Details

Time bar (total: 5.4s)

analyze730.0ms

Algorithm
search

sample41.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
2.0ms25×body80nan
1.0ms9×body80invalid

simplify373.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03518
16618
211618
314418
415918
516118
616118

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 19.6b

Counts
2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 60
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series69.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify119.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (112.0ms)

IterNodesCost
0223579
1875551
23958543
35001540

prune179.0ms

Filtered
55 candidates to 72 candidates (-30.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New66672
Fresh000
Picked101
Done000
Total67673

Merged error: 7.2b

Counts
73 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

10.6b
(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(cbrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×pow1
4×add-exp-log cbrt-div add-cbrt-cube
3×flip3-- sqrt-prod flip--
2×pow1/3 sqrt-div sum-log
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 54
Calls
4 calls:
4.0ms
(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series98.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ (neg b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
27.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0382835
11434761
25002721

prune255.0ms

Filtered
60 candidates to 66 candidates (-10.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New63366
Fresh055
Picked011
Done000
Total63972

Merged error: 7.2b

Counts
72 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×sqrt-div
4×add-exp-log flip3-- add-cbrt-cube flip-- add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 58
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series68.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify80.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
0218573
1674547
22668538
35001527

prune285.0ms

Filtered
59 candidates to 70 candidates (-18.6%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New70070
Fresh077
Picked011
Done011
Total70979

Merged error: 7.2b

Counts
79 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- add-log-exp
Counts
4 → 60
Calls
4 calls:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series57.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify69.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
0127536
1460520
21957516
35001512

prune243.0ms

Filtered
60 candidates to 72 candidates (-20.0%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New72072
Fresh066
Picked011
Done022
Total72981

Merged error: 7.2b

Counts
81 → 9

regimes332.0ms

Accuracy

86.9% (1.6b remaining)

Error of 9.2b against oracle of 7.6b and baseline of 20.0b

bsearch621.0ms

Steps
ItersRangePoint
8
7.46136622472857e+32
7.748373076335356e+35
7.618354846156723e+35
9
-3.92077716217826e+69
-9.006433092459695e+60
-3.823940436355579e+69

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05559
15559

end0.0ms

analyze514.0ms

Algorithm
search

sample991.0ms

Algorithm
intervals
Results
709.0ms8000×body80valid
56.0ms681×body80nan
32.0ms385×body80invalid

Profiling

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