Details

Time bar (total: 4.0s)

sample20.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1227
2247
3247

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

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)
35.9b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite57.0ms

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:
11.0ms
(+ (+ (* x x) (* y y)) (* z z))
2.0ms
(+ (* x x) (* y y))
28.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
14.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series295.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(+ (+ (* x x) (* y y)) (* z z))
28.0ms
(+ (* x x) (* y y))
55.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
171.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0325828
11345761
25001755

prune248.0ms

Filtered
90 candidates to 71 candidates (78.9%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(+ (* x x) (* y y))
0.2b
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
35.9b
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
13×add-exp-log *-un-lft-identity associate-*r*
12×add-cube-cbrt
11×times-frac add-log-exp
9×pow1 add-cbrt-cube
6×flip3-+ sqrt-div flip-+
4×frac-times associate-*l/ prod-exp sum-log
3×associate-*l* unswap-sqr
2×+-commutative sqrt-pow1 associate-*r/ div-exp pow-prod-down un-div-inv cbrt-unprod
1×cbrt-undiv rec-exp associate-+l+ pow1/2 1-exp sqrt-prod *-commutative div-inv
Counts
4 → 81
Calls
4 calls:
14.0ms
(+ (+ (* x x) (* y y)) (* z z))
3.0ms
(+ (* x x) (* y y))
37.0ms
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
11.0ms
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(+ (+ (* x x) (* y y)) (* z z))
28.0ms
(+ (* x x) (* y y))
52.0ms
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
175.0ms
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

simplify55.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0407839
12148760
25002742

prune222.0ms

Filtered
93 candidates to 65 candidates (69.9%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 17.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0)))
0.2b
(* (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (/ (cbrt 1) (cbrt 3.0)))
1.0b
(/ (cbrt 1) (cbrt 3.0))
35.9b
(sqrt (* (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (/ (cbrt 1) (cbrt 3.0))))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
97×add-sqr-sqrt times-frac
92×cbrt-prod
65×*-un-lft-identity
61×add-cube-cbrt
40×associate-*r*
32×add-exp-log
18×add-cbrt-cube
14×unswap-sqr
10×cbrt-undiv div-exp
9×pow1 prod-exp cbrt-unprod associate-/l*
7×associate-*l* associate-/r*
4×div-inv add-log-exp
3×sqrt-div
2×frac-times frac-2neg sqrt-pow1 associate-*r/ pow-prod-down associate-*l/ clear-num associate-/l/
1×flip3-+ pow1/2 sqrt-prod *-commutative flip-+
Counts
4 → 182
Calls
4 calls:
30.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0)))
59.0ms
(* (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (/ (cbrt 1) (cbrt 3.0)))
4.0ms
(/ (cbrt 1) (cbrt 3.0))
20.0ms
(sqrt (* (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (/ (cbrt 1) (cbrt 3.0))))

series707.0ms

Counts
4 → 10
Calls
4 calls:
216.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0)))
143.0ms
(* (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (/ (cbrt 1) (cbrt 3.0)))
0.0ms
(/ (cbrt 1) (cbrt 3.0))
349.0ms
(sqrt (* (/ (+ (+ (* x x) (* y y)) (* z z)) (* (cbrt 3.0) (cbrt 3.0))) (/ (cbrt 1) (cbrt 3.0))))

simplify106.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
07052528
142162299
250012226

prune632.0ms

Filtered
192 candidates to 149 candidates (77.6%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 17.6b

localize4.0ms

Local error

Found 1 expressions with local error:

0.2b
(* x (sqrt 0.3333333333333333))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×associate-*r*
4×add-cube-cbrt *-un-lft-identity sqrt-prod
3×pow1 add-exp-log associate-*l* add-cbrt-cube
2×unswap-sqr
1×pow-prod-down prod-exp *-commutative cbrt-unprod add-log-exp
Counts
1 → 22
Calls
1 calls:
4.0ms
(* x (sqrt 0.3333333333333333))

series46.0ms

Counts
1 → 3
Calls
1 calls:
46.0ms
(* x (sqrt 0.3333333333333333))

simplify57.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
06984
124580
256978
389378
4200178
5500178

prune38.0ms

Filtered
25 candidates to 14 candidates (56.0%)
Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 17.6b

regimes392.0ms

Accuracy

62% (7.4b remaining)

Error of 25.7b against oracle of 18.3b and baseline of 37.9b

bsearch74.0ms

Steps
ItersRangePoint
10
7.491092794297452e+92
6.705329414328681e+109
6.601942283666501e+109
6
-1.6055413863283287e+120
-1.9275148810805934e+119
-4.241172532402712e+119

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03717
14317
24817
34817

end0.0ms

sample459.0ms

Algorithm
intervals
Results
290.0ms8000×body80valid