Details

Time bar (total: 8.0s)

analyze1.1s

Algorithm
search

sample33.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
3.0ms65×body80nan
2.0ms32×body80invalid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 21.3b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
4.4b
(* (* x y) z)
9.1b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.7b
(sqrt (- (* z z) (* t a)))

rewrite26.0ms

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))
4.0ms
(* (* x y) z)
9.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
7.0ms
(sqrt (- (* z z) (* t a)))

series53.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(- (* z z) (* t a))
5.0ms
(* (* x y) z)
29.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
12.0ms
(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0343583
11850515
25003510

prune140.0ms

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

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New771188
Fresh000
Picked101
Done000
Total781189

Merged error: 3.7b

Counts
89 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.4b
(- (* z z) (* t a))
2.9b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
22.7b
(sqrt (- (* z z) (* t a)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
24×associate-*r* sqrt-prod
18×add-exp-log add-cbrt-cube
10×pow1
6×sqrt-div prod-exp associate-/r* cbrt-unprod add-log-exp
4×flip3-- associate-/r/ flip--
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 112
Calls
4 calls:
6.0ms
(/ z (sqrt (- (* z z) (* t a))))
3.0ms
(- (* z z) (* t a))
11.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
3.0ms
(sqrt (- (* z z) (* t a)))

series61.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ z (sqrt (- (* z z) (* t a))))
8.0ms
(- (* z z) (* t a))
31.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
12.0ms
(sqrt (- (* z z) (* t a)))

simplify62.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04281014
12153912
25002894

prune139.0ms

Filtered
81 candidates to 124 candidates (-53.1%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1213124
Fresh2810
Picked011
Done000
Total12312135

Merged error: 3.5b

Counts
135 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

5.2b
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
22.7b
(sqrt (- (* z z) (* t a)))
22.7b
(sqrt (- (* z z) (* t a)))
22.7b
(sqrt (- (* z z) (* t a)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
8×sqrt-div
7×pow1
4×add-exp-log flip3-- add-cbrt-cube flip-- add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 78
Calls
4 calls:
5.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
3.0ms
(sqrt (- (* z z) (* t a)))
3.0ms
(sqrt (- (* z z) (* t a)))
3.0ms
(sqrt (- (* z z) (* t a)))

series82.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
12.0ms
(sqrt (- (* z z) (* t a)))
12.0ms
(sqrt (- (* z z) (* t a)))
12.0ms
(sqrt (- (* z z) (* t a)))

simplify93.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 3 (83.0ms)

IterNodesCost
0337846
1899824
23263794
35001789

prune139.0ms

Filtered
72 candidates to 90 candidates (-25.0%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New90090
Fresh01010
Picked011
Done011
Total9012102

Merged error: 3.5b

Counts
102 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.4b
(- (* z z) (* t a))
3.1b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.7b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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)))

series61.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ (sqrt (- (* z z) (* t a))) z)
7.0ms
(- (* z z) (* t a))
29.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
12.0ms
(sqrt (- (* z z) (* t a)))

simplify68.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05121325
123581230
250021214

prune108.0ms

Filtered
99 candidates to 144 candidates (-45.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1422144
Fresh369
Picked101
Done112
Total1479156

Merged error: 3.5b

Counts
156 → 9

regimes765.0ms

Accuracy

82.2% (3.5b remaining)

Error of 6.7b against oracle of 3.2b and baseline of 22.8b

bsearch2.8s

Steps
ItersRangePoint
8
2.5574825704894126e+71
1.751680610479245e+75
1.6387934609127881e+75
9
-4.677413610244142e+75
-1.2008551795626694e+70
-1.809372504935346e+74

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02717
13317
23317

end0.0ms

analyze1.1s

Algorithm
search

sample965.0ms

Algorithm
intervals
Results
459.0ms8000×body80valid
107.0ms2223×body80nan
46.0ms874×body80invalid

Profiling

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