Details

Time bar (total: 3.6s)

sample28.0ms

Algorithm
intervals
Results
10.0ms278×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
08211
18211

prune10.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 5.3b

Counts
2 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

2.1b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.9b
(* y (+ 1.0 (* z z)))

rewrite17.0ms

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

series29.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
11.0ms
(* y (+ 1.0 (* z z)))

simplify57.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
04985885
14985885

prune125.0ms

Filtered
56 candidates to 76 candidates (-35.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New69776
Fresh011
Picked101
Done000
Total70878

Merged error: 4.3b

Counts
78 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
2.1b
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
16.6b
(sqrt (+ 1.0 (* z z)))
16.6b
(sqrt (+ 1.0 (* z z)))

rewrite37.0ms

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:
11.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
15.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series40.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
21.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
4.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

simplify67.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049911716
149911716

prune211.0ms

Filtered
94 candidates to 129 candidates (-37.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1290129
Fresh077
Picked011
Done000
Total1298137

Merged error: 4.3b

Counts
137 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ 1.0 x))
0.6b
(cbrt (/ 1.0 x))
1.6b
(/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z)))
4.2b
(* (* (cbrt (/ 1.0 x)) (/ (cbrt (/ 1.0 x)) y)) (/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
177×times-frac
117×cbrt-prod
108×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
54×associate-*r*
27×add-exp-log
17×add-cbrt-cube
16×associate-/l*
11×div-inv
10×prod-exp cbrt-unprod
9×pow1
7×cbrt-div
6×cbrt-undiv div-exp
5×frac-times associate-*l/
4×associate-/r/ add-log-exp
3×associate-*r/ pow-prod-down associate-/r*
2×flip3-+ pow1/3 flip-+
1×frac-2neg associate-*l* clear-num *-commutative associate-/l/
Counts
4 → 210
Calls
4 calls:
2.0ms
(cbrt (/ 1.0 x))
2.0ms
(cbrt (/ 1.0 x))
8.0ms
(/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z)))
28.0ms
(* (* (cbrt (/ 1.0 x)) (/ (cbrt (/ 1.0 x)) y)) (/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z))))

series119.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(cbrt (/ 1.0 x))
25.0ms
(cbrt (/ 1.0 x))
42.0ms
(/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z)))
27.0ms
(* (* (cbrt (/ 1.0 x)) (/ (cbrt (/ 1.0 x)) y)) (/ (cbrt (/ 1.0 x)) (+ 1.0 (* z z))))

simplify122.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 0 (94.0ms)

IterNodesCost
049353712
149353712

prune610.0ms

Filtered
179 candidates to 222 candidates (-24.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2193222
Fresh156
Picked011
Done011
Total22010230

Merged error: 3.4b

Counts
230 → 10

localize8.0ms

Local error

Found 2 expressions with local error:

3.3b
(/ (/ (/ 1.0 x) (+ 1.0 (* z z))) y)
4.3b
(/ (/ 1.0 x) (+ 1.0 (* z z)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
474×times-frac
230×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
58×associate-/l*
22×div-inv
16×add-exp-log add-cbrt-cube
10×associate-/r/
9×cbrt-undiv div-exp
6×associate-/r*
5×flip3-+ flip-+
2×pow1 frac-2neg clear-num associate-/l/ add-log-exp
Counts
2 → 272
Calls
2 calls:
18.0ms
(/ (/ (/ 1.0 x) (+ 1.0 (* z z))) y)
7.0ms
(/ (/ 1.0 x) (+ 1.0 (* z z)))

series31.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(/ (/ (/ 1.0 x) (+ 1.0 (* z z))) y)
14.0ms
(/ (/ 1.0 x) (+ 1.0 (* z z)))

simplify102.0ms

Algorithm
egg-herbie
Counts
278 → 278
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
049735877
149735877

prune543.0ms

Filtered
245 candidates to 278 candidates (-13.5%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New2771278
Fresh077
Picked011
Done022
Total27711288

Merged error: 0.8b

Counts
288 → 11

regimes701.0ms

Accuracy

56.3% (2.1b remaining)

Error of 3.7b against oracle of 1.6b and baseline of 6.5b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04536
14536

end0.0ms

sample599.0ms

Algorithm
intervals
Results
296.0ms8646×body80valid

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