Details

Time bar (total: 8.4s)

sample18.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify10.0ms

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: 39.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.6b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1
3×expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative fma-def frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num sum-log
Counts
3 → 72
Calls
3 calls:
3.0ms
(+ (* x x) (* y y))
30.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
19.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series251.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(+ (* x x) (* y y))
50.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
170.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify133.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0310730
11303650
24811634
35001634

prune255.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
0.4b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
36.6b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
75×times-frac sqrt-prod
53×*-un-lft-identity
49×add-cube-cbrt
35×cbrt-prod
25×associate-*r*
16×unswap-sqr
10×associate-*l*
9×pow1
8×add-exp-log
7×add-cbrt-cube
6×associate-/r* add-log-exp
5×sqrt-div
4×expm1-log1p-u log1p-expm1-u div-inv
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-/l*
2×flip3-+ flip-+ associate-/l/
1×cbrt-undiv +-commutative frac-times fma-def frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num sum-log *-commutative cbrt-unprod
Counts
4 → 164
Calls
4 calls:
3.0ms
(+ (* x x) (* y y))
30.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
70.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
17.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series860.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (* x x) (* y y))
134.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
339.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
358.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify72.0ms

Algorithm
egg-herbie
Counts
176 → 176
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04832511
118692385
250012351

prune642.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 18.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
0.3b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
36.5b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.5b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
150×sqrt-prod
132×add-sqr-sqrt
106×times-frac
64×add-cube-cbrt *-un-lft-identity
47×cbrt-prod
43×associate-*r*
24×unswap-sqr
13×associate-*l*
10×pow1 sqrt-div
8×add-exp-log
7×add-cbrt-cube
6×associate-/r* associate-/l*
4×expm1-log1p-u sqrt-pow1 pow1/2 log1p-expm1-u add-log-exp
3×flip3-+ pow-prod-down flip-+ div-inv
2×rem-sqrt-square hypot-def associate-/l/
1×cbrt-undiv frac-times frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
4 → 199
Calls
4 calls:
97.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
26.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
15.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
15.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series835.0ms

Counts
4 → 12
Calls
4 calls:
387.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
238.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
104.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
106.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify150.0ms

Algorithm
egg-herbie
Counts
211 → 211
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04244060
113653943
245693843
350013843

prune771.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 18.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
0.4b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
6.0b
(exp (log (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))))
36.6b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
91×add-sqr-sqrt
75×times-frac sqrt-prod
54×*-un-lft-identity
50×add-cube-cbrt
35×cbrt-prod
25×associate-*r*
16×unswap-sqr
14×pow1
10×associate-*l*
9×sqrt-div
8×add-exp-log
7×exp-prod add-cbrt-cube
6×pow-prod-down associate-/r*
5×sqrt-pow1 pow1/2
4×expm1-log1p-u log-pow log1p-expm1-u div-inv add-log-exp
3×rem-sqrt-square log-div exp-diff associate-/l*
2×frac-times associate-*r/ associate-*l/ associate-/l/
1×cbrt-undiv log-prod frac-2neg flip3-+ sqrt-unprod div-exp exp-sum prod-exp clear-num *-commutative cbrt-unprod flip-+ rem-exp-log
Counts
4 → 171
Calls
4 calls:
30.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
71.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
142.0ms
(exp (log (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))))
17.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series1.6s

Counts
4 → 12
Calls
4 calls:
159.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
395.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
396.0ms
(exp (log (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))))
648.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify76.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04422714
115702584
250022549

prune761.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 18.9b

regimes768.0ms

Accuracy

64.7% (7.1b remaining)

Error of 25.7b against oracle of 18.6b and baseline of 38.7b

bsearch105.0ms

Steps
ItersRangePoint
8
1.2548328817032444e+126
4.884715246864704e+128
1.096043779466603e+127
10
-4.6853696568247485e+141
-1.1373822395753508e+128
-1.4467202670789784e+138

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03828
14528
24828
34828

end0.0ms

sample454.0ms

Algorithm
intervals
Results
275.0ms8000×body80valid