Details

Time bar (total: 18.5s)

sample99.0ms

Algorithm
intervals
Results
28.0ms184×body80valid
16.0ms32×body2560valid
12.0ms31×body1280valid
7.0ms84×body80nan
5.0ms17×body640valid
1.0ms6×body320valid
1.0ms3×body5120valid
0.0ms1×body160valid

simplify119.0ms

Counts
1 → 1
Iterations
IterNodes
done128
5128
4119
386
246
125
014

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) a)
0.2b
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
1.4b
(- (* b b) (* (* 4.0 c) a))
24.6b
(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- log1p-expm1-u 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 → 118
Calls
4 calls:
98.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) a)
65.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
11.0ms
(- (* b b) (* (* 4.0 c) a))
17.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

series463.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) a)
145.0ms
(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
69.0ms
(- (* b b) (* (* 4.0 c) a))
113.0ms
(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify2.8s

Counts
130 → 130
Iterations
IterNodes
done5000
22147
1509
0198

prune815.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* a (* c 4.0)))) b) a)
0.2b
(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
1.4b
(- (* b b) (* a (* c 4.0)))
24.6b
(sqrt (- (* b b) (* a (* c 4.0))))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- log1p-expm1-u 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 → 118
Calls
4 calls:
104.0ms
(/ (- (sqrt (- (* b b) (* a (* c 4.0)))) b) a)
57.0ms
(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
13.0ms
(- (* b b) (* a (* c 4.0)))
17.0ms
(sqrt (- (* b b) (* a (* c 4.0))))

series504.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(/ (- (sqrt (- (* b b) (* a (* c 4.0)))) b) a)
143.0ms
(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
89.0ms
(- (* b b) (* a (* c 4.0)))
108.0ms
(sqrt (- (* b b) (* a (* c 4.0))))

simplify3.0s

Counts
130 → 130
Iterations
IterNodes
done5002
22220
1510
0199

prune678.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b b) (* a (* c 4.0)))) b)))
0.2b
(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
1.4b
(- (* b b) (* a (* c 4.0)))
24.6b
(sqrt (- (* b b) (* a (* c 4.0))))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
137×add-sqr-sqrt
110×*-un-lft-identity
84×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
24×associate-/r*
19×prod-diff
15×add-exp-log
13×distribute-lft-out--
9×add-cbrt-cube associate-/r/
8×add-log-exp
7×flip3-- fma-neg div-exp flip--
6×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u
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 → 196
Calls
4 calls:
57.0ms
(/ 1 (/ a (- (sqrt (- (* b b) (* a (* c 4.0)))) b)))
49.0ms
(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
11.0ms
(- (* b b) (* a (* c 4.0)))
18.0ms
(sqrt (- (* b b) (* a (* c 4.0))))

series477.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(/ 1 (/ a (- (sqrt (- (* b b) (* a (* c 4.0)))) b)))
124.0ms
(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
57.0ms
(- (* b b) (* a (* c 4.0)))
94.0ms
(sqrt (- (* b b) (* a (* c 4.0))))

simplify2.2s

Counts
208 → 208
Iterations
IterNodes
done5001
23555
1763
0303

prune895.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

localize77.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* a (* c 4.0)))
24.6b
(sqrt (- (* b b) (* a (* c 4.0))))
24.6b
(sqrt (- (* b b) (* a (* c 4.0))))
24.6b
(sqrt (- (* b b) (* a (* c 4.0))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div add-log-exp
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log log1p-expm1-u flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg fma-neg diff-log prod-diff
Counts
4 → 67
Calls
4 calls:
14.0ms
(- (* b b) (* a (* c 4.0)))
20.0ms
(sqrt (- (* b b) (* a (* c 4.0))))
17.0ms
(sqrt (- (* b b) (* a (* c 4.0))))
12.0ms
(sqrt (- (* b b) (* a (* c 4.0))))

series391.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (* b b) (* a (* c 4.0)))
88.0ms
(sqrt (- (* b b) (* a (* c 4.0))))
96.0ms
(sqrt (- (* b b) (* a (* c 4.0))))
126.0ms
(sqrt (- (* b b) (* a (* c 4.0))))

simplify1.4s

Counts
79 → 79
Iterations
IterNodes
done5000
2864
1190
071

prune565.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.8b

regimes377.0ms

Accuracy

84.2% (4.5b remaining)

Error of 10.6b against oracle of 6.1b and baseline of 34.4b

bsearch176.0ms

Steps
ItersRangePoint
8
2.8373581988670566e-35
2.2677514638291856e-31
2.8983489306952693e-35
8
-2.748004767191833e+152
-7.260401024913698e+147
-2.221067196710922e+149

simplify6.0ms

Iterations
IterNodes
done32
132
028

end0.0ms

sample2.7s

Algorithm
intervals
Results
866.0ms1040×body2560valid
529.0ms5835×body80valid
320.0ms906×body1280valid
293.0ms2881×body80nan
144.0ms456×body640valid
130.0ms232×body320valid
79.0ms102×body5120valid
14.0ms116×body160valid