Details

Time bar (total: 5.5s)

sample19.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1227
2247
3247

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize9.0ms

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))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
8×add-log-exp
5×add-exp-log add-cbrt-cube
4×pow1
3×associate-/r* sum-log 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 → 67
Calls
3 calls:
12.0ms
(+ (+ (* x x) (* y y)) (* z z))
29.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
14.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series245.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(+ (+ (* x x) (* y y)) (* z z))
53.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
158.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify113.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 3 (105.0ms)

IterNodesCost
0259758
11001695
24269689
35002687

prune234.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.9b

localize12.0ms

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)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
39×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×frac-times sqrt-pow1 associate-*l/ add-log-exp
3×pow1/2
2×rem-sqrt-square associate-*r/ pow-prod-down prod-exp cbrt-unprod
1×cbrt-undiv div-exp *-commutative div-inv
Counts
4 → 98
Calls
4 calls:
66.0ms
(* (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)))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
14.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
164.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
102.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
96.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify46.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03321540
114551341
250011274

prune281.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.9b

localize15.0ms

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)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt 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×sqrt-pow1 add-log-exp
3×flip3-+ pow1/2 flip-+
2×rem-sqrt-square associate-/l/
1×cbrt-undiv frac-times frac-2neg associate-*r/ div-exp pow-prod-down associate-*l/ clear-num div-inv
Counts
4 → 106
Calls
4 calls:
22.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
28.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
17.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series757.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
339.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
96.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
100.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify62.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
02481522
16521452
220151426
350021411

prune339.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1 (sqrt (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))))
36.2b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (* (/ 1 (sqrt (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))))))
36.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
225×add-sqr-sqrt
165×times-frac sqrt-prod
83×*-un-lft-identity
62×add-cube-cbrt
58×associate-*r*
55×cbrt-prod
49×unswap-sqr
31×associate-*l*
26×add-exp-log
16×add-cbrt-cube
14×pow1
11×sqrt-div
8×div-exp prod-exp
6×frac-times associate-*r/
5×sqrt-pow1
4×cbrt-undiv pow-prod-down associate-*l/ cbrt-unprod add-log-exp
3×pow1/2
2×rem-sqrt-square rec-exp flip3-+ 1-exp flip-+ div-inv
1×*-commutative
Counts
4 → 211
Calls
4 calls:
76.0ms
(* (/ 1 (sqrt (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))))
75.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (* (/ 1 (sqrt (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))))))
14.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
27.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series762.0ms

Counts
4 → 12
Calls
4 calls:
226.0ms
(* (/ 1 (sqrt (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))))
334.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (* (/ 1 (sqrt (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))))))
104.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
97.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify95.0ms

Algorithm
egg-herbie
Counts
223 → 223
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
07593954
136343641
250023516

prune556.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 19.9b

regimes558.0ms

Accuracy

61.2% (7.6b remaining)

Error of 26.4b against oracle of 18.8b and baseline of 38.4b

bsearch73.0ms

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

sample416.0ms

Algorithm
intervals
Results
254.0ms8000×body80valid