Details

Time bar (total: 3.3s)

sample17.0ms

Algorithm
intervals
Results
8.0ms280×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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.0b

localize7.0ms

Local error

Found 2 expressions with local error:

3.4b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
3.6b
(* y (+ 1.0 (* z z)))

rewrite15.0ms

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:
8.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
5.0ms
(* y (+ 1.0 (* z z)))

series112.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
55.0ms
(* y (+ 1.0 (* z z)))

simplify49.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0409511
11963443
25001443

prune164.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
3.4b
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
13.6b
(sqrt (+ 1.0 (* z z)))
13.6b
(sqrt (+ 1.0 (* z z)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
30×add-exp-log add-cbrt-cube
28×sqrt-div
24×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
16×associate-*r/
14×flip3-+ flip-+
13×associate-/l*
11×pow1
9×cbrt-undiv div-exp prod-exp sqrt-prod cbrt-unprod
8×frac-times associate-/r/
6×associate-*r*
4×associate-*l/ add-log-exp
3×pow-prod-down div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-2neg associate-*l* clear-num associate-/r* *-commutative associate-/l/
Counts
4 → 117
Calls
4 calls:
10.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
13.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
2.0ms
(sqrt (+ 1.0 (* z z)))

series195.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
55.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
44.0ms
(sqrt (+ 1.0 (* z z)))
42.0ms
(sqrt (+ 1.0 (* z z)))

simplify72.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06101244
128801023
250021005

prune316.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1.0 (* y (sqrt (+ 1.0 (* z z)))))
1.1b
(* (/ 1.0 (* y (sqrt (+ 1.0 (* z z))))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
13.6b
(sqrt (+ 1.0 (* z z)))
13.6b
(sqrt (+ 1.0 (* z z)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
148×times-frac
103×add-sqr-sqrt
84×associate-*r*
81×*-un-lft-identity
79×add-cube-cbrt
69×add-exp-log
48×sqrt-prod
45×add-cbrt-cube
30×div-exp
21×prod-exp
17×cbrt-undiv
13×cbrt-unprod
10×sqrt-div
9×associate-*l* div-inv
8×pow1
7×unswap-sqr
6×associate-/r/
5×flip3-+ associate-*r/ flip-+
4×add-log-exp
3×rec-exp 1-exp associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg pow-prod-down associate-*l/ clear-num associate-/r* *-commutative
Counts
4 → 189
Calls
4 calls:
6.0ms
(/ 1.0 (* y (sqrt (+ 1.0 (* z z)))))
37.0ms
(* (/ 1.0 (* y (sqrt (+ 1.0 (* z z))))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
2.0ms
(sqrt (+ 1.0 (* z z)))
2.0ms
(sqrt (+ 1.0 (* z z)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ 1.0 (* y (sqrt (+ 1.0 (* z z)))))
64.0ms
(* (/ 1.0 (* y (sqrt (+ 1.0 (* z z))))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
48.0ms
(sqrt (+ 1.0 (* z z)))
42.0ms
(sqrt (+ 1.0 (* z z)))

simplify46.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011032373
150022105

prune443.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ 1 x))
2.8b
(/ (* 1.0 (* (cbrt (/ 1 x)) (cbrt (/ 1 x)))) (* y (sqrt (+ 1.0 (* z z)))))
13.6b
(sqrt (+ 1.0 (* z z)))
13.6b
(sqrt (+ 1.0 (* z z)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
21×add-cbrt-cube
15×add-sqr-sqrt
13×cbrt-prod add-cube-cbrt *-un-lft-identity
10×times-frac
9×prod-exp cbrt-unprod
6×pow1 cbrt-undiv sqrt-div associate-*r/ div-exp sqrt-prod
5×cbrt-div
4×add-log-exp
3×flip3-+ flip-+ associate-/l/
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ div-inv
1×frac-times frac-2neg pow1/3 associate-*l/ clear-num associate-/r* associate-/l*
Counts
4 → 82
Calls
4 calls:
2.0ms
(cbrt (/ 1 x))
19.0ms
(/ (* 1.0 (* (cbrt (/ 1 x)) (cbrt (/ 1 x)))) (* y (sqrt (+ 1.0 (* z z)))))
2.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series449.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(cbrt (/ 1 x))
183.0ms
(/ (* 1.0 (* (cbrt (/ 1 x)) (cbrt (/ 1 x)))) (* y (sqrt (+ 1.0 (* z z)))))
48.0ms
(sqrt (+ 1.0 (* z z)))
42.0ms
(sqrt (+ 1.0 (* z z)))

simplify65.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
0500814
12605686
25001641

prune284.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.6b

regimes198.0ms

Accuracy

0% (1.2b remaining)

Error of 5.9b against oracle of 4.8b and baseline of 5.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01811
11811

end0.0ms

sample447.0ms

Algorithm
intervals
Results
256.0ms8642×body80valid