Details

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	7
1	22	7
2	24	7
3	24	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 40.4b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
37.3b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`sqrt-prod`
11×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`sum-log`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`+-commutative` `rem-sqrt-square` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `associate-+l+` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

4 → 78

Calls

4 calls:

6.0ms	(+ (+ (* x x) (* y y)) (* z z))
4.0ms	(+ (* x x) (* y y))
8.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series294.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
31.0ms	(+ (* x x) (* y y))
48.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
179.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	325	828
1	1345	761
2	5001	755

prune228.0ms

Filtered

90 candidates to 71 candidates (78.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	7	91

Merged error: 22.1b

Counts

91 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
0.3b	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
37.5b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.5b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

150×	`sqrt-prod`
130×	`add-sqr-sqrt`
106×	`times-frac`
64×	`add-cube-cbrt` `*-un-lft-identity`
47×	`cbrt-prod`
43×	`associate-r`
24×	`unswap-sqr`
13×	`associate-l`
10×	`pow1` `sqrt-div`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r` `associate-/l`
4×	`sqrt-pow1` `pow1/2` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `flip-+` `div-inv`
2×	`rem-sqrt-square` `associate-/l/`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 189

Calls

4 calls:

13.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
30.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series773.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
334.0ms	(* (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
101.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
104.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify128.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	414	3970
1	1331	3861
2	4412	3765
3	5001	3713

prune591.0ms

Filtered

201 candidates to 125 candidates (62.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	201	7	208

Merged error: 22.1b

Counts

208 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt 3.0))
37.5b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.5b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
37.5b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
54×	`times-frac`
51×	`add-sqr-sqrt`
48×	`add-cube-cbrt` `*-un-lft-identity`
30×	`cbrt-prod`
10×	`sqrt-div`
9×	`associate-/l*`
7×	`pow1`
6×	`add-exp-log` `associate-/r*`
5×	`add-cbrt-cube`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 128

Calls

4 calls:

11.0ms	(/ (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt 3.0))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series512.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(/ (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (cbrt 3.0))
102.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
100.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify111.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	288	1937
1	839	1872
2	3194	1844
3	5002	1823

prune487.0ms

Filtered

140 candidates to 92 candidates (65.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	140	7	147

Merged error: 22.1b

Counts

147 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cbrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)
0.3b	(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (cbrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
38.6b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
38.6b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
28×	`cbrt-prod`
25×	`associate-r` `sqrt-prod`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`pow1` `cbrt-div` `associate-/l*`
4×	`add-log-exp` `unswap-sqr`
3×	`flip3-+` `associate-l` `associate-/r*` `flip-+`
2×	`pow1/3` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-div` `associate-r/` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `-commutative` `cbrt-unprod`

Counts

4 → 111

Calls

4 calls:

8.0ms	(/ (cbrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)
12.0ms	(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (cbrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
5.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

series724.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (cbrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)
212.0ms	(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (/ (cbrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
109.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
284.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify63.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	465	1855
1	1778	1748
2	5002	1729

prune414.0ms

Filtered

123 candidates to 109 candidates (88.6%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	123	7	130

Merged error: 22.1b

Counts

130 → 7

regimes504.0ms

Accuracy

62.7% (7.1b remaining)

Error of 25.6b against oracle of 18.5b and baseline of 37.5b

bsearch83.0ms

Steps

Iters	Range		Point
9	2.6532170287404195e+152	9.899160405665484e+160	2.7115116257003536e+152
8	-5.4516863711246e+114	-4.4782588713311843e+111	-9.39299411254326e+113

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	12
1	33	12
2	33	12

end0.0ms

sample538.0ms

Algorithm

intervals

Results

364.0ms

8000×

body

valid