Details

Time bar (total: 3.8s)

sample18.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify9.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(+ (* x x) (* y y))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.9b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite68.0ms

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:
16.0ms
(+ (+ (* x x) (* y y)) (* z z))
3.0ms
(+ (* x x) (* y y))
31.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
16.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series466.0ms

Counts
4 → 12
Calls
4 calls:
230.0ms
(+ (+ (* x x) (* y y)) (* z z))
26.0ms
(+ (* x x) (* y y))
48.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
162.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify43.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0345852
11445759
25001739

prune292.0ms

Filtered
102 candidates to 84 candidates (82.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(+ (* x x) (* y y))
0.2b
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
35.9b
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

rewrite73.0ms

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:
13.0ms
(+ (+ (* x x) (* y y)) (* z z))
3.0ms
(+ (* x x) (* y y))
42.0ms
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
12.0ms
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

series282.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ (+ (* x x) (* y y)) (* z z))
31.0ms
(+ (* x x) (* y y))
51.0ms
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
164.0ms
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

simplify60.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0427847
12248724
25001708

prune273.0ms

Filtered
105 candidates to 79 candidates (75.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 17.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.0b
(+ (* x x) (* y y))
0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.8b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×add-sqr-sqrt times-frac
34×add-cube-cbrt *-un-lft-identity
11×add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube associate-/l*
5×pow1
4×expm1-log1p-u fma-def flip3-+ sqrt-div sum-log flip-+ log1p-expm1-u
2×+-commutative associate-/l/
1×cbrt-undiv rem-sqrt-square associate-+l+ sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
Counts
4 → 115
Calls
4 calls:
13.0ms
(+ (+ (* x x) (* y y)) (* z z))
3.0ms
(+ (* x x) (* y y))
24.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
15.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series387.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(+ (+ (* x x) (* y y)) (* z z))
32.0ms
(+ (* x x) (* y y))
219.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
100.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify47.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03481349
114261262
250021230

prune298.0ms

Filtered
127 candidates to 86 candidates (67.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.4b
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
28.4b
(sqrt (+ (* x x) (* y y)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
18×times-frac
15×sqrt-prod
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1
3×expm1-log1p-u log1p-expm1-u associate-/l*
2×flip3-+ sqrt-div flip-+
1×cbrt-undiv +-commutative rem-sqrt-square sqrt-undiv hypot-udef fma-def frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log hypot-def div-inv
Counts
3 → 74
Calls
3 calls:
3.0ms
(+ (* x x) (* y y))
3.0ms
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
4.0ms
(sqrt (+ (* x x) (* y y)))

series343.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* x x) (* y y))
278.0ms
(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
38.0ms
(sqrt (+ (* x x) (* y y)))

simplify89.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
0249728
1912678
23040660
35002659

prune206.0ms

Filtered
83 candidates to 62 candidates (74.7%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes322.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
084

end0.0ms

sample425.0ms

Algorithm
intervals
Results
261.0ms8000×body80valid