Details

Time bar (total: 3.8s)

sample18.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0167
1277
2337
3347
4347

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.8b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×times-frac
17×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
4×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×expm1-log1p-u rem-sqrt-square log1p-expm1-u div-inv associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg sqrt-pow1 flip3-+ pow1/2 sqrt-div div-exp clear-num flip-+
Counts
2 → 58
Calls
2 calls:
33.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
14.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series246.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
185.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify125.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0223655
1877586
23651577
35001577

prune225.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
34.8b
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×associate-*r*
11×add-exp-log *-un-lft-identity times-frac
10×add-cube-cbrt
7×pow1 add-cbrt-cube
6×sqrt-div
4×frac-times flip3-+ associate-*l/ prod-exp flip-+
3×associate-*l* unswap-sqr
2×expm1-log1p-u sqrt-pow1 associate-*r/ div-exp pow-prod-down un-div-inv cbrt-unprod log1p-expm1-u add-log-exp
1×cbrt-undiv rec-exp pow1/2 1-exp sqrt-prod *-commutative div-inv
Counts
2 → 61
Calls
2 calls:
42.0ms
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
11.0ms
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

series246.0ms

Counts
2 → 6
Calls
2 calls:
56.0ms
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
190.0ms
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

simplify63.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0326655
11771554
25003542

prune201.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 19.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
34.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.8b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
49×sqrt-prod
38×add-sqr-sqrt
36×times-frac
34×add-cube-cbrt *-un-lft-identity
14×pow1
9×sqrt-div
8×sqrt-pow1
6×add-exp-log associate-/r* add-cbrt-cube associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square flip3-+ pow1/2 flip-+
2×hypot-def associate-/l/
1×cbrt-undiv pow2 frac-times sqrt-undiv frac-2neg pow-plus associate-*r/ div-exp pow-prod-down associate-*l/ clear-num pow-sqr pow-prod-up div-inv
Counts
4 → 122
Calls
4 calls:
23.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
14.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
14.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
23.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

series742.0ms

Counts
4 → 12
Calls
4 calls:
252.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
112.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
114.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
263.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))))

simplify120.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
02481565
17621485
237731460
350011460

prune409.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 19.4b

localize5.0ms

Local error

Found 1 expressions with local error:

0.2b
(* x (sqrt 0.3333333333333333))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×associate-*r*
4×add-cube-cbrt *-un-lft-identity sqrt-prod
3×pow1 add-exp-log associate-*l* add-cbrt-cube
2×unswap-sqr
1×expm1-log1p-u pow-prod-down prod-exp *-commutative cbrt-unprod log1p-expm1-u add-log-exp
Counts
1 → 24
Calls
1 calls:
5.0ms
(* x (sqrt 0.3333333333333333))

series50.0ms

Counts
1 → 3
Calls
1 calls:
50.0ms
(* x (sqrt 0.3333333333333333))

simplify87.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
07190
124786
257184
389584
4201284
5500184

prune50.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 19.4b

regimes476.0ms

Accuracy

63.1% (7.1b remaining)

Error of 25.3b against oracle of 18.2b and baseline of 37.5b

bsearch85.0ms

Steps
ItersRangePoint
7
2.1107569983319055e+123
3.822258813287361e+125
1.960163308790063e+125
9
-4.343385320743243e+112
-5.8247123831858766e+107
-1.5642124103045844e+110

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03213
13813
23813

end0.0ms

sample435.0ms

Algorithm
intervals
Results
272.0ms8000×body80valid