Details

Time bar (total: 5.3s)

sample34.0ms

Algorithm
intervals
Results
15.0ms292×body80valid
4.0ms73×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 23.6b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
6.7b
(* (* x y) z)
7.8b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
27.6b
(sqrt (- (* z z) (* t a)))

rewrite27.0ms

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))
8.0ms
(* (* x y) z)
10.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series207.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (* z z) (* t a))
24.0ms
(* (* x y) z)
85.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0346584
11863515
25001510

prune214.0ms

Filtered
88 candidates to 60 candidates (68.2%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New781088
Fresh000
Picked011
Done000
Total781189

Merged error: 4.6b

Counts
89 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

1.7b
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
4.7b
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
27.6b
(sqrt (- (* z z) (* t a)))
27.6b
(sqrt (- (* z z) (* t a)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
63×sqrt-prod
48×add-sqr-sqrt times-frac
35×add-cube-cbrt *-un-lft-identity
33×associate-*r*
30×add-exp-log add-cbrt-cube
16×sqrt-div
15×associate-*l*
9×cbrt-undiv div-exp prod-exp associate-/r* cbrt-unprod
8×pow1
6×associate-/r/
5×flip3-- flip--
4×add-log-exp unswap-sqr
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 141
Calls
4 calls:
9.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
26.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series342.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
108.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
78.0ms
(sqrt (- (* z z) (* t a)))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify83.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
06291951
133621738
250011614

prune379.0ms

Filtered
153 candidates to 99 candidates (64.7%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1503153
Fresh279
Picked011
Done011
Total15212164

Merged error: 4.5b

Counts
164 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

3.0b
(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
5.7b
(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
28.4b
(cbrt (- (* z z) (* t a)))
28.4b
(cbrt (- (* z z) (* t a)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
413×times-frac
157×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
114×sqrt-prod
63×cbrt-prod
34×add-exp-log add-cbrt-cube
24×div-inv
22×associate-/r*
19×associate-/l*
17×cbrt-undiv div-exp
13×associate-/r/
6×cbrt-div
4×pow1 prod-exp cbrt-unprod add-log-exp
3×flip3-- flip--
2×frac-2neg pow1/3 sqrt-div clear-num
1×associate-/l/
Counts
4 → 284
Calls
4 calls:
19.0ms
(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
7.0ms
(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
3.0ms
(cbrt (- (* z z) (* t a)))
3.0ms
(cbrt (- (* z z) (* t a)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
67.0ms
(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
87.0ms
(cbrt (- (* z z) (* t a)))
91.0ms
(cbrt (- (* z z) (* t a)))

simplify80.0ms

Algorithm
egg-herbie
Counts
296 → 296
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012616499
150016166

prune920.0ms

Filtered
296 candidates to 223 candidates (75.3%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2942296
Fresh369
Picked101
Done022
Total29810308

Merged error: 4.5b

Counts
308 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

5.7b
(* (/ (* x y) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ z (cbrt (sqrt (- (* z z) (* t a))))))
27.6b
(sqrt (- (* z z) (* t a)))
27.6b
(sqrt (- (* z z) (* t a)))
27.6b
(sqrt (- (* z z) (* t a)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
41×add-sqr-sqrt
33×associate-*r*
32×add-cbrt-cube
31×times-frac
27×add-cube-cbrt *-un-lft-identity
20×cbrt-prod sqrt-div
19×sqrt-prod
18×prod-exp cbrt-unprod
14×cbrt-div
13×cbrt-undiv div-exp associate-*l*
10×flip3-- associate-/r/ flip--
9×pow1
5×frac-times
4×add-log-exp unswap-sqr
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ associate-*l/
2×div-inv
1×pow-prod-down *-commutative
Counts
4 → 127
Calls
4 calls:
31.0ms
(* (/ (* x y) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ z (cbrt (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(* (/ (* x y) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ z (cbrt (sqrt (- (* z z) (* t a))))))
58.0ms
(sqrt (- (* z z) (* t a)))
63.0ms
(sqrt (- (* z z) (* t a)))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify106.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
06702387
137522044
250031867

prune377.0ms

Filtered
139 candidates to 98 candidates (70.5%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1390139
Fresh077
Picked011
Done022
Total13910149

Merged error: 4.5b

Counts
149 → 10

regimes427.0ms

Accuracy

80.7% (4.0b remaining)

Error of 7.1b against oracle of 3.2b and baseline of 23.8b

bsearch99.0ms

Steps
ItersRangePoint
9
1.3362163214547356e+116
3.7053107102584596e+124
4.203285180343617e+120
7
-1.6352009508465234e+49
-6.694513796974998e+47
-1.2806604334740692e+49

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02717
13317
23317

end0.0ms

sample1.0s

Algorithm
intervals
Results
489.0ms8895×body80valid
153.0ms2940×body80nan

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