Details

Time bar (total: 2.6s)

sample18.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0136
1206
2226
3226

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: 37.0b

Counts
2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(+ (* x x) (* y y))
34.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
5×add-sqr-sqrt
4×pow1 add-cube-cbrt *-un-lft-identity sum-log
3×add-exp-log flip3-+ sqrt-prod add-cbrt-cube flip-+
2×+-commutative sqrt-div
1×rem-sqrt-square associate-+l+ sqrt-pow1 pow1/2
Counts
3 → 39
Calls
3 calls:
6.0ms
(+ (+ (* x x) (* y y)) (* z z))
4.0ms
(+ (* x x) (* y y))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series161.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(+ (+ (* x x) (* y y)) (* z z))
28.0ms
(+ (* x x) (* y y))
97.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify89.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0209340
1959320
23316316
35001315

prune103.0ms

Filtered
48 candidates to 37 candidates (77.1%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New43548
Fresh000
Picked011
Done000
Total43649

Merged error: 18.2b

Counts
49 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.5b
(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
34.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
18×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-down pow-sqr
4×frac-times
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 124
Calls
4 calls:
4.0ms
(+ (* x x) (* y y))
17.0ms
(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (* x x) (* y y))
95.0ms
(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
95.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
100.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify49.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
02941310
112881219
250021188

prune214.0ms

Filtered
136 candidates to 71 candidates (52.2%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1360136
Fresh044
Picked011
Done011
Total1366142

Merged error: 18.2b

Counts
142 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

4.5b
(- (* x x) (* y y))
8.2b
(+ (* (- (pow y 3)) y) (pow x 4))
34.4b
(sqrt (+ (/ (+ (* (- (pow y 3)) y) (pow x 4)) (- (* x x) (* y y))) (* z z)))
43.4b
(/ (+ (* (- (pow y 3)) y) (pow x 4)) (- (* x x) (* y y)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
12×times-frac
8×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 difference-of-squares
4×associate-/r*
3×flip3-+ sqrt-prod flip-+ associate-/l*
2×flip3-- sqrt-div associate-/r/ flip-- associate-/l/
1×cbrt-undiv +-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-exp clear-num sum-log div-inv
Counts
4 → 74
Calls
4 calls:
3.0ms
(- (* x x) (* y y))
7.0ms
(+ (* (- (pow y 3)) y) (pow x 4))
14.0ms
(sqrt (+ (/ (+ (* (- (pow y 3)) y) (pow x 4)) (- (* x x) (* y y))) (* z z)))
12.0ms
(/ (+ (* (- (pow y 3)) y) (pow x 4)) (- (* x x) (* y y)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(- (* x x) (* y y))
48.0ms
(+ (* (- (pow y 3)) y) (pow x 4))
164.0ms
(sqrt (+ (/ (+ (* (- (pow y 3)) y) (pow x 4)) (- (* x x) (* y y))) (* z z)))
69.0ms
(/ (+ (* (- (pow y 3)) y) (pow x 4)) (- (* x x) (* y y)))

simplify51.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0353967
11580858
25001838

prune237.0ms

Filtered
86 candidates to 69 candidates (80.2%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New84286
Fresh033
Picked011
Done022
Total84892

Merged error: 7.6b

Counts
92 → 8

localize1.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New000
Fresh044
Picked011
Done033
Total088

Merged error: 7.6b

Counts
8 → 8

regimes394.0ms

Accuracy

40% (18.8b remaining)

Error of 25.4b against oracle of 6.6b and baseline of 37.9b

bsearch42.0ms

Steps
ItersRangePoint
5
1.5751293102757547e+115
3.2847437481319114e+115
2.9887864209975186e+115
7
-4.866704026213251e+114
-2.1959671689766027e+112
-4.1883907689960167e+114

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0217
1217

end0.0ms

sample469.0ms

Algorithm
intervals
Results
310.0ms8000×body80valid