Details

Time bar (total: 16.2s)

sample111.0ms

Algorithm
intervals
Results
21.0ms204×body80valid
18.0ms29×body2560valid
15.0ms31×body1280valid
10.0ms106×body80nan
3.0ms9×body640valid
3.0ms9×body320valid
1.0ms2×body5120valid
0.0ms1×body160valid

simplify162.0ms

Counts
1 → 1
Iterations
IterNodes
done98
798
697
595
487
372
242
124
014

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) a)
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)))

rewrite144.0ms

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:
74.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) a)
6.0ms
(- (* b b) (* (* c a) 4.0))
49.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
13.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

series447.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) a)
79.0ms
(- (* b b) (* (* c a) 4.0))
116.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
103.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.5s

Counts
96 → 96
Iterations
IterNodes
done5000
21163
1390
0158

prune658.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ a (- (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)))

rewrite104.0ms

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:
50.0ms
(/ a (- (sqrt (- (* b b) (* (* c a) 4.0))) b))
6.0ms
(- (* b b) (* (* c a) 4.0))
39.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
7.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
262.0ms
(/ a (- (sqrt (- (* b b) (* (* c a) 4.0))) b))
52.0ms
(- (* b b) (* (* c a) 4.0))
98.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
86.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

simplify2.7s

Counts
95 → 95
Iterations
IterNodes
done5000
33954
21038
1347
0153

prune711.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (- (sqrt (- (* b b) (* (* c a) 4.0))) b) (/ 1 a))
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)))

rewrite232.0ms

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 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 → 85
Calls
4 calls:
162.0ms
(* (- (sqrt (- (* b b) (* (* c a) 4.0))) b) (/ 1 a))
6.0ms
(- (* b b) (* (* c a) 4.0))
52.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
9.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(* (- (sqrt (- (* b b) (* (* c a) 4.0))) b) (/ 1 a))
57.0ms
(- (* b b) (* (* c a) 4.0))
114.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
95.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.5s

Counts
97 → 97
Iterations
IterNodes
done5001
21389
1455
0178

prune611.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) a)
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)))

rewrite156.0ms

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:
83.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) a)
9.0ms
(- (* b b) (* (* c a) 4.0))
46.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
14.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

series433.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) a)
74.0ms
(- (* b b) (* (* c a) 4.0))
113.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
108.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.3s

Counts
96 → 96
Iterations
IterNodes
done5000
21163
1390
0158

prune558.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.9b

regimes476.0ms

Accuracy

84.3% (4.5b remaining)

Error of 10.2b against oracle of 5.7b and baseline of 34.4b

bsearch189.0ms

Steps
ItersRangePoint
8
1.5119020269574885e-23
1.8921341643334238e-20
9.136492990928292e-23
6
-1.7989235910837076e+89
-1.4585470499056154e+88
-1.7633154797394035e+89

simplify5.0ms

Iterations
IterNodes
done34
134
029

end0.0ms

sample3.1s

Algorithm
intervals
Results
623.0ms5865×body80valid
621.0ms434×body640valid
578.0ms1057×body2560valid
467.0ms902×body1280valid
209.0ms2875×body80nan
58.0ms124×body5120valid
42.0ms224×body320valid
14.0ms112×body160valid