Details

sample16.0ms

Algorithm

intervals

Results

7.0ms

276×

body

valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	5
1	37	5
2	61	5
3	91	5
4	115	5
5	121	5
6	121	5

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: 4.5b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.7b	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.1b	(* 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:

7.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
5.0ms	(* y (+ 1.0 (* z z)))

series109.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
51.0ms	(* y (+ 1.0 (* z z)))

simplify48.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	409	511
1	1963	443
2	5001	443

prune147.0ms

Filtered

76 candidates to 56 candidates (73.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	8	77

Merged error: 4.4b

Counts

77 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
1.7b	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
15.7b	(sqrt (+ 1.0 (* z z)))
15.7b	(sqrt (+ 1.0 (* z z)))

rewrite31.0ms

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:

9.0ms	(* (* 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)))))
2.0ms	(sqrt (+ 1.0 (* z z)))
2.0ms	(sqrt (+ 1.0 (* z z)))

series200.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
59.0ms	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
41.0ms	(sqrt (+ 1.0 (* z z)))
46.0ms	(sqrt (+ 1.0 (* z z)))

simplify68.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	610	1242
1	2886	1023
2	5001	1005

prune249.0ms

Filtered

129 candidates to 93 candidates (72.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	130	7	137

Merged error: 4.4b

Counts

137 → 7

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b	(* (/ 1.0 x) (/ (/ 1 y) (+ 1.0 (* z z))))
4.6b	(/ (/ 1 y) (+ 1.0 (* z z)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac`
114×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
86×	`add-cube-cbrt`
46×	`add-exp-log`
45×	`associate-r`
28×	`add-cbrt-cube`
23×	`div-exp`
13×	`associate-l` `associate-/l*`
12×	`cbrt-undiv`
10×	`prod-exp` `div-inv`
8×	`unswap-sqr`
6×	`cbrt-unprod`
4×	`pow1` `associate-/r/`
3×	`rec-exp` `1-exp` `associate-/r*`
2×	`flip3-+` `flip-+` `add-log-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `associate-/l/`

Counts

2 → 168

Calls

2 calls:

21.0ms	(* (/ 1.0 x) (/ (/ 1 y) (+ 1.0 (* z z))))
7.0ms	(/ (/ 1 y) (+ 1.0 (* z z)))

series109.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(* (/ 1.0 x) (/ (/ 1 y) (+ 1.0 (* z z))))
50.0ms	(/ (/ 1 y) (+ 1.0 (* z z)))

simplify88.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	889	1623
1	4357	1446
2	5002	1361

prune258.0ms

Filtered

174 candidates to 111 candidates (63.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	174	7	181

Merged error: 4.4b

Counts

181 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.0b	(/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x))) (* (/ (* y (+ 1.0 (* z z))) (cbrt 1.0)) (cbrt x)))
1.0b	(* (/ (* y (+ 1.0 (* z z))) (cbrt 1.0)) (cbrt x))
4.1b	(* y (+ 1.0 (* z z)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-exp-log`
55×	`add-cbrt-cube`
48×	`cbrt-undiv` `div-exp`
41×	`prod-exp` `cbrt-unprod`
20×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`times-frac` `associate-l`
10×	`cbrt-prod`
9×	`associate-r`
8×	`pow1`
5×	`associate-/l*`
4×	`div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `*-commutative`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `flip3-+` `pow1/3` `clear-num` `associate-/r*` `associate-/r/` `flip-+` `associate-/l/`

Counts

4 → 130

Calls

4 calls:

1.0ms	(cbrt x)
16.0ms	(/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x))) (* (/ (* y (+ 1.0 (* z z))) (cbrt 1.0)) (cbrt x)))
9.0ms	(* (/ (* y (+ 1.0 (* z z))) (cbrt 1.0)) (cbrt x))
9.0ms	(* y (+ 1.0 (* z z)))

series677.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt x)
155.0ms	(/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt x) (cbrt x))) (* (/ (* y (+ 1.0 (* z z))) (cbrt 1.0)) (cbrt x)))
279.0ms	(* (/ (* y (+ 1.0 (* z z))) (cbrt 1.0)) (cbrt x))
56.0ms	(* y (+ 1.0 (* z z)))

simplify108.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	766	1905
1	4158	1410
2	5001	1187

prune250.0ms

Filtered

142 candidates to 79 candidates (55.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	142	7	149

Merged error: 4.4b

Counts

149 → 7

regimes407.0ms

Accuracy

0% (1.5b remaining)

Error of 6.2b against oracle of 4.7b and baseline of 6.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	10
1	14	10

end0.0ms

sample434.0ms

Algorithm

intervals

Results

250.0ms

8623×

body

valid