Details

Time bar (total: 13.3s)

analyze1.4s

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
1.6%98.2%0.2%10
3.1%90.4%6.5%11
9.2%84.4%6.5%12
13%80.6%6.5%13
24.8%68.7%6.5%14

sample34.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
3.0ms66×body80nan
2.0ms33×body80invalid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 23.8b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
5.8b
(* (* x y) z)
8.1b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.1b
(sqrt (- (* z z) (* t a)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
4×sqrt-div
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
5.0ms
(* (* x y) z)
9.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms
(sqrt (- (* z z) (* t a)))

series62.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(- (* z z) (* t a))
9.0ms
(* (* x y) z)
30.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
13.0ms
(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0343583
11850515
25003510

prune182.0ms

Filtered
60 candidates to 88 candidates (-46.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New80888
Fresh000
Picked101
Done000
Total81889

Merged error: 5.0b

Counts
89 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt (- (* z z) (* t a))) z)
0.2b
(- (* z z) (* t a))
4.1b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.1b
(sqrt (- (* z z) (* t a)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×sqrt-div div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/
Counts
4 → 132
Calls
4 calls:
6.0ms
(/ (sqrt (- (* z z) (* t a))) z)
3.0ms
(- (* z z) (* t a))
9.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
3.0ms
(sqrt (- (* z z) (* t a)))

series63.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ (sqrt (- (* z z) (* t a))) z)
7.0ms
(- (* z z) (* t a))
31.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
12.0ms
(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
05121325
123581230
250021230

prune155.0ms

Filtered
109 candidates to 144 candidates (-32.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1404144
Fresh347
Picked101
Done000
Total1448152

Merged error: 5.0b

Counts
152 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
2.1b
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
2.4b
(/ y (/ (sqrt (- (* z z) (* t a))) z))
24.1b
(sqrt (- (* z z) (* t a)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
263×times-frac
157×add-sqr-sqrt
143×add-cube-cbrt *-un-lft-identity
71×associate-*r*
67×sqrt-prod
22×associate-/r*
18×add-exp-log add-cbrt-cube
9×div-inv
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×unswap-sqr
3×associate-*l* prod-exp cbrt-unprod associate-/l*
2×flip3-- sqrt-div associate-/r/ flip--
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 227
Calls
4 calls:
4.0ms
(- (* z z) (* t a))
23.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
8.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
3.0ms
(sqrt (- (* z z) (* t a)))

series70.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(- (* z z) (* t a))
29.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
19.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
12.0ms
(sqrt (- (* z z) (* t a)))

simplify102.0ms

Algorithm
egg-herbie
Counts
239 → 239
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08142502
140092347
250022347

prune231.0ms

Filtered
161 candidates to 239 candidates (-48.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2381239
Fresh077
Picked011
Done000
Total2389247

Merged error: 5.0b

Counts
247 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
0.2b
(/ x (/ (sqrt 1) y))
4.1b
(/ (/ x (/ (sqrt 1) y)) (/ (sqrt (- (* z z) (* t a))) z))
24.1b
(sqrt (- (* z z) (* t a)))

rewrite327.0ms

Algorithm
rewrite-expression-head
Rules
5756×times-frac
2443×add-sqr-sqrt
2442×add-cube-cbrt *-un-lft-identity
1308×sqrt-prod
170×div-inv
74×associate-/l*
44×associate-/r*
30×add-exp-log add-cbrt-cube
25×associate-/r/
18×cbrt-undiv div-exp
6×add-log-exp
5×pow1
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 → 1812
Calls
4 calls:
4.0ms
(- (* z z) (* t a))
12.0ms
(/ x (/ (sqrt 1) y))
68.0ms
(/ (/ x (/ (sqrt 1) y)) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms
(sqrt (- (* z z) (* t a)))

series60.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(- (* z z) (* t a))
3.0ms
(/ x (/ (sqrt 1) y))
34.0ms
(/ (/ x (/ (sqrt 1) y)) (/ (sqrt (- (* z z) (* t a))) z))
15.0ms
(sqrt (- (* z z) (* t a)))

simplify530.0ms

Algorithm
egg-herbie
Counts
1824 → 1824
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
0500240949

prune3.6s

Filtered
1244 candidates to 1824 candidates (-46.6%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New182401824
Fresh077
Picked011
Done011
Total182491833

Merged error: 5.0b

Counts
1833 → 9

regimes771.0ms

Accuracy

84.8% (2.9b remaining)

Error of 6.2b against oracle of 3.3b and baseline of 22.6b

bsearch3.2s

Steps
ItersRangePoint
8
3.964890554572138e+86
1.3806392689779519e+90
1.000711234774603e+90
10
-2.231007350080654e+110
-6.257394200670923e+97
-8.735053047960022e+109

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02610
13210
23210

end0.0ms

analyze1.2s

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
1.6%98.2%0.2%10
3.1%90.4%6.5%11
9.2%84.4%6.5%12
13%80.6%6.5%13
24.8%68.7%6.5%14

sample1.0s

Algorithm
intervals
Results
461.0ms8000×body80valid
122.0ms2145×body80nan
49.0ms816×body80invalid

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