Details

Time bar (total: 4.9s)

sample18.0ms

Algorithm
intervals
Results
9.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1227
2247
3247

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1
3×associate-/r* associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num sum-log
Counts
3 → 65
Calls
3 calls:
3.0ms
(+ (* x x) (* y y))
30.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
14.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series241.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* x x) (* y y))
51.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
164.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify126.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (118.0ms)

IterNodesCost
0294707
11224644
24405642
35001640

prune221.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
34.4b
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
7×pow1
6×add-sqr-sqrt associate-*r*
5×distribute-lft-out
4×add-exp-log add-cube-cbrt associate-*r/ add-cbrt-cube
3×unpow-prod-down associate-*l*
2×sqrt-pow1 flip3-+ sqrt-div pow-prod-down flip-+ add-log-exp
1×distribute-rgt-in distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
2 → 38
Calls
2 calls:
111.0ms
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
31.0ms
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

series219.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2))))
167.0ms
(sqrt (* 0.3333333333333333 (+ (pow x 2) (+ (pow y 2) (pow z 2)))))

simplify38.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0211340
11120308
25002307

prune115.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 19.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
34.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.4b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt times-frac
34×add-cube-cbrt *-un-lft-identity
28×sqrt-prod
21×cbrt-prod
9×pow1 sqrt-div
6×add-exp-log associate-/r* associate-/l*
5×add-cbrt-cube
4×sqrt-pow1 add-log-exp
3×flip3-+ pow1/2 flip-+
2×rem-sqrt-square associate-/l/
1×cbrt-undiv frac-times frac-2neg associate-*r/ div-exp pow-prod-down associate-*l/ clear-num div-inv
Counts
4 → 106
Calls
4 calls:
23.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
15.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
28.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

series733.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
97.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
98.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
319.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

simplify63.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
02481526
16521452
220151426
350021411

prune325.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 19.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
0.2b
(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
1.0b
(/ 1 (sqrt 3.0))
34.4b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
170×sqrt-prod
148×add-sqr-sqrt
120×times-frac
83×*-un-lft-identity
75×add-cube-cbrt
25×associate-*r* associate-*l*
24×unswap-sqr
12×add-exp-log associate-/r*
11×pow1
10×add-cbrt-cube
6×associate-/l*
5×sqrt-div div-inv
4×sqrt-pow1 pow1/2 add-log-exp
3×rem-sqrt-square pow-flip div-exp pow-prod-down
2×cbrt-undiv frac-2neg clear-num associate-/l/
1×frac-times rec-exp flip3-+ sqrt-unprod 1-exp associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod flip-+ inv-pow
Counts
4 → 212
Calls
4 calls:
30.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
61.0ms
(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
3.0ms
(/ 1 (sqrt 3.0))
16.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

series674.0ms

Counts
4 → 10
Calls
4 calls:
123.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
214.0ms
(* (sqrt (/ 1 (sqrt 3.0))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))))
0.0ms
(/ 1 (sqrt 3.0))
337.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)))

simplify62.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04522923
119282734
250012688

prune483.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 18.9b

regimes559.0ms

Accuracy

63% (7.2b remaining)

Error of 25.9b against oracle of 18.7b and baseline of 38.1b

bsearch86.0ms

Steps
ItersRangePoint
7
2.8540072411378333e+150
6.799686113877851e+152
7.792733426685086e+150
10
-2.036247561034917e+138
-1.3682670211914512e+128
-1.895586491161729e+137

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02912
13512
23512

end0.0ms

sample460.0ms

Algorithm
intervals
Results
282.0ms8000×body80valid