))))
159.0ms
(cbrt (- (* b b) (* (* 3 a) c)))
155.0ms
(cbrt (- (* b b) (* (* 3 a) c)))
151.0ms
(cbrt (- (* b b) (* (* 3 a) c)))

simplify1.2s

Counts
105 → 105
Iterations
IterNodes
done2002
32002
2730
1350
0188

prune1.9s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 13.5b

regimes697.0ms

Accuracy

85.9% (3.0b remaining)

Error of 14.8b against oracle of 11.9b and baseline of 32.9b

bsearch193.0ms

Steps
ItersRangePoint
8
5.833527798943191e-77
3.6732813120885656e-72
6.235673785124529e-73
7
-2.005420514903704e+154
-2.9230384601346835e+152
-1.3376190644449892e+154

simplify9.0ms

Iterations
IterNodes
done32
132
027

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.3s1025×body2560valid
1.1s882×body1280valid
857.0ms5891×body80valid
320.0ms2952×body80nan
242.0ms462×body640valid
116.0ms238×body320valid
109.0ms96×body5120valid
24.0ms104×body160valid