Details

Time bar (total: 17.0s)

sample132.0ms

Algorithm
intervals
Results
35.0ms31×body1280valid
30.0ms39×body2560valid
25.0ms188×body80valid
11.0ms87×body80nan
6.0ms13×body640valid
4.0ms3×body5120valid
3.0ms6×body320valid
0.0ms1×body160valid

simplify84.0ms

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize45.0ms

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))
0.4b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite168.0ms

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:
89.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
9.0ms
(- (* b b) (* (* 4 a) c))
52.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series403.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
61.0ms
(- (* b b) (* (* 4 a) c))
106.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
92.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.2s

Counts
100 → 100
Iterations
IterNodes
done5000
21158
1394
0161

prune575.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
0.4b
(- (* b b) (* (* 4 a) c))
0.4b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
123×add-sqr-sqrt
96×*-un-lft-identity
70×add-cube-cbrt
26×difference-of-squares
24×associate-/r*
16×sqrt-prod
15×add-exp-log
13×distribute-lft-out--
9×add-cbrt-cube associate-/r/
8×add-log-exp
7×flip3-- div-exp flip--
6×pow1
5×div-inv
4×insert-posit16
3×cbrt-undiv associate-/l*
2×rec-exp sub-neg sqrt-div diff-log 1-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-flip inv-pow
Counts
4 → 166
Calls
4 calls:
60.0ms
(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
12.0ms
(- (* b b) (* (* 4 a) c))
57.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
13.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series471.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
60.0ms
(- (* b b) (* (* 4 a) c))
130.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
106.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.8s

Counts
178 → 178
Iterations
IterNodes
done5001
21712
1648
0265

prune912.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 a) (- (sqrt (- (* b b) (* (* 4 a) c))) b))
0.4b
(- (* b b) (* (* 4 a) c))
0.4b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
18×*-un-lft-identity
13×associate-*l* add-exp-log add-cube-cbrt
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1
6×associate-*r*
5×flip3-- sqrt-prod flip--
4×sub-neg prod-exp insert-posit16 difference-of-squares
3×unswap-sqr
2×distribute-rgt-in frac-times distribute-lft-in sqrt-div diff-log div-exp associate-*r/ cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 92
Calls
4 calls:
113.0ms
(* (/ 1 a) (- (sqrt (- (* b b) (* (* 4 a) c))) b))
19.0ms
(- (* b b) (* (* 4 a) c))
42.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
10.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series455.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(* (/ 1 a) (- (sqrt (- (* b b) (* (* 4 a) c))) b))
54.0ms
(- (* b b) (* (* 4 a) c))
106.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
102.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.5s

Counts
104 → 104
Iterations
IterNodes
done5000
21385
1440
0169

prune523.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.4b

localize65.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
0.4b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite121.0ms

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:
40.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
63.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
127.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
93.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
99.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.6s

Counts
76 → 76
Iterations
IterNodes
done5002
32079
2595
1194
082

prune530.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.3b

regimes382.0ms

Accuracy

83.4% (4.6b remaining)

Error of 10.4b against oracle of 5.8b and baseline of 33.7b

bsearch186.0ms

Steps
ItersRangePoint
8
1.287554927770862e-68
8.304725640954512e-66
4.5810084990875205e-68
8
-3.370135567630554e+133
-1.481129451033522e+129
-2.1144981103869975e+131

simplify6.0ms

Iterations
IterNodes
done35
135
029

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.4s1064×body2560valid
1.3s901×body1280valid
890.0ms5890×body80valid
560.0ms2854×body80nan
238.0ms447×body640valid
118.0ms95×body5120valid
86.0ms207×body320valid
37.0ms133×body160valid