Details

Time bar (total: 15.9s)

sample79.0ms

Algorithm
intervals
Results
13.0ms33×body2560valid
13.0ms35×body1280valid
12.0ms168×body80valid
6.0ms92×body80nan
4.0ms15×body640valid
4.0ms6×body5120valid
2.0ms9×body320valid
1.0ms8×body160valid

simplify136.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
1.2b
(- (* b b) (* 4.0 (* a c)))
2.0b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite276.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
169.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
19.0ms
(- (* b b) (* 4.0 (* a c)))
56.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
28.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series461.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
71.0ms
(- (* b b) (* 4.0 (* a c)))
126.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
115.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.1s

Counts
84 → 84
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01521592
13851488
212041332
344311324
done50001324

prune346.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.4b

localize9.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune32.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a)
1.2b
(- (* b b) (* 4.0 (* a c)))
2.0b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite238.0ms

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:
134.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a)
12.0ms
(- (* b b) (* 4.0 (* a c)))
60.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
28.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series479.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a)
71.0ms
(- (* b b) (* 4.0 (* a c)))
136.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
101.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.8s

Counts
96 → 96
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01561888
13711774
210221658
331451650
done50011643

prune424.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.3b

localize34.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
3.8b
(/ (/ (- 0 (* 4.0 (* a c))) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
11.8b
(/ (- 0 (* 4.0 (* a c))) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite246.0ms

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:
17.0ms
(- (* b b) (* 4.0 (* a c)))
130.0ms
(/ (/ (- 0 (* 4.0 (* a c))) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
67.0ms
(/ (- 0 (* 4.0 (* a c))) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b))
19.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series766.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (* b b) (* 4.0 (* a c)))
280.0ms
(/ (/ (- 0 (* 4.0 (* a c))) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
299.0ms
(/ (- 0 (* 4.0 (* a c))) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) b))
117.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
168 → 168
Iterations

Useful iterations: 2 (692.0ms)

IterNodesCost
02745314
16854830
224704584
done50004584

prune672.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.2b

regimes286.0ms

Accuracy

88% (3.2b remaining)

Error of 8.8b against oracle of 5.6b and baseline of 32.5b

bsearch304.0ms

Steps
ItersRangePoint
5
1.2073698495971617e+61
2.9312978430050554e+61
1.3572844331324948e+61
9
6.262918217783262e-188
1.0824447814377013e-180
3.8495586393832845e-181
10
-3.742210988141449e+103
-1.1204690717208776e+87
-8.301687926884189e+98

simplify11.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03873
15371
26171
done6171

end0.0ms

sample3.6s

Algorithm
intervals
Results
961.0ms5870×body80valid
930.0ms1051×body2560valid
414.0ms893×body1280valid
314.0ms2845×body80nan
140.0ms98×body5120valid
135.0ms480×body640valid
98.0ms218×body320valid
16.0ms108×body160valid