Details

Time bar (total: 6.6s)

sample17.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0167
1277
2337
3347
4347

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.3b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.2b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×sqrt-prod
8×add-log-exp
5×add-exp-log add-cbrt-cube
4×pow1
3×expm1-log1p-u fma-def associate-/r* sum-log log1p-expm1-u associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative associate-+l+ frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
3 → 76
Calls
3 calls:
13.0ms
(+ (+ (* x x) (* y y)) (* z z))
30.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
15.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series270.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(+ (+ (* x x) (* y y)) (* z z))
57.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
175.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify127.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (118.0ms)

IterNodesCost
0272784
11063695
24582674
35001673

prune278.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
36.2b
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
36.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
24×sqrt-prod
22×times-frac associate-*r*
21×add-cube-cbrt *-un-lft-identity
17×sqrt-div
11×pow1
9×add-exp-log add-cbrt-cube
6×flip3-+ associate-*l* flip-+ unswap-sqr
4×expm1-log1p-u frac-times sqrt-pow1 associate-*l/ log1p-expm1-u add-log-exp
3×pow1/2
2×rem-sqrt-square associate-*r/ pow-prod-down prod-exp cbrt-unprod hypot-def
1×cbrt-undiv div-exp *-commutative div-inv
Counts
4 → 108
Calls
4 calls:
69.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
19.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
15.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
18.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
172.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
104.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
106.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify57.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
03441625
115051406
250011336

prune350.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
36.2b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
36.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
36×times-frac
34×add-cube-cbrt *-un-lft-identity
28×sqrt-prod
21×cbrt-prod
9×pow1 sqrt-div
6×add-exp-log associate-/r* associate-/l*
5×add-cbrt-cube
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×flip3-+ pow1/2 flip-+
2×rem-sqrt-square hypot-def associate-/l/
1×cbrt-undiv frac-times frac-2neg associate-*r/ div-exp pow-prod-down associate-*l/ clear-num div-inv
Counts
4 → 116
Calls
4 calls:
27.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
30.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
16.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
16.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series793.0ms

Counts
4 → 12
Calls
4 calls:
234.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
350.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
103.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
106.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify76.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
02581610
16861532
221711508
350011493

prune417.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))) (sqrt (cbrt 3.0)))
36.2b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))) (sqrt (cbrt 3.0)))))
36.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
1062×times-frac
991×sqrt-prod
557×add-sqr-sqrt
553×add-cube-cbrt *-un-lft-identity
357×cbrt-prod
58×associate-/l*
11×div-inv
9×pow1 add-exp-log associate-/r* add-cbrt-cube
7×sqrt-div
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×cbrt-undiv pow1/2 div-exp
2×rem-sqrt-square sqrt-undiv flip3-+ flip-+ hypot-def
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/l/
Counts
4 → 659
Calls
4 calls:
46.0ms
(/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))) (sqrt (cbrt 3.0)))
64.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))) (sqrt (cbrt 3.0)))))
19.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
15.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series840.0ms

Counts
4 → 12
Calls
4 calls:
245.0ms
(/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))) (sqrt (cbrt 3.0)))
370.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))) (sqrt (cbrt 3.0)))))
114.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
111.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify168.0ms

Algorithm
egg-herbie
Counts
671 → 671
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0143916080
1500115171

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 19.9b

regimes390.0ms

Accuracy

61.1% (7.6b remaining)

Error of 26.4b against oracle of 18.7b and baseline of 38.4b

bsearch80.0ms

Steps
ItersRangePoint
8
3.196397393917939e+72
1.0649312883679304e+77
1.0479353069555717e+77
8
-1.3887243973495253e+108
-7.060621971491881e+103
-1.356128363832856e+108

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03325
13925
23925

end0.0ms

sample427.0ms

Algorithm
intervals
Results
259.0ms8000×body80valid