Details

Time bar (total: 14.7s)

sample69.0ms

Algorithm
intervals
Results
15.0ms37×body2560valid
13.0ms191×body80valid
10.0ms30×body1280valid
8.0ms103×body80nan
5.0ms16×body640valid
1.0ms6×body320valid
1.0ms6×body160valid

simplify99.0ms

Counts
1 → 1
Iterations
IterNodes
done95
795
694
592
484
367
243
124
014

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
0.4b
(- (* b b) (* (* 4 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
21.3b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
130.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
18.0ms
(- (* b b) (* (* 4 a) c))
77.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
10.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series422.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
61.0ms
(- (* b b) (* (* 4 a) c))
109.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
124.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.2s

Counts
100 → 100
Iterations
IterNodes
done5000
21158
1394
0161

prune460.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
0.4b
(- (* b b) (* (* 4 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
21.3b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
106.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
9.0ms
(- (* b b) (* (* 4 a) c))
44.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
10.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series375.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
57.0ms
(- (* b b) (* (* 4 a) c))
86.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
90.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.2s

Counts
100 → 100
Iterations
IterNodes
done5000
21158
1394
0161

prune655.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
0.4b
(- (* b b) (* (* 4 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
21.3b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite285.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
18×*-un-lft-identity
13×associate-*r* add-exp-log add-cube-cbrt
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1
6×associate-*l*
5×flip3-- sqrt-prod flip--
4×prod-exp insert-posit16 difference-of-squares
3×unswap-sqr
2×frac-times sub-neg sqrt-div diff-log div-exp associate-*l/ cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 89
Calls
4 calls:
196.0ms
(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
8.0ms
(- (* b b) (* (* 4 a) c))
66.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
11.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series497.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
84.0ms
(- (* b b) (* (* 4 a) c))
130.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
103.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.5s

Counts
101 → 101
Iterations
IterNodes
done5003
21455
1458
0181

prune628.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.8b

localize50.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
1.6b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
21.3b
(sqrt (- (* b b) (* (* 4 a) c)))
21.3b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
52.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
86.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series508.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
134.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
117.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
128.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts
76 → 76
Iterations
IterNodes
done5002
32079
2595
1194
082

prune543.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 7.8b

regimes509.0ms

Accuracy

81.3% (5.1b remaining)

Error of 10.8b against oracle of 5.7b and baseline of 33.1b

bsearch248.0ms

Steps
ItersRangePoint
7
3.2723221096518622e-21
8.349665184990521e-19
3.325219738594455e-21
7
5.034617224646791e-70
8.084342686052032e-69
1.0350377446088803e-69
1
1.8923753200636452e-106
2.0232344302868159e-106
1.990519652731023e-106
8
-5.8501169415505e+41
-1.816545290760657e+37
-2.9862044966069494e+41

simplify25.0ms

Iterations
IterNodes
done51
351
248
145
035

end0.0ms

sample3.2s

Algorithm
intervals
Results
642.0ms5918×body80valid
606.0ms1071×body2560valid
603.0ms463×body640valid
442.0ms834×body1280valid
431.0ms3077×body80nan
73.0ms123×body5120valid
58.0ms241×body320valid
19.0ms122×body160valid