Details

Time bar (total: 10.4s)

sample19.0ms

Algorithm
intervals
Results
8.0ms273×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

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.8b

localize7.0ms

Local error

Found 2 expressions with local error:

3.0b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.5b
(* y (+ 1.0 (* z z)))

rewrite16.0ms

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:
7.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
7.0ms
(* y (+ 1.0 (* z z)))

series106.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
53.0ms
(* y (+ 1.0 (* z z)))

simplify48.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0409511
11963443
25001443

prune165.0ms

Filtered
76 candidates to 56 candidates (73.7%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ 1.0 y) x)
5.3b
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
468×times-frac
228×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
56×associate-/l*
22×div-inv
16×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×associate-/r*
2×pow1 frac-2neg clear-num associate-/r/ associate-/l/ add-log-exp
1×flip3-+ flip-+
Counts
2 → 264
Calls
2 calls:
5.0ms
(/ (/ 1.0 y) x)
16.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series76.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(/ (/ 1.0 y) x)
58.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify111.0ms

Algorithm
egg-herbie
Counts
270 → 270
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
011322994
145722919
250022919

prune715.0ms

Filtered
270 candidates to 232 candidates (85.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
1.5b
(/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z))))
16.8b
(sqrt (+ 1.0 (* z z)))
16.8b
(sqrt (+ 1.0 (* z z)))

rewrite572.0ms

Algorithm
rewrite-expression-head
Rules
6882×times-frac
2950×add-sqr-sqrt
2948×add-cube-cbrt *-un-lft-identity
1836×sqrt-prod
307×associate-/l*
205×div-inv
27×add-exp-log add-cbrt-cube
22×sqrt-div
18×associate-/r/
16×cbrt-undiv div-exp
12×associate-/r*
11×flip3-+ flip-+
6×pow1
4×add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 2231
Calls
4 calls:
89.0ms
(/ (/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
22.0ms
(/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z))))
2.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ (/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
83.0ms
(/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z))))
46.0ms
(sqrt (+ 1.0 (* z z)))
41.0ms
(sqrt (+ 1.0 (* z z)))

simplify430.0ms

Algorithm
egg-herbie
Counts
2243 → 2243
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
0500151298

prune6.1s

Filtered
2243 candidates to 1495 candidates (66.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

localize24.0ms

Local error

Found 4 expressions with local error:

1.7b
(/ (/ 1 (* (cbrt y) (cbrt y))) (* (fabs (cbrt (+ 1.0 (* z z)))) (* (cbrt x) (cbrt x))))
16.8b
(sqrt (+ 1.0 (* z z)))
17.3b
(cbrt (+ 1.0 (* z z)))
17.3b
(cbrt (+ 1.0 (* z z)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
82×add-exp-log
33×div-exp
30×prod-exp
28×add-cbrt-cube
15×cbrt-undiv
13×times-frac
12×add-sqr-sqrt cbrt-unprod
11×add-cube-cbrt *-un-lft-identity
7×associate-/l*
6×cbrt-prod rec-exp 1-exp
5×pow1
4×cbrt-div add-log-exp
3×flip3-+ sqrt-prod flip-+ div-inv
2×pow1/3 sqrt-div
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r* associate-/l/
Counts
4 → 97
Calls
4 calls:
20.0ms
(/ (/ 1 (* (cbrt y) (cbrt y))) (* (fabs (cbrt (+ 1.0 (* z z)))) (* (cbrt x) (cbrt x))))
3.0ms
(sqrt (+ 1.0 (* z z)))
1.0ms
(cbrt (+ 1.0 (* z z)))
2.0ms
(cbrt (+ 1.0 (* z z)))

series540.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(/ (/ 1 (* (cbrt y) (cbrt y))) (* (fabs (cbrt (+ 1.0 (* z z)))) (* (cbrt x) (cbrt x))))
48.0ms
(sqrt (+ 1.0 (* z z)))
168.0ms
(cbrt (+ 1.0 (* z z)))
172.0ms
(cbrt (+ 1.0 (* z z)))

simplify69.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06821397
127561159
250011117

prune407.0ms

Filtered
109 candidates to 68 candidates (62.4%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.5b

regimes258.0ms

Accuracy

0% (1.0b remaining)

Error of 6.1b against oracle of 5.2b and baseline of 6.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02827
12827

end0.0ms

sample441.0ms

Algorithm
intervals
Results
254.0ms8615×body80valid