Details

Time bar (total: 6.5s)

sample19.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0167
1277
2337
3347
4347

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

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)
34.0b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite148.0ms

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:
32.0ms
(+ (+ (* x x) (* y y)) (* z z))
8.0ms
(+ (* x x) (* y y))
77.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
29.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series260.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (+ (* x x) (* y y)) (* z z))
24.0ms
(+ (* x x) (* y y))
50.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
152.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify41.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0345852
11445759
25001739

prune316.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.5b

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))))
34.0b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite249.0ms

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))
75.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
120.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
35.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series821.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (* x x) (* y y))
138.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
315.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
344.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify65.0ms

Algorithm
egg-herbie
Counts
176 → 176
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04832511
118692385
250012351

prune649.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ 1 (cbrt 3.0))))
0.4b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
1.0b
(/ 1 (cbrt 3.0))
33.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite418.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
45×sqrt-prod
43×times-frac
41×*-un-lft-identity
39×add-cube-cbrt
31×associate-*r*
29×sqrt-div
21×cbrt-prod
18×pow1
15×add-exp-log
12×add-cbrt-cube
11×frac-times associate-*l*
10×pow-prod-down
8×associate-*l/ unswap-sqr
7×flip3-+ associate-*r/ flip-+
6×sqrt-pow1 pow1/2 associate-/r*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×sqrt-unprod div-inv associate-/l*
2×pow-flip div-exp *-commutative
1×cbrt-undiv rem-sqrt-square rec-exp frac-2neg pow1/3 1-exp clear-num hypot-def inv-pow
Counts
4 → 165
Calls
4 calls:
254.0ms
(* (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ 1 (cbrt 3.0))))
117.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
6.0ms
(/ 1 (cbrt 3.0))
35.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series633.0ms

Counts
4 → 10
Calls
4 calls:
325.0ms
(* (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ 1 (cbrt 3.0))))
215.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
0.0ms
(/ 1 (cbrt 3.0))
92.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify67.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05082156
121881979
250021869

prune552.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 14.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (hypot (sqrt (+ (* x x) (* y y))) z)) (sqrt (/ 1 (cbrt 3.0))))
0.4b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (hypot (sqrt (+ (* x x) (* y y))) z))
1.0b
(/ 1 (cbrt 3.0))
27.1b
(sqrt (+ (* x x) (* y y)))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
41×times-frac
39×*-un-lft-identity
38×add-cube-cbrt
35×sqrt-prod
28×associate-*r*
21×cbrt-prod
15×add-exp-log
13×pow1
12×add-cbrt-cube
11×associate-*l*
7×sqrt-div
6×associate-/r*
4×expm1-log1p-u pow-prod-down associate-*l/ prod-exp cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
3×sqrt-unprod div-inv associate-/l*
2×hypot-udef pow-flip div-exp *-commutative
1×cbrt-undiv frac-times rem-sqrt-square rec-exp frac-2neg sqrt-pow1 flip3-+ pow1/2 pow1/3 1-exp associate-*r/ clear-num flip-+ hypot-def inv-pow
Counts
4 → 142
Calls
4 calls:
169.0ms
(* (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (hypot (sqrt (+ (* x x) (* y y))) z)) (sqrt (/ 1 (cbrt 3.0))))
52.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (hypot (sqrt (+ (* x x) (* y y))) z))
6.0ms
(/ 1 (cbrt 3.0))
8.0ms
(sqrt (+ (* x x) (* y y)))

series617.0ms

Counts
4 → 10
Calls
4 calls:
316.0ms
(* (* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (hypot (sqrt (+ (* x x) (* y y))) z)) (sqrt (/ 1 (cbrt 3.0))))
269.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (hypot (sqrt (+ (* x x) (* y y))) z))
0.0ms
(/ 1 (cbrt 3.0))
32.0ms
(sqrt (+ (* x x) (* y y)))

simplify60.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04711576
119351418
250011280

prune467.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes281.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01912
11912

end0.0ms

sample520.0ms

Algorithm
intervals
Results
280.0ms8000×body80valid