Details

Time bar (total: 6.5s)

sample41.0ms

Algorithm
intervals
Results
30.0ms256×body80valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0167
1277
2337
3347
4347

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.4b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×sqrt-prod
8×add-log-exp
5×add-exp-log add-cbrt-cube
4×pow1
3×expm1-log1p-u fma-def associate-/r* sum-log log1p-expm1-u associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative associate-+l+ frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
3 → 76
Calls
3 calls:
18.0ms
(+ (+ (* x x) (* y y)) (* z z))
31.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
16.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series290.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(+ (+ (* x x) (* y y)) (* z z))
58.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
189.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify149.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (135.0ms)

IterNodesCost
0272784
11063695
24582674
35001673

prune304.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
34.3b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.3b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.4b
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
532×times-frac
424×sqrt-prod
295×add-sqr-sqrt
274×add-cube-cbrt *-un-lft-identity
33×sqrt-div
28×associate-/r/
24×associate-/r*
16×flip3-+ flip-+
15×div-inv
9×add-exp-log rem-sqrt-square add-cbrt-cube
7×pow1
6×associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv sqrt-pow1 pow1/2 div-exp
2×hypot-def associate-/l/
1×frac-2neg clear-num
Counts
4 → 397
Calls
4 calls:
46.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
16.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
19.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
51.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

series487.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
116.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
114.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
194.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

simplify184.0ms

Algorithm
egg-herbie
Counts
409 → 409
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
086711029
1365210187
250019908

prune950.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
28.2b
(sqrt (+ (* x x) (* y y)))
34.3b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.4b
(sqrt (/ (hypot (sqrt (+ (* x x) (* y y))) z) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
275×times-frac
159×add-sqr-sqrt
147×add-cube-cbrt *-un-lft-identity sqrt-prod
24×associate-/r*
19×sqrt-div
16×associate-/r/
9×add-exp-log flip3-+ add-cbrt-cube flip-+ div-inv
7×pow1
6×rem-sqrt-square
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv sqrt-pow1 pow1/2 div-exp associate-/l*
2×hypot-def
1×frac-2neg clear-num
Counts
4 → 245
Calls
4 calls:
28.0ms
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
4.0ms
(sqrt (+ (* x x) (* y y)))
15.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
30.0ms
(sqrt (/ (hypot (sqrt (+ (* x x) (* y y))) z) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

series974.0ms

Counts
4 → 12
Calls
4 calls:
227.0ms
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
41.0ms
(sqrt (+ (* x x) (* y y)))
117.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
588.0ms
(sqrt (/ (hypot (sqrt (+ (* x x) (* y y))) z) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

simplify143.0ms

Algorithm
egg-herbie
Counts
257 → 257
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
08215881
131215273
250014899

prune901.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(hypot x y)
0.3b
(* (sqrt (/ 1 3.0)) (hypot z (hypot x y)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×associate-*l* sqrt-prod
12×*-un-lft-identity
11×add-cube-cbrt times-frac
4×pow1 add-exp-log add-cbrt-cube unswap-sqr
3×associate-*r*
2×expm1-log1p-u hypot-udef log1p-expm1-u add-log-exp
1×sqrt-unprod sqrt-div pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod div-inv
Counts
2 → 48
Calls
2 calls:
0.0ms
(hypot x y)
12.0ms
(* (sqrt (/ 1 3.0)) (hypot z (hypot x y)))

series316.0ms

Counts
2 → 6
Calls
2 calls:
51.0ms
(hypot x y)
264.0ms
(* (sqrt (/ 1 3.0)) (hypot z (hypot x y)))

simplify115.0ms

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 3 (32.0ms)

IterNodesCost
0157308
1396290
2899283
31444280
43063280
55001280

prune166.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes47.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1135

end0.0ms

sample1.1s

Algorithm
intervals
Results
858.0ms8000×body80valid