Details

Time bar (total: 20.2s)

sample352.0ms

Algorithm
intervals
Results
37.0ms15×body640valid
18.0ms35×body1280valid
16.0ms33×body2560valid
13.0ms168×body80valid
6.0ms92×body80nan
4.0ms6×body5120valid
2.0ms9×body320valid
1.0ms8×body160valid

simplify146.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
01013
11413
22212
32512
42712
52912
done2912

prune50.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.2b
(- (* b_2 b_2) (* a c))
2.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite216.0ms

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:
86.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
8.0ms
(- (* b_2 b_2) (* a c))
101.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
37.0ms
(- (* b_2 b_2) (* a c))
87.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
93.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts
96 → 96
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01541624
13611526
29271426
323271418
done50001410

prune376.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.3b

localize29.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
3.8b
(/ (/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.8b
(/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite276.0ms

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))
122.0ms
(/ (/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
106.0ms
(/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series678.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b_2 b_2) (* a c))
270.0ms
(/ (/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
271.0ms
(/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
87.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts
168 → 168
Iterations

Useful iterations: 2 (625.0ms)

IterNodesCost
02744426
16843974
223843772
done50003772

prune663.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.2b

localize30.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
1.9b
(/ c (/ (+ (sqrt (- (* b_2 b_2) (* a c))) b_2) a))
3.8b
(/ (/ c (/ (+ (sqrt (- (* b_2 b_2) (* a c))) b_2) a)) (- a))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
1550×times-frac
889×*-un-lft-identity
668×add-sqr-sqrt
667×add-cube-cbrt
162×distribute-lft-neg-in distribute-rgt-neg-in
111×distribute-lft-out
56×associate-/l*
54×neg-mul-1
50×div-inv
26×associate-/r*
18×add-exp-log add-cbrt-cube
12×associate-/r/
9×cbrt-undiv div-exp
6×add-log-exp
5×pow1
3×sqrt-prod
2×flip3-- frac-2neg sqrt-div clear-num flip--
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 719
Calls
4 calls:
8.0ms
(- (* b_2 b_2) (* a c))
55.0ms
(/ c (/ (+ (sqrt (- (* b_2 b_2) (* a c))) b_2) a))
99.0ms
(/ (/ c (/ (+ (sqrt (- (* b_2 b_2) (* a c))) b_2) a)) (- a))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series756.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b_2 b_2) (* a c))
309.0ms
(/ c (/ (+ (sqrt (- (* b_2 b_2) (* a c))) b_2) a))
309.0ms
(/ (/ c (/ (+ (sqrt (- (* b_2 b_2) (* a c))) b_2) a)) (- a))
95.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts
731 → 731
Iterations

Useful iterations: done (1.6s)

IterNodesCost
099624306
1242923078
done500022324

prune2.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.7b
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b
(- (* b_2 b_2) (* a c))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite165.0ms

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:
81.0ms
(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
57.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series503.0ms

Counts
4 → 12
Calls
4 calls:
240.0ms
(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
119.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
59.0ms
(- (* b_2 b_2) (* a c))
84.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.5s

Counts
84 → 84
Iterations

Useful iterations: done (3.5s)

IterNodesCost
01281320
12791222
27131124
316991121
443631109
done50011107

prune263.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.2b

regimes232.0ms

Accuracy

94.5% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 29.5b

bsearch183.0ms

Steps
ItersRangePoint
5
1.2073698495971617e+61
2.9312978430050554e+61
2.5231041875643557e+61
8
-4.3193946104502796e-226
-4.381317687258745e-230
-7.892835993842436e-230
10
-3.742210988141449e+103
-1.1204690717208776e+87
-8.301687926884189e+98

simplify8.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03358
14355
25055
done5055

end0.0ms

sample3.0s

Algorithm
intervals
Results
717.0ms2846×body80nan
605.0ms1050×body2560valid
475.0ms5871×body80valid
338.0ms895×body1280valid
168.0ms479×body640valid
48.0ms101×body5120valid
40.0ms218×body320valid
13.0ms106×body160valid