Details

Time bar (total: 19.3s)

sample164.0ms

Algorithm
intervals
Results
12.0ms184×body80valid
11.0ms45×body1280valid
8.0ms25×body2560valid
3.0ms69×body80nan
3.0ms17×body640valid
1.0ms9×body320valid
1.0ms2×body5120valid
0.0ms1×body160valid

simplify98.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
01013
11413
22212
32512
42712
52912
done2912

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b
(- (* b_2 b_2) (* a c))
22.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite489.0ms

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-exp-log add-cbrt-cube 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 frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num div-inv
Counts
4 → 84
Calls
4 calls:
208.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
190.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
58.0ms
(- (* b_2 b_2) (* a c))
22.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series607.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
126.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
81.0ms
(- (* b_2 b_2) (* a c))
227.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts
96 → 96
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01541624
13611526
29281426
323331418
done50001410

prune428.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
3.5b
(/ (/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.2b
(/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite271.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
97×*-un-lft-identity
66×add-sqr-sqrt
65×add-cube-cbrt
21×associate-/l*
16×distribute-lft-out
11×add-exp-log add-cbrt-cube
10×associate-/r/
7×associate-/r*
6×div-inv add-log-exp
5×pow1 flip3-+ flip-+
4×cbrt-undiv div-exp
3×flip3-- div-sub distribute-frac-neg sqrt-prod flip-- associate-/l/
2×frac-2neg sub0-neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 156
Calls
4 calls:
16.0ms
(- (* b_2 b_2) (* a c))
110.0ms
(/ (/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
109.0ms
(/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series705.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- (* b_2 b_2) (* a c))
264.0ms
(/ (/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
299.0ms
(/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
84.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts
168 → 168
Iterations

Useful iterations: 2 (606.0ms)

IterNodesCost
02744426
16843974
223843772
done50003772

prune780.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.2b

localize28.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
2.5b
(/ c (/ (+ (sqrt (- (* b_2 b_2) (* a c))) b_2) a))
3.5b
(/ (- 0 (/ c (/ (+ (sqrt (- (* b_2 b_2) (* a c))) b_2) a))) a)
22.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite421.0ms

Algorithm
rewrite-expression-head
Rules
129×times-frac
103×add-sqr-sqrt
98×*-un-lft-identity
66×add-cube-cbrt
19×associate-/r*
12×distribute-lft-out difference-of-squares
11×add-exp-log add-cbrt-cube
10×associate-/l*
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp distribute-lft-out--
3×flip3-- sqrt-prod flip--
2×frac-2neg sqrt-div clear-num associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 sub0-neg pow1/2 diff-log div-sub distribute-frac-neg associate-/r/
Counts
4 → 156
Calls
4 calls:
16.0ms
(- (* b_2 b_2) (* a c))
56.0ms
(/ c (/ (+ (sqrt (- (* b_2 b_2) (* a c))) b_2) a))
315.0ms
(/ (- 0 (/ c (/ (+ (sqrt (- (* b_2 b_2) (* a c))) b_2) a))) a)
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series704.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b_2 b_2) (* a c))
262.0ms
(/ c (/ (+ (sqrt (- (* b_2 b_2) (* a c))) b_2) a))
288.0ms
(/ (- 0 (/ c (/ (+ (sqrt (- (* b_2 b_2) (* a c))) b_2) a))) a)
108.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts
168 → 168
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02934012
16623768
219603530
done50003458

prune759.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.9b
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b
(- (* b_2 b_2) (* a c))
22.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
15×add-sqr-sqrt
14×add-cube-cbrt
12×times-frac
8×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 distribute-lft-out
4×associate-/r*
3×sqrt-prod associate-/l*
2×flip3-- flip3-+ sqrt-div associate-/r/ flip-- flip-+
1×cbrt-undiv +-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-exp clear-num sum-log div-inv
Counts
4 → 72
Calls
4 calls:
60.0ms
(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
58.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms
(- (* b_2 b_2) (* a c))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series480.0ms

Counts
4 → 12
Calls
4 calls:
249.0ms
(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
95.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
41.0ms
(- (* b_2 b_2) (* a c))
94.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.4s

Counts
84 → 84
Iterations

Useful iterations: done (3.4s)

IterNodesCost
01281320
12791222
27131124
316991121
443631109
done50011107

prune311.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.2b

regimes352.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.4b against oracle of 5.4b and baseline of 29.6b

bsearch201.0ms

Steps
ItersRangePoint
2
5.341589198600723e+134
5.967668210703041e+134
5.732888581164671e+134
10
-1.2529167750641135e-296
-2.859335985249397e-307
-3.5177987696791986e-300
9
-5.2045971803048284e+128
-5.738453298103652e+119
-1.406599291770867e+122

simplify10.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03357
14555
25055
35155
done5155

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.1s1056×body2560valid
969.0ms5847×body80valid
431.0ms926×body1280valid
273.0ms2938×body80nan
136.0ms477×body640valid
51.0ms113×body5120valid
40.0ms209×body320valid
14.0ms108×body160valid