Details

Time bar (total: 18.9s)

sample200.0ms

Algorithm
intervals
Results
18.0ms202×body80valid
17.0ms29×body2560valid
13.0ms31×body1280valid
9.0ms106×body80nan
4.0ms9×body640valid
2.0ms9×body320valid
1.0ms2×body5120valid
0.0ms3×body160valid

simplify104.0ms

Counts
1 → 1
Iterations
IterNodes
done29
529
427
325
222
114
010

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b
(- (* b_2 b_2) (* a c))
0.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite246.0ms

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:
125.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
13.0ms
(- (* b_2 b_2) (* a c))
83.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series439.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
63.0ms
(- (* b_2 b_2) (* a c))
100.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
131.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts
96 → 96
Iterations
IterNodes
done5019
34108
21027
1375
0154

prune532.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.3b
(sqrt (- (* b_2 b_2) (* a c)))
24.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite137.0ms

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:
69.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
45.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series447.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
99.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
112.0ms
(sqrt (- (* b_2 b_2) (* a c)))
97.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts
72 → 72
Iterations
IterNodes
done5001
31612
2534
1183
078

prune534.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.9b

localize38.0ms

Local error

Found 4 expressions with local error:

24.3b
(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
25.1b
(cbrt (- (* b_2 b_2) (* a c)))
25.1b
(cbrt (- (* b_2 b_2) (* a c)))
25.1b
(cbrt (- (* b_2 b_2) (* a c)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
30×flip3-- flip--
28×frac-times
26×sqrt-div
24×pow1
15×sqrt-pow1
14×associate-*l/
12×pow1/3
9×cbrt-prod pow-prod-up
8×associate-*r/
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow-plus
5×pow-prod-down
4×add-cbrt-cube add-exp-log add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 89
Calls
4 calls:
77.0ms
(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
5.0ms
(cbrt (- (* b_2 b_2) (* a c)))
5.0ms
(cbrt (- (* b_2 b_2) (* a c)))
5.0ms
(cbrt (- (* b_2 b_2) (* a c)))

series512.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
136.0ms
(cbrt (- (* b_2 b_2) (* a c)))
141.0ms
(cbrt (- (* b_2 b_2) (* a c)))
138.0ms
(cbrt (- (* b_2 b_2) (* a c)))

simplify3.0s

Counts
101 → 101
Iterations
IterNodes
done5000
44535
31473
2657
1342
0182

prune559.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (pow (- (* b_2 b_2) (* a c)) 1/2) b_2) a)
0.8b
(- (* b_2 b_2) (* a c))
0.8b
(- (pow (- (* b_2 b_2) (* a c)) 1/2) b_2)
24.3b
(pow (- (* b_2 b_2) (* a c)) 1/2)

rewrite319.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
28×*-un-lft-identity
21×times-frac
18×add-cube-cbrt
15×difference-of-squares
8×unpow-prod-down add-log-exp
7×add-exp-log associate-/l*
6×add-cbrt-cube sqr-pow
5×pow1 distribute-lft-out--
3×pow-unpow associate-/r* flip3-- flip--
2×sub-neg diff-log associate-/l/
1×pow-to-exp cbrt-undiv clear-num pow-pow frac-2neg div-sub div-exp pow-exp div-inv unpow1/2
Counts
4 → 92
Calls
4 calls:
190.0ms
(/ (- (pow (- (* b_2 b_2) (* a c)) 1/2) b_2) a)
12.0ms
(- (* b_2 b_2) (* a c))
106.0ms
(- (pow (- (* b_2 b_2) (* a c)) 1/2) b_2)
8.0ms
(pow (- (* b_2 b_2) (* a c)) 1/2)

series351.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(/ (- (pow (- (* b_2 b_2) (* a c)) 1/2) b_2) a)
54.0ms
(- (* b_2 b_2) (* a c))
88.0ms
(- (pow (- (* b_2 b_2) (* a c)) 1/2) b_2)
80.0ms
(pow (- (* b_2 b_2) (* a c)) 1/2)

simplify2.6s

Counts
104 → 104
Iterations
IterNodes
done5002
34522
21154
1415
0165

prune584.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.9b

regimes516.0ms

Accuracy

84.3% (4.5b remaining)

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

bsearch160.0ms

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

simplify8.0ms

Iterations
IterNodes
done28
128
024

end0.0ms

sample2.9s

Algorithm
intervals
Results
971.0ms1059×body2560valid
494.0ms5860×body80valid
315.0ms902×body1280valid
238.0ms2871×body80nan
126.0ms434×body640valid
105.0ms124×body5120valid
39.0ms224×body320valid
13.0ms115×body160valid