Details

Time bar (total: 19.1s)

sample171.0ms

Algorithm
intervals
Results
16.0ms29×body2560valid
15.0ms202×body80valid
11.0ms31×body1280valid
7.0ms106×body80nan
3.0ms9×body640valid
2.0ms9×body320valid
1.0ms2×body5120valid
0.0ms3×body160valid

simplify24.0ms

Counts
1 → 1
Iterations
IterNodes
done34
534
432
330
223
115
010

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize21.0ms

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)))

rewrite151.0ms

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:
76.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms
(- (* b_2 b_2) (* a c))
50.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series366.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
47.0ms
(- (* b_2 b_2) (* a c))
92.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
86.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts
130 → 130
Iterations
IterNodes
done5000
22129
1493
0195

prune775.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.9b

localize55.0ms

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)))

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×expm1-log1p-u flip3-- add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
86.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
82.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series391.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
109.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
78.0ms
(sqrt (- (* b_2 b_2) (* a c)))
87.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts
128 → 128
Iterations
IterNodes
done5000
21150
1287
0110

prune739.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.9b

localize103.0ms

Local error

Found 4 expressions with local error:

24.3b
(sqrt (- (* 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)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log log1p-expm1-u flip-- add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 62
Calls
4 calls:
10.0ms
(sqrt (- (* 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)))

series518.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(sqrt (- (* b_2 b_2) (* a c)))
136.0ms
(cbrt (- (* b_2 b_2) (* a c)))
138.0ms
(cbrt (- (* b_2 b_2) (* a c)))
141.0ms
(cbrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts
74 → 74
Iterations
IterNodes
done5000
33152
2671
1213
087

prune817.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.9b

localize48.0ms

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)))

rewrite122.0ms

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×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 97
Calls
4 calls:
99.0ms
(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)))

series492.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
133.0ms
(cbrt (- (* b_2 b_2) (* a c)))
125.0ms
(cbrt (- (* b_2 b_2) (* a c)))
139.0ms
(cbrt (- (* b_2 b_2) (* a c)))

simplify3.1s

Counts
109 → 109
Iterations
IterNodes
done5002
33206
2863
1369
0186

prune723.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.9b

regimes577.0ms

Accuracy

84.5% (4.4b remaining)

Error of 10.2b against oracle of 5.8b and baseline of 34.4b

bsearch129.0ms

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

simplify7.0ms

Iterations
IterNodes
done27
127
024

end0.0ms

sample2.8s

Algorithm
intervals
Results
770.0ms902×body1280valid
634.0ms1059×body2560valid
442.0ms5860×body80valid
294.0ms2871×body80nan
105.0ms434×body640valid
69.0ms224×body320valid
55.0ms124×body5120valid
14.0ms115×body160valid