Details

Time bar (total: 19.9s)

sample17.0ms

Algorithm
intervals
Results
8.0ms274×body80valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0215
1404
2694
31044
41464
51604
61604

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.7b

localize7.0ms

Local error

Found 2 expressions with local error:

3.1b
(* y (+ 1.0 (* z z)))
3.7b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite35.0ms

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:
18.0ms
(* y (+ 1.0 (* z z)))
15.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series99.0ms

Counts
2 → 6
Calls
2 calls:
48.0ms
(* y (+ 1.0 (* z z)))
50.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify48.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0416531
12028428
25001420

prune252.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (/ 1.0 y) x)
5.1b
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

rewrite55.0ms

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:
10.0ms
(/ (/ 1.0 y) x)
26.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series66.0ms

Counts
2 → 6
Calls
2 calls:
16.0ms
(/ (/ 1.0 y) x)
50.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify106.0ms

Algorithm
egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
011383012
145962854
250022850

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cbrt 1.0) (/ (sqrt (+ 1.0 (* z z))) (cbrt 1.0))) (/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z)))))
1.5b
(/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z))))
15.2b
(sqrt (+ 1.0 (* z z)))
15.2b
(sqrt (+ 1.0 (* z z)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
3216×times-frac
1888×add-sqr-sqrt
1326×add-cube-cbrt *-un-lft-identity
682×cbrt-prod
617×sqrt-prod
426×associate-*r*
245×associate-*l*
99×unswap-sqr
70×associate-/l*
67×add-exp-log
61×div-inv
51×add-cbrt-cube
36×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
8×pow1 sqrt-div
6×associate-/r*
5×associate-/r/
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 1361
Calls
4 calls:
1.2s
(* (/ (cbrt 1.0) (/ (sqrt (+ 1.0 (* z z))) (cbrt 1.0))) (/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z)))))
42.0ms
(/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z))))
5.0ms
(sqrt (+ 1.0 (* z z)))
6.0ms
(sqrt (+ 1.0 (* z z)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(* (/ (cbrt 1.0) (/ (sqrt (+ 1.0 (* z z))) (cbrt 1.0))) (/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z)))))
111.0ms
(/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z))))
39.0ms
(sqrt (+ 1.0 (* z z)))
47.0ms
(sqrt (+ 1.0 (* z z)))

simplify286.0ms

Algorithm
egg-herbie
Counts
1373 → 1373
Iterations

Useful iterations: 1 (78.0ms)

IterNodesCost
0479826392
1500126036

prune8.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt y) (cbrt y))
0.8b
(/ (/ (/ (sqrt 1.0) (cbrt y)) x) (sqrt (+ 1.0 (* z z))))
15.2b
(sqrt (+ 1.0 (* z z)))
15.2b
(sqrt (+ 1.0 (* z z)))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
2340×times-frac
1088×add-sqr-sqrt
1076×add-cube-cbrt *-un-lft-identity
759×sqrt-prod
394×cbrt-prod
124×associate-/l*
29×div-inv
15×add-exp-log
13×pow1
12×add-cbrt-cube
6×cbrt-undiv pow1/3 sqrt-div swap-sqr div-exp associate-*r* associate-*l* associate-/r*
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×flip3-+ flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-/r/ pow-sqr pow-prod-up hypot-def
1×pow2 frac-2neg pow-plus prod-exp clear-num *-commutative cbrt-unprod associate-/l/
Counts
4 → 973
Calls
4 calls:
16.0ms
(* (cbrt y) (cbrt y))
91.0ms
(/ (/ (/ (sqrt 1.0) (cbrt y)) x) (sqrt (+ 1.0 (* z z))))
9.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series468.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(* (cbrt y) (cbrt y))
193.0ms
(/ (/ (/ (sqrt 1.0) (cbrt y)) x) (sqrt (+ 1.0 (* z z))))
38.0ms
(sqrt (+ 1.0 (* z z)))
39.0ms
(sqrt (+ 1.0 (* z z)))

simplify201.0ms

Algorithm
egg-herbie
Counts
985 → 985
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
0274618521
1500217824

prune5.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.5b

regimes290.0ms

Accuracy

0% (1.7b remaining)

Error of 6.7b against oracle of 5.0b and baseline of 6.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01615
11615

end0.0ms

sample438.0ms

Algorithm
intervals
Results
260.0ms8625×body80valid