Details

Time bar (total: 8.9s)

sample20.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify12.0ms

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: 37.9b

localize14.0ms

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))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
19×times-frac
13×sqrt-prod
11×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u fma-def sum-log log1p-expm1-u
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 → 90
Calls
4 calls:
34.0ms
(+ (+ (* x x) (* y y)) (* z z))
9.0ms
(+ (* x x) (* y y))
80.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
32.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series316.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(+ (+ (* x x) (* y y)) (* z z))
34.0ms
(+ (* x x) (* y y))
58.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
182.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify45.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0345852
11445759
25001739

prune328.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.1b

localize15.0ms

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)))

rewrite261.0ms

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:
8.0ms
(+ (* x x) (* y y))
80.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
129.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
36.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series872.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ (* x x) (* y y))
135.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
347.0ms
(* (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 (48.0ms)

IterNodesCost
04832512
118692385
250012351

prune663.0ms

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)))

rewrite273.0ms

Algorithm
rewrite-expression-head
Rules
152×sqrt-prod
124×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×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down div-inv
2×flip3-+ flip-+ hypot-def
1×frac-times sqrt-unprod associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 166
Calls
4 calls:
35.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
160.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
36.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series591.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
188.0ms
(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1)) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
109.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
113.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify66.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04033047
113642901
250012851

prune548.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.0b

localize19.0ms

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)))

rewrite545.0ms

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×expm1-log1p-u associate-*r/ prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×sqrt-unprod
2×*-commutative
Counts
4 → 206
Calls
4 calls:
325.0ms
(* (* (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)))))
136.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))))
34.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
37.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series1.9s

Counts
4 → 12
Calls
4 calls:
381.0ms
(* (* (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)))))
740.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))))
385.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
382.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify92.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05784071
121003838
250023781

prune980.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 18.0b

regimes538.0ms

Accuracy

64.2% (7.1b remaining)

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

bsearch70.0ms

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

sample492.0ms

Algorithm
intervals
Results
263.0ms8000×body80valid