Details

Time bar (total: 11.0s)

sample17.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0167
1277
2337
3347
4347

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: 38.2b

Counts
2 → 1

localize44.0ms

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)
35.5b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
379×*-un-lft-identity
190×distribute-lft-out
128×associate-*l*
85×times-frac
54×add-sqr-sqrt
49×add-cube-cbrt
46×sqrt-prod
34×swap-sqr
28×associate-/l*
23×fma-def
22×sqrt-div
11×add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-+ sum-log flip-+ log1p-expm1-u associate-/l/
3×+-commutative associate-*r*
2×rem-sqrt-square associate-+l+ frac-2neg clear-num div-inv
1×cbrt-undiv sqrt-pow1 pow1/2 div-exp *-commutative unswap-sqr
Counts
4 → 224
Calls
4 calls:
16.0ms
(+ (* x x) (* y y))
28.0ms
(+ (+ (* x x) (* y y)) (* z z))
30.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
32.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series298.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ (* x x) (* y y))
38.0ms
(+ (+ (* x x) (* y y)) (* z z))
56.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
173.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify61.0ms

Algorithm
egg-herbie
Counts
236 → 236
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03711795
114701596
250011567

prune302.0ms

Filtered
236 candidates to 110 candidates (46.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2306236
Fresh000
Picked101
Done000
Total2316237

Merged error: 19.6b

Counts
237 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
35.5b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.5b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.5b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
4946×*-un-lft-identity
2529×sqrt-prod
2420×distribute-lft-out
2312×associate-*l*
2014×add-sqr-sqrt
1615×sqrt-div
1372×frac-times
1361×associate-/l*
1187×cbrt-prod
1089×associate-/r*
995×times-frac
831×add-cube-cbrt
681×swap-sqr
456×unswap-sqr
382×associate-*r*
160×associate-/l/
98×rem-sqrt-square
82×flip3-+ flip-+
81×clear-num
80×frac-2neg
69×*-commutative
49×associate-*l/
28×associate-*r/
10×hypot-def
9×pow1
7×add-cbrt-cube
6×add-exp-log
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×pow1/2 div-inv
2×cbrt-undiv un-div-inv
1×div-exp pow-prod-down
Counts
4 → 2436
Calls
4 calls:
31.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
29.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
27.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
724.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

series802.0ms

Counts
4 → 12
Calls
4 calls:
233.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
109.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
106.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
354.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

simplify643.0ms

Algorithm
egg-herbie
Counts
2448 → 2448
Iterations

Useful iterations: 1 (101.0ms)

IterNodesCost
0457863150
1500162632

prune2.1s

Filtered
2448 candidates to 529 candidates (21.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New244622448
Fresh145
Picked101
Done000
Total244862454

Merged error: 19.6b

Counts
2454 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.3b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (* (- (* (cbrt 3.0) (cbrt 3.0))) (- (cbrt 3.0)))))
35.5b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite376.0ms

Algorithm
rewrite-expression-head
Rules
3595×*-un-lft-identity
2630×sqrt-prod
2389×associate-*l*
1730×distribute-lft-out
1411×times-frac
984×add-sqr-sqrt
684×cbrt-prod
647×add-cube-cbrt
594×distribute-lft-neg-in distribute-rgt-neg-in
507×associate-*r*
482×swap-sqr
164×unswap-sqr
83×associate-/r*
56×*-commutative
36×neg-mul-1
23×fma-def
17×associate-/l*
11×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 hypot-def
4×expm1-log1p-u flip3-+ sqrt-div sum-log flip-+ log1p-expm1-u
3×+-commutative
2×associate-+l+ associate-/l/
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 1629
Calls
4 calls:
16.0ms
(+ (* x x) (* y y))
25.0ms
(+ (+ (* x x) (* y y)) (* z z))
89.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (* (- (* (cbrt 3.0) (cbrt 3.0))) (- (cbrt 3.0)))))
26.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series514.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (* x x) (* y y))
37.0ms
(+ (+ (* x x) (* y y)) (* z z))
343.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (* (- (* (cbrt 3.0) (cbrt 3.0))) (- (cbrt 3.0)))))
107.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify409.0ms

Algorithm
egg-herbie
Counts
1641 → 1641
Iterations

Useful iterations: 2 (129.0ms)

IterNodesCost
0148735319
1467933626
2500133622

prune1.4s

Filtered
1641 candidates to 385 candidates (23.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New163741641
Fresh055
Picked101
Done000
Total163891647

Merged error: 14.0b

Counts
1647 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (sqrt (+ (* x x) (* y y))) z)
0.0b
(+ (* x x) (* y y))
0.3b
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt (* (- (* (cbrt 3.0) (cbrt 3.0))) (- (cbrt 3.0)))))
29.7b
(sqrt (+ (* x x) (* y y)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
328×sqrt-prod
323×add-sqr-sqrt
291×associate-*l*
249×times-frac
222×*-un-lft-identity
198×add-cube-cbrt
152×cbrt-prod
132×distribute-lft-neg-in distribute-rgt-neg-in
115×associate-*r*
83×associate-/r*
65×swap-sqr
47×unswap-sqr
26×hypot-def
23×*-commutative
15×fma-def
10×distribute-lft-out
8×neg-mul-1
6×add-exp-log add-cbrt-cube add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×associate-/l*
2×+-commutative hypot-udef flip3-+ sqrt-div flip-+
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
4 → 441
Calls
4 calls:
1.0ms
(hypot (sqrt (+ (* x x) (* y y))) z)
16.0ms
(+ (* x x) (* y y))
41.0ms
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt (* (- (* (cbrt 3.0) (cbrt 3.0))) (- (cbrt 3.0)))))
17.0ms
(sqrt (+ (* x x) (* y y)))

series569.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(hypot (sqrt (+ (* x x) (* y y))) z)
27.0ms
(+ (* x x) (* y y))
338.0ms
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt (* (- (* (cbrt 3.0) (cbrt 3.0))) (- (cbrt 3.0)))))
36.0ms
(sqrt (+ (* x x) (* y y)))

simplify176.0ms

Algorithm
egg-herbie
Counts
453 → 453
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
011528227
139267934
250027768

prune1.0s

Filtered
453 candidates to 287 candidates (63.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4485453
Fresh538
Picked101
Done000
Total4548462

Merged error: 0.1b

Counts
462 → 8

regimes302.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02011
13011
23911
35711
46711
56711

end0.0ms

sample419.0ms

Algorithm
intervals
Results
260.0ms8000×body80valid