Details

Time bar (total: 3.8s)

sample19.0ms

Algorithm
intervals
Results
9.0ms256×body80valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0167
1277
2337
3347
4347

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.4b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite63.0ms

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:
3.0ms
(+ (* x x) (* y y))
13.0ms
(+ (+ (* x x) (* y y)) (* z z))
29.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
16.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series323.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (* x x) (* y y))
41.0ms
(+ (+ (* x x) (* y y)) (* z z))
60.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
186.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify55.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0345852
11445759
25001739

prune339.0ms

Filtered
102 candidates to 84 candidates (82.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
35.4b
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×*-un-lft-identity
13×add-exp-log add-cube-cbrt associate-*r*
11×times-frac add-log-exp
9×pow1 add-cbrt-cube
6×flip3-+ sqrt-div flip-+
4×expm1-log1p-u frac-times fma-def associate-*l/ prod-exp sum-log log1p-expm1-u
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 → 93
Calls
4 calls:
3.0ms
(+ (* x x) (* y y))
13.0ms
(+ (+ (* x x) (* y y)) (* z z))
39.0ms
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
11.0ms
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

series322.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (* x x) (* y y))
41.0ms
(+ (+ (* x x) (* y y)) (* z z))
62.0ms
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
185.0ms
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

simplify72.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
0427847
12248724
25001708

prune296.0ms

Filtered
105 candidates to 79 candidates (75.2%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.5b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y y (* z z))
0.1b
(* (fma x x (fma y y (* z z))) (/ (sqrt 1) 3.0))
35.4b
(sqrt (* (fma x x (fma y y (* z z))) (/ (sqrt 1) 3.0)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
22×associate-*r*
21×times-frac
18×*-un-lft-identity
17×add-cube-cbrt
12×sqrt-prod
8×pow1 add-exp-log add-cbrt-cube
4×unswap-sqr
3×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
2×sqrt-pow1 associate-*r/ pow-prod-down prod-exp cbrt-unprod
1×cbrt-undiv pow1/2 sqrt-div div-exp *-commutative fma-udef div-inv
Counts
3 → 69
Calls
3 calls:
0.0ms
(fma y y (* z z))
11.0ms
(* (fma x x (fma y y (* z z))) (/ (sqrt 1) 3.0))
5.0ms
(sqrt (* (fma x x (fma y y (* z z))) (/ (sqrt 1) 3.0)))

series315.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(fma y y (* z z))
72.0ms
(* (fma x x (fma y y (* z z))) (/ (sqrt 1) 3.0))
204.0ms
(sqrt (* (fma x x (fma y y (* z z))) (/ (sqrt 1) 3.0)))

simplify66.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0274570
11243513
25003448

prune231.0ms

Filtered
78 candidates to 54 candidates (69.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y y (* z z))
0.4b
(/ (sqrt (fma x x (fma y y (* z z)))) (sqrt 3.0))
35.3b
(sqrt (fma x x (fma y y (* z z))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
33×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
5×add-exp-log add-cbrt-cube
4×pow1
3×expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num fma-udef div-inv
Counts
3 → 88
Calls
3 calls:
0.0ms
(fma y y (* z z))
4.0ms
(/ (sqrt (fma x x (fma y y (* z z)))) (sqrt 3.0))
1.0ms
(sqrt (fma x x (fma y y (* z z))))

series432.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(fma y y (* z z))
266.0ms
(/ (sqrt (fma x x (fma y y (* z z)))) (sqrt 3.0))
127.0ms
(sqrt (fma x x (fma y y (* z z))))

simplify74.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0175889
1498836
22320813
35001813

prune248.0ms

Filtered
97 candidates to 61 candidates (62.9%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 18.4b

regimes190.0ms

Accuracy

64.3% (7.0b remaining)

Error of 25.6b against oracle of 18.6b and baseline of 38.2b

bsearch97.0ms

Steps
ItersRangePoint
9
1.8130882697008765e+84
7.489722728138725e+90
7.402306065731599e+90
10
-1.041760357593436e+169
-4.358594791243697e+152
-4.904012598659074e+153

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03112
13712
23712

end0.0ms

sample448.0ms

Algorithm
intervals
Results
281.0ms8000×body80valid