Details

Time bar (total: 11.2s)

sample20.0ms

Algorithm
intervals
Results
10.0ms273×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0215
1404
2694
31044
41464
51604
61604

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.6b

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)))

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×expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u 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 → 74
Calls
2 calls:
8.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
7.0ms
(* y (+ 1.0 (* z z)))

series113.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
56.0ms
(* y (+ 1.0 (* z z)))

simplify49.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0416531
12028428
25001420

prune214.0ms

Filtered
80 candidates to 63 candidates (78.8%)
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)))

rewrite48.0ms

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 expm1-log1p-u frac-2neg clear-num associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
1×flip3-+ flip-+
Counts
2 → 268
Calls
2 calls:
6.0ms
(/ (/ 1.0 y) x)
22.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series84.0ms

Counts
2 → 6
Calls
2 calls:
20.0ms
(/ (/ 1.0 y) x)
64.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify130.0ms

Algorithm
egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
011383012
145962854
250022850

prune1.0s

Filtered
274 candidates to 238 candidates (86.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.5b

localize10.0ms

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)))

rewrite444.0ms

Algorithm
rewrite-expression-head
Rules
6882×times-frac
2952×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×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num hypot-def associate-/l/
Counts
4 → 2241
Calls
4 calls:
101.0ms
(/ (/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
24.0ms
(/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ (/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
91.0ms
(/ (/ (/ 1.0 y) x) (sqrt (+ 1.0 (* z z))))
48.0ms
(sqrt (+ 1.0 (* z z)))
44.0ms
(sqrt (+ 1.0 (* z z)))

simplify462.0ms

Algorithm
egg-herbie
Counts
2253 → 2253
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
0500151372

prune6.6s

Filtered
2253 candidates to 1505 candidates (66.8%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.5b

localize8.0ms

Local error

Found 2 expressions with local error:

3.1b
(/ (/ 1.0 x) (fma z z 1.0))
4.2b
(/ (/ (/ 1.0 x) (fma z z 1.0)) y)

rewrite48.0ms

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 expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
Counts
2 → 266
Calls
2 calls:
6.0ms
(/ (/ 1.0 x) (fma z z 1.0))
21.0ms
(/ (/ (/ 1.0 x) (fma z z 1.0)) y)

series138.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(/ (/ 1.0 x) (fma z z 1.0))
75.0ms
(/ (/ (/ 1.0 x) (fma z z 1.0)) y)

simplify106.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
011482808
146382733
250032733

prune827.0ms

Filtered
272 candidates to 237 candidates (87.1%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.5b

regimes180.0ms

Accuracy

0% (1.5b remaining)

Error of 6.7b against oracle of 5.2b and baseline of 6.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01210
11210

end0.0ms

sample429.0ms

Algorithm
intervals
Results
244.0ms8615×body80valid