Details

Time bar (total: 5.7s)

sample18.0ms

Algorithm
intervals
Results
8.0ms282×body80valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0215
1375
2615
3915
41155
51215
61215

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.0b

localize7.0ms

Local error

Found 2 expressions with local error:

2.9b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.3b
(* y (+ 1.0 (* z z)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
4×pow1 associate-*r/
3×associate-*r* associate-*l* prod-exp cbrt-unprod div-inv
2×flip3-+ associate-/r/ flip-+ add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* *-commutative associate-/l/ unswap-sqr
Counts
2 → 70
Calls
2 calls:
10.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
7.0ms
(* y (+ 1.0 (* z z)))

series107.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
50.0ms
(* y (+ 1.0 (* z z)))

simplify49.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0409511
11963443
25001443

prune158.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize9.0ms

Local error

Found 2 expressions with local error:

2.9b
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
3.8b
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
299×times-frac
199×add-sqr-sqrt
152×add-cube-cbrt *-un-lft-identity
79×sqrt-prod
72×associate-*r*
28×add-exp-log add-cbrt-cube
22×associate-*l* associate-/l*
12×cbrt-undiv div-exp unswap-sqr
10×div-inv
6×prod-exp cbrt-unprod
4×pow1 associate-/r/
3×associate-/r*
2×flip3-+ flip-+ add-log-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
2 → 238
Calls
2 calls:
57.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
11.0ms
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

series269.0ms

Counts
2 → 6
Calls
2 calls:
161.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))
108.0ms
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))

simplify49.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
011122815
150012605

prune598.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (fabs (cbrt 1.0)) (sqrt (+ 1.0 (* z z)))) (/ (/ (sqrt (cbrt 1.0)) x) (sqrt (+ 1.0 (* z z)))))
2.9b
(* (/ (sqrt 1.0) y) (* (/ (fabs (cbrt 1.0)) (sqrt (+ 1.0 (* z z)))) (/ (/ (sqrt (cbrt 1.0)) x) (sqrt (+ 1.0 (* z z))))))
15.0b
(sqrt (+ 1.0 (* z z)))
15.0b
(sqrt (+ 1.0 (* z z)))

rewrite242.0ms

Algorithm
rewrite-expression-head
Rules
444×times-frac
325×add-sqr-sqrt
258×sqrt-prod
209×add-cube-cbrt *-un-lft-identity
193×associate-*r*
90×add-exp-log add-cbrt-cube
60×cbrt-prod
46×associate-*l*
34×cbrt-undiv div-exp
32×prod-exp cbrt-unprod
27×unswap-sqr
13×pow1
9×div-inv
8×sqrt-div
6×frac-times associate-*r/
4×flip3-+ pow-prod-down associate-*l/ associate-/r/ flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative
Counts
4 → 365
Calls
4 calls:
125.0ms
(* (/ (fabs (cbrt 1.0)) (sqrt (+ 1.0 (* z z)))) (/ (/ (sqrt (cbrt 1.0)) x) (sqrt (+ 1.0 (* z z)))))
83.0ms
(* (/ (sqrt 1.0) y) (* (/ (fabs (cbrt 1.0)) (sqrt (+ 1.0 (* z z)))) (/ (/ (sqrt (cbrt 1.0)) x) (sqrt (+ 1.0 (* z z))))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series766.0ms

Counts
4 → 12
Calls
4 calls:
246.0ms
(* (/ (fabs (cbrt 1.0)) (sqrt (+ 1.0 (* z z)))) (/ (/ (sqrt (cbrt 1.0)) x) (sqrt (+ 1.0 (* z z)))))
428.0ms
(* (/ (sqrt 1.0) y) (* (/ (fabs (cbrt 1.0)) (sqrt (+ 1.0 (* z z)))) (/ (/ (sqrt (cbrt 1.0)) x) (sqrt (+ 1.0 (* z z))))))
41.0ms
(sqrt (+ 1.0 (* z z)))
51.0ms
(sqrt (+ 1.0 (* z z)))

simplify95.0ms

Algorithm
egg-herbie
Counts
377 → 377
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
020596907
150016219

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

localize21.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (/ (sqrt 1.0) y) (* (sqrt (/ (fabs (cbrt 1.0)) (sqrt (+ 1.0 (* z z))))) (* (sqrt (/ (fabs (cbrt 1.0)) (sqrt (+ 1.0 (* z z))))) (/ (/ (sqrt (cbrt 1.0)) x) (sqrt (+ 1.0 (* z z)))))))
15.0b
(sqrt (+ 1.0 (* z z)))
15.0b
(sqrt (+ 1.0 (* z z)))
15.0b
(sqrt (+ 1.0 (* z z)))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log add-cbrt-cube
24×prod-exp cbrt-unprod
23×add-sqr-sqrt
22×sqrt-div associate-*l*
20×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
17×frac-times associate-*r/
16×pow1
11×cbrt-undiv div-exp
7×associate-*l/
6×pow-prod-down
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×associate-*r* *-commutative div-inv
Counts
4 → 114
Calls
4 calls:
249.0ms
(* (/ (sqrt 1.0) y) (* (sqrt (/ (fabs (cbrt 1.0)) (sqrt (+ 1.0 (* z z))))) (* (sqrt (/ (fabs (cbrt 1.0)) (sqrt (+ 1.0 (* z z))))) (/ (/ (sqrt (cbrt 1.0)) x) (sqrt (+ 1.0 (* z z)))))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series550.0ms

Counts
4 → 12
Calls
4 calls:
420.0ms
(* (/ (sqrt 1.0) y) (* (sqrt (/ (fabs (cbrt 1.0)) (sqrt (+ 1.0 (* z z))))) (* (sqrt (/ (fabs (cbrt 1.0)) (sqrt (+ 1.0 (* z z))))) (/ (/ (sqrt (cbrt 1.0)) x) (sqrt (+ 1.0 (* z z)))))))
42.0ms
(sqrt (+ 1.0 (* z z)))
45.0ms
(sqrt (+ 1.0 (* z z)))
42.0ms
(sqrt (+ 1.0 (* z z)))

simplify83.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07222220
134941666
250011666

prune483.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.8b

regimes217.0ms

Accuracy

0% (1.4b remaining)

Error of 6.0b against oracle of 4.6b and baseline of 6.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02017
12017

end0.0ms

sample450.0ms

Algorithm
intervals
Results
259.0ms8608×body80valid