Details

Time bar (total: 17.3s)

sample96.0ms

Algorithm
intervals
Results
26.0ms204×body80valid
15.0ms29×body2560valid
13.0ms31×body1280valid
9.0ms106×body80nan
2.0ms9×body640valid
2.0ms9×body320valid
1.0ms2×body5120valid
0.0ms1×body160valid

simplify91.0ms

Counts
1 → 1
Iterations
IterNodes
done107
5107
499
379
244
124
014

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
0.8b
(- (* b b) (* (* 4.0 a) c))
0.8b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite195.0ms

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-- 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 → 84
Calls
4 calls:
92.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
13.0ms
(- (* b b) (* (* 4.0 a) c))
71.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series441.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
84.0ms
(- (* b b) (* (* 4.0 a) c))
114.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
96 → 96
Iterations
IterNodes
done5001
21525
1378
0153

prune607.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2.0 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
0.8b
(- (* b b) (* (* 4.0 a) c))
0.8b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite119.0ms

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×associate-/r* add-cbrt-cube add-exp-log
5×pow1 distribute-lft-out--
4×flip3-- flip--
3×associate-/l*
2×sub-neg sqrt-div diff-log associate-/r/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 83
Calls
4 calls:
47.0ms
(/ 2.0 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
7.0ms
(- (* b b) (* (* 4.0 a) c))
49.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(/ 2.0 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
65.0ms
(- (* b b) (* (* 4.0 a) c))
112.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
95.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
95 → 95
Iterations
IterNodes
done5000
21536
1375
0158

prune772.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.7b

localize59.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.8b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite108.0ms

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 flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
52.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
40.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
121.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
100.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts
72 → 72
Iterations
IterNodes
done5000
34453
2792
1199
081

prune376.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.7b

localize73.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×sqrt-prod
9×*-un-lft-identity
7×pow1 add-cube-cbrt
6×sqrt-div add-log-exp
4×flip3-- add-cbrt-cube add-exp-log flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×difference-of-squares
1×sub-neg diff-log distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
35.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series385.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
92.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
104.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.0s

Counts
72 → 72
Iterations
IterNodes
done5000
34453
2792
1199
081

prune540.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.7b

regimes448.0ms

Accuracy

80.4% (5.0b remaining)

Error of 14.1b against oracle of 9.2b and baseline of 34.5b

bsearch179.0ms

Steps
ItersRangePoint
5
4.244596206919672e-17
1.6775967427727985e-16
4.330541687749955e-17
8
-1.4137780731624028e+101
-4.084920897753177e+97
-1.3906582137854214e+101

simplify11.0ms

Iterations
IterNodes
done39
139
032

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.1s5865×body80valid
611.0ms1057×body2560valid
425.0ms902×body1280valid
372.0ms2875×body80nan
138.0ms434×body640valid
114.0ms224×body320valid
82.0ms124×body5120valid
17.0ms112×body160valid