Details

Time bar (total: 16.8s)

sample105.0ms

Algorithm
intervals
Results
19.0ms204×body80valid
17.0ms29×body2560valid
15.0ms9×body320valid
14.0ms31×body1280valid
9.0ms106×body80nan
3.0ms9×body640valid
1.0ms2×body5120valid
0.0ms1×body160valid

simplify96.0ms

Counts
1 → 1
Iterations
IterNodes
done111
5111
4102
378
244
124
014

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite155.0ms

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:
91.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0)
12.0ms
(- (* b b) (* (* c a) 4.0))
41.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
7.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

series374.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0)
51.0ms
(- (* b b) (* (* c a) 4.0))
95.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
123.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.9s

Counts
96 → 96
Iterations
IterNodes
done5001
21542
1378
0153

prune714.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.2b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

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:
38.0ms
(/ 2.0 (- (sqrt (- (* b b) (* (* c a) 4.0))) b))
8.0ms
(- (* b b) (* (* c a) 4.0))
33.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
7.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ 2.0 (- (sqrt (- (* b b) (* (* c a) 4.0))) b))
73.0ms
(- (* b b) (* (* c a) 4.0))
101.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
95.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.1s

Counts
95 → 95
Iterations
IterNodes
done5000
21573
1375
0158

prune683.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.8b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite133.0ms

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:
59.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
44.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
13.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))
14.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

series489.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
131.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
91.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))
123.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

simplify3.3s

Counts
72 → 72
Iterations
IterNodes
done5001
34798
2826
1198
081

prune511.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.8b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt 2.0) (- (sqrt (- (* b b) (* (* c a) 4.0))) b))
0.8b
(- (* b b) (* (* c a) 4.0))
0.8b
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
24.3b
(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
42×*-un-lft-identity
36×times-frac
32×sqrt-prod
26×add-cube-cbrt
16×difference-of-squares
8×distribute-lft-out-- add-log-exp
6×associate-/r* add-cbrt-cube add-exp-log associate-/l*
5×pow1
4×flip3-- flip--
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 → 104
Calls
4 calls:
49.0ms
(/ (sqrt 2.0) (- (sqrt (- (* b b) (* (* c a) 4.0))) b))
12.0ms
(- (* b b) (* (* c a) 4.0))
63.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
14.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

series542.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(/ (sqrt 2.0) (- (sqrt (- (* b b) (* (* c a) 4.0))) b))
80.0ms
(- (* b b) (* (* c a) 4.0))
127.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
127.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.4s

Counts
116 → 116
Iterations
IterNodes
done5000
21660
1416
0178

prune654.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 10.7b

regimes560.0ms

Accuracy

85.5% (3.4b remaining)

Error of 14.1b against oracle of 10.7b and baseline of 34.5b

bsearch159.0ms

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

simplify14.0ms

Iterations
IterNodes
done39
139
033

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.0s5865×body80valid
634.0ms1057×body2560valid
443.0ms902×body1280valid
261.0ms2875×body80nan
178.0ms434×body640valid
106.0ms124×body5120valid
52.0ms224×body320valid
16.0ms112×body160valid