Details

Time bar (total: 7.3s)

sample19.0ms

Algorithm
intervals
Results
9.0ms270×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0215
1404
2694
31044
41464
51604
61604

prune8.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 5.6b

Counts
2 → 2

localize7.0ms

Local error

Found 2 expressions with local error:

4.5b
(* y (+ 1.0 (* z z)))
4.9b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
4×pow1 associate-*r/
3×associate-*r* associate-*l* prod-exp cbrt-unprod div-inv
2×expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* *-commutative associate-/l/ unswap-sqr
Counts
2 → 74
Calls
2 calls:
5.0ms
(* y (+ 1.0 (* z z)))
8.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series107.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(* y (+ 1.0 (* z z)))
54.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify48.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0416531
12028428
25001420

prune176.0ms

Filtered
80 candidates to 63 candidates (78.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New74680
Fresh011
Picked011
Done000
Total74882

Merged error: 5.4b

Counts
82 → 8

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ 1.0 y) x)
6.4b
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
468×times-frac
228×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
56×associate-/l*
22×div-inv
16×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×associate-/r*
2×pow1 expm1-log1p-u frac-2neg clear-num associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
1×flip3-+ flip-+
Counts
2 → 268
Calls
2 calls:
6.0ms
(/ (/ 1.0 y) x)
14.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series77.0ms

Counts
2 → 6
Calls
2 calls:
23.0ms
(/ (/ 1.0 y) x)
54.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify108.0ms

Algorithm
egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
011383012
145962854
250022850

prune632.0ms

Filtered
274 candidates to 238 candidates (86.9%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2722274
Fresh246
Picked011
Done101
Total2757282

Merged error: 5.4b

Counts
282 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (/ 1 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z)))))
2.9b
(/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z))))
16.8b
(sqrt (+ 1.0 (* z z)))
16.8b
(sqrt (+ 1.0 (* z z)))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
1480×times-frac
797×add-sqr-sqrt
663×*-un-lft-identity
649×add-cube-cbrt
305×sqrt-prod
264×associate-*r*
73×add-exp-log
55×div-inv
45×add-cbrt-cube
43×associate-/l*
38×div-exp
35×unswap-sqr
24×associate-*l*
22×cbrt-undiv
16×prod-exp
10×sqrt-div
8×pow1 cbrt-unprod
6×associate-/r* associate-/r/
5×flip3-+ flip-+
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 725
Calls
4 calls:
128.0ms
(* (/ 1 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z)))))
17.0ms
(/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (/ 1 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z)))))
84.0ms
(/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z))))
46.0ms
(sqrt (+ 1.0 (* z z)))
41.0ms
(sqrt (+ 1.0 (* z z)))

simplify152.0ms

Algorithm
egg-herbie
Counts
737 → 737
Iterations

Useful iterations: 1 (50.0ms)

IterNodesCost
0291910993
1500110558

prune1.5s

Filtered
737 candidates to 456 candidates (61.9%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New7370737
Fresh055
Picked011
Done011
Total7377744

Merged error: 5.4b

Counts
744 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ 1.0 x))
0.6b
(cbrt (/ 1.0 x))
3.3b
(/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) (/ (fma z z 1.0) (/ (cbrt (/ 1.0 x)) y)))
4.7b
(/ (fma z z 1.0) (/ (cbrt (/ 1.0 x)) y))

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
1397×times-frac
587×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
416×cbrt-prod
213×associate-/r*
46×div-inv
30×add-exp-log
21×add-cbrt-cube
15×cbrt-undiv div-exp
6×cbrt-div
4×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l* add-log-exp
3×prod-exp cbrt-unprod associate-/l/
2×frac-2neg pow1/3 clear-num
1×frac-times associate-*r/ associate-*l/
Counts
4 → 627
Calls
4 calls:
2.0ms
(cbrt (/ 1.0 x))
2.0ms
(cbrt (/ 1.0 x))
33.0ms
(/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) (/ (fma z z 1.0) (/ (cbrt (/ 1.0 x)) y)))
13.0ms
(/ (fma z z 1.0) (/ (cbrt (/ 1.0 x)) y))

series798.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(cbrt (/ 1.0 x))
188.0ms
(cbrt (/ 1.0 x))
147.0ms
(/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) (/ (fma z z 1.0) (/ (cbrt (/ 1.0 x)) y)))
265.0ms
(/ (fma z z 1.0) (/ (cbrt (/ 1.0 x)) y))

simplify138.0ms

Algorithm
egg-herbie
Counts
639 → 639
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
025689669
150019536

prune2.0s

Filtered
639 candidates to 574 candidates (89.8%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New6390639
Fresh044
Picked011
Done022
Total6397646

Merged error: 5.4b

Counts
646 → 7

regimes184.0ms

Accuracy

77.9% (0.4b remaining)

Error of 5.2b against oracle of 4.8b and baseline of 6.5b

bsearch75.0ms

Steps
ItersRangePoint
8
0.5354793519810654
1538.2388859235716
161.8978563228144
10
-7.470896749520786e-10
-1.113797997846539e-26
-1.0660078161072246e-11

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02513
12513

end0.0ms

sample496.0ms

Algorithm
intervals
Results
306.0ms8635×body80valid

Profiling

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