Details

Time bar (total: 3.4s)

sample20.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1227
2247
3247

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 37.7b

Counts
2 → 1

localize10.0ms

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)
35.0b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite25.0ms

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:
4.0ms
(+ (* x x) (* y y))
6.0ms
(+ (+ (* x x) (* y y)) (* z z))
8.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
5.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series458.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (* x x) (* y y))
217.0ms
(+ (+ (* x x) (* y y)) (* z z))
50.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
165.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify41.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0325828
11345761
25001755

prune230.0ms

Filtered
90 candidates to 71 candidates (78.9%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New85590
Fresh000
Picked011
Done000
Total85691

Merged error: 20.7b

Counts
91 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.0b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
11×add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube associate-/l*
5×pow1
4×flip3-+ sqrt-div sum-log flip-+
2×+-commutative associate-/l/
1×cbrt-undiv rem-sqrt-square associate-+l+ sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 102
Calls
4 calls:
4.0ms
(+ (* x x) (* y y))
6.0ms
(+ (+ (* x x) (* y y)) (* z z))
9.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* x x) (* y y))
36.0ms
(+ (+ (* x x) (* y y)) (* z z))
235.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
104.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify50.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03301316
113381241
250021218

prune224.0ms

Filtered
114 candidates to 72 candidates (63.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1113114
Fresh044
Picked011
Done011
Total1119120

Merged error: 20.6b

Counts
120 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
35.1b
(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
9×pow1
8×add-sqr-sqrt
6×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×flip3-+ associate-*r/ sum-log flip-+
3×associate-*r* associate-*l*
2×+-commutative sqrt-pow1 sqrt-div pow-prod-down
1×distribute-rgt-in associate-+l+ distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
4 → 59
Calls
4 calls:
4.0ms
(+ (* x x) (* y y))
6.0ms
(+ (+ (* x x) (* y y)) (* z z))
8.0ms
(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
10.0ms
(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series292.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (* x x) (* y y))
44.0ms
(+ (+ (* x x) (* y y)) (* z z))
49.0ms
(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
171.0ms
(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify49.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0310541
11615492
25001492

prune149.0ms

Filtered
71 candidates to 50 candidates (70.4%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New71071
Fresh066
Picked011
Done022
Total71980

Merged error: 20.6b

Counts
80 → 9

localize3.0ms

Local error

Found 1 expressions with local error:

0.4b
(/ x (sqrt 3.0))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
18×times-frac
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×sqrt-prod
6×associate-/r*
3×add-exp-log add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv frac-2neg div-exp clear-num div-inv add-log-exp
Counts
1 → 39
Calls
1 calls:
4.0ms
(/ x (sqrt 3.0))

series60.0ms

Counts
1 → 3
Calls
1 calls:
60.0ms
(/ x (sqrt 3.0))

simplify58.0ms

Algorithm
egg-herbie
Counts
42 → 42
Iterations

Useful iterations: 4 (54.0ms)

IterNodesCost
0103217
1273207
2729197
32027197
45001196

prune60.0ms

Filtered
42 candidates to 26 candidates (61.9%)
Pruning

16 alts after pruning (12 fresh and 4 done)

PrunedKeptTotal
New35742
Fresh055
Picked011
Done033
Total351651

Merged error: 20.6b

Counts
51 → 16

regimes646.0ms

Accuracy

62.5% (7.5b remaining)

Error of 25.4b against oracle of 17.9b and baseline of 37.8b

bsearch54.0ms

Steps
ItersRangePoint
6
2.842128016850388e+109
1.3565839810964883e+110
1.316205855455904e+110
7
-4.710268451496385e+120
-2.2813421540518005e+119
-4.665779699475443e+120

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02912
13512
23512

end0.0ms

sample435.0ms

Algorithm
intervals
Results
275.0ms8000×body80valid