Details

Time bar (total: 14.8s)

sample85.0ms

Algorithm
intervals
Results
18.0ms44×body2560valid
14.0ms167×body80valid
12.0ms32×body1280valid
7.0ms100×body80nan
4.0ms14×body640valid
1.0ms7×body320valid
1.0ms3×body5120valid
0.0ms3×body160valid

simplify103.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize412.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 4.0 a) c)
0.8b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.0b
(- (* b b) (* (* 4.0 a) c))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-exp-log add-cbrt-cube
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
22.0ms
(* (* 4.0 a) c)
68.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
17.0ms
(- (* b b) (* (* 4.0 a) c))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series327.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (* 4.0 a) c)
120.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
58.0ms
(- (* b b) (* (* 4.0 a) c))
111.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
72 → 72
Iterations

Useful iterations: 2 (238.0ms)

IterNodesCost
01201001
1302911
21541825
done5000825

prune302.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.9b

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
11.6b
(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
8×add-log-exp
6×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log cbrt-div flip3-- add-cbrt-cube flip--
2×sub-neg pow1/3 diff-log
Counts
4 → 50
Calls
4 calls:
17.0ms
(- (* b b) (* (* 4.0 a) c))
32.0ms
(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series561.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (* b b) (* (* 4.0 a) c))
149.0ms
(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
188.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
143.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify850.0ms

Counts
62 → 62
Iterations

Useful iterations: done (846.0ms)

IterNodesCost
01251383
13181346
212101182
done50011126

prune304.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.9b

localize42.0ms

Local error

Found 4 expressions with local error:

26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log flip3-- pow1/3 add-cbrt-cube flip-- add-log-exp
Counts
4 → 52
Calls
4 calls:
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series501.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
151.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
110.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
107.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts
64 → 64
Iterations

Useful iterations: done (2.2s)

IterNodesCost
0651180
11611144
25711024
330881004
done5001964

prune450.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.9b

localize82.0ms

Local error

Found 4 expressions with local error:

26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log flip3-- pow1/3 add-cbrt-cube flip-- add-log-exp
Counts
4 → 52
Calls
4 calls:
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series509.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
125.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
114.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
146.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts
64 → 64
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0651180
11611144
25711024
330881004
done5001964

prune551.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.9b

regimes238.0ms

Accuracy

87.2% (2.9b remaining)

Error of 14.9b against oracle of 12.0b and baseline of 34.9b

bsearch199.0ms

Steps
ItersRangePoint
8
2.5460852775314814e-33
4.614087934274923e-30
4.678096336022247e-33
9
-5.388960530500634e+155
-8.097032161796104e+150
-1.3613714418567412e+154

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02850
13450
done3450

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.0s1127×body2560valid
566.0ms5717×body80valid
558.0ms936×body1280valid
339.0ms2905×body80nan
176.0ms448×body640valid
58.0ms111×body5120valid
47.0ms223×body320valid
16.0ms112×body160valid