Details

Time bar (total: 7.9s)

sample19.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1227
2247
3247

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.3b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×sqrt-prod
11×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1
4×sum-log
3×flip3-+ associate-/r* flip-+ associate-/l*
2×+-commutative rem-sqrt-square div-inv associate-/l/
1×cbrt-undiv associate-+l+ frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
4 → 78
Calls
4 calls:
29.0ms
(+ (+ (* x x) (* y y)) (* z z))
8.0ms
(+ (* x x) (* y y))
76.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
32.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series295.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (+ (* x x) (* y y)) (* z z))
27.0ms
(+ (* x x) (* y y))
67.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
164.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify39.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0325828
11345761
25001755

prune229.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.2b
(/ (+ (+ (* 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))))
35.3b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite254.0ms

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×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 frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num sum-log *-commutative cbrt-unprod
Counts
4 → 155
Calls
4 calls:
8.0ms
(+ (* x x) (* y y))
72.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
137.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
30.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series837.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(+ (* x x) (* y y))
122.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
330.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
340.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify84.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04672452
117972356
250022337

prune542.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
0.4b
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
35.2b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.2b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite250.0ms

Algorithm
rewrite-expression-head
Rules
152×sqrt-prod
122×add-sqr-sqrt
84×times-frac
55×*-un-lft-identity
47×add-cube-cbrt
25×associate-*r* associate-*l*
24×unswap-sqr
11×pow1
9×sqrt-div
6×add-exp-log add-cbrt-cube
5×rem-sqrt-square sqrt-pow1 pow1/2
4×add-log-exp
3×pow-prod-down div-inv
2×flip3-+ flip-+
1×frac-times sqrt-unprod associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 156
Calls
4 calls:
31.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
148.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
28.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series520.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
161.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
101.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
104.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify56.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03912965
113182831
250022779

prune422.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))) (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))))
0.4b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))))
35.3b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
35.3b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite492.0ms

Algorithm
rewrite-expression-head
Rules
188×sqrt-prod
116×add-sqr-sqrt
97×times-frac
68×*-un-lft-identity
63×add-cube-cbrt
56×associate-*r*
42×cbrt-prod
28×sqrt-div
20×unswap-sqr
18×pow1
11×add-exp-log associate-*l* add-cbrt-cube
10×pow-prod-down
7×sqrt-pow1 pow1/2
6×frac-times rem-sqrt-square associate-*l/
5×div-inv
4×associate-*r/ prod-exp cbrt-unprod add-log-exp
3×sqrt-unprod
2×*-commutative
Counts
4 → 198
Calls
4 calls:
296.0ms
(* (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))) (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))))
123.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))))
33.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
30.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series1.7s

Counts
4 → 12
Calls
4 calls:
340.0ms
(* (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))) (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))))
672.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))))
345.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
345.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify74.0ms

Algorithm
egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05693952
120763725
250023667

prune833.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 18.0b

regimes479.0ms

Accuracy

64.2% (7.1b remaining)

Error of 25.5b against oracle of 18.3b and baseline of 38.2b

bsearch61.0ms

Steps
ItersRangePoint
8
1.4676110776348385e+142
1.1574277099819921e+145
2.8916513065434067e+143
6
-4.90358144502769e+128
-1.1729788455269108e+128
-3.731627177350631e+128

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03828
14528
24828
34828

end0.0ms

sample505.0ms

Algorithm
intervals
Results
271.0ms8000×body80valid