Details

Time bar (total: 10.5s)

sample16.0ms

Algorithm
intervals
Results
7.0ms280×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: 7.9b

localize7.0ms

Local error

Found 2 expressions with local error:

3.3b
(* y (+ 1.0 (* z z)))
5.0b
(/ (/ 1.0 x) (* 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:
9.0ms
(* y (+ 1.0 (* z z)))
7.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series106.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(* y (+ 1.0 (* z z)))
54.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify49.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0409511
11963443
25001443

prune154.0ms

Filtered
76 candidates to 56 candidates (73.7%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.3b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ 1.0 y) x)
7.1b
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

rewrite42.0ms

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:
8.0ms
(/ (/ 1.0 y) x)
17.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series76.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(/ (/ 1.0 y) x)
53.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify103.0ms

Algorithm
egg-herbie
Counts
270 → 270
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
011322994
145722919
250022919

prune691.0ms

Filtered
270 candidates to 233 candidates (86.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
1.0b
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
15.4b
(sqrt (+ 1.0 (* z z)))
15.4b
(sqrt (+ 1.0 (* z z)))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
497×times-frac
375×add-sqr-sqrt
231×*-un-lft-identity
221×add-cube-cbrt
155×sqrt-prod
84×associate-*r* associate-*l*
73×add-exp-log
45×add-cbrt-cube
39×div-exp
35×unswap-sqr
22×div-inv
21×cbrt-undiv
15×prod-exp
13×associate-/l*
10×sqrt-div
9×cbrt-unprod
8×pow1
6×associate-/r* associate-/r/
5×flip3-+ flip-+
4×rec-exp 1-exp add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 385
Calls
4 calls:
9.0ms
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
133.0ms
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
2.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series209.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
66.0ms
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
45.0ms
(sqrt (+ 1.0 (* z z)))
40.0ms
(sqrt (+ 1.0 (* z z)))

simplify79.0ms

Algorithm
egg-herbie
Counts
397 → 397
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015705406
150015036

prune831.0ms

Filtered
397 candidates to 230 candidates (57.9%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.3b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x) (sqrt (+ 1.0 (* z z))))
3.0b
(/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x)
15.4b
(sqrt (+ 1.0 (* z z)))
15.4b
(sqrt (+ 1.0 (* z z)))

rewrite392.0ms

Algorithm
rewrite-expression-head
Rules
6852×times-frac
2927×add-sqr-sqrt
2925×add-cube-cbrt *-un-lft-identity
1752×sqrt-prod
340×associate-/l*
184×div-inv
56×sqrt-div
52×associate-/r/
28×flip3-+ flip-+
27×add-exp-log add-cbrt-cube
16×cbrt-undiv div-exp
9×associate-/r*
6×pow1
4×add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 2205
Calls
4 calls:
102.0ms
(/ (/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x) (sqrt (+ 1.0 (* z z))))
27.0ms
(/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x)
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ (/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x) (sqrt (+ 1.0 (* z z))))
82.0ms
(/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) x)
41.0ms
(sqrt (+ 1.0 (* z z)))
52.0ms
(sqrt (+ 1.0 (* z z)))

simplify442.0ms

Algorithm
egg-herbie
Counts
2217 → 2217
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
0500151407

prune6.2s

Filtered
2217 candidates to 1530 candidates (69.0%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.3b

regimes241.0ms

Accuracy

0% (1.1b remaining)

Error of 6.1b against oracle of 5.0b and baseline of 6.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01210
11210

end0.0ms

sample410.0ms

Algorithm
intervals
Results
241.0ms8650×body80valid