Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	248×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	16×	body	160	valid
1.0ms	9×	body	320	valid

simplify75.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	6
1	44	6
2	122	6
3	327	6
4	868	6
5	1727	6
6	3544	6
7	5001	6

prune3.0ms

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: 15.2b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
4.3b	(+ x (* (- y z) (/ (- t x) (- a z))))
7.5b	(* (- y z) (/ (- t x) (- a z)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

8.0ms	(/ (- t x) (- a z))
4.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
17.0ms	(* (- y z) (/ (- t x) (- a z)))

series325.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- t x) (- a z))
147.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
126.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	473	869
1	2012	820
2	5001	820

prune308.0ms

Filtered

128 candidates to 88 candidates (68.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	115	13	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	13	129

Merged error: 3.5b

Counts

129 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
1.0b	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
9.5b	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`*-un-lft-identity` `add-cbrt-cube`
13×	`associate-r`
10×	`cbrt-prod` `flip3--` `flip--`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `associate-/r/`
6×	`pow1` `frac-times` `add-log-exp`
5×	`associate-l`
4×	`cbrt-undiv` `div-exp` `associate-*l/`
3×	`associate-*r/` `distribute-lft-out--` `difference-of-squares`
2×	`times-frac` `pow1/3` `unswap-sqr`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 85

Calls

4 calls:

3.0ms	(cbrt (- t x))
3.0ms	(cbrt (- t x))
28.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
3.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series708.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (- t x))
143.0ms	(cbrt (- t x))
274.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
149.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	680	1363
1	2654	1151
2	5001	1129

prune336.0ms

Filtered

97 candidates to 74 candidates (76.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	96	14	110

Merged error: 3.5b

Counts

110 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.7b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.2b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
40.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
4.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series738.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (- a z))
145.0ms	(cbrt (- a z))
288.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
153.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	744	1831
1	3287	1663
2	5001	1576

prune400.0ms

Filtered

146 candidates to 104 candidates (71.2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	145	15	160

Merged error: 3.5b

Counts

160 → 15

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- t x) (/ 1 (- a z)))
5.8b	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
7.5b	(* (- y z) (* (- t x) (/ 1 (- a z))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
25×	`add-cube-cbrt`
22×	`associate-r`
20×	`frac-times` `add-cbrt-cube`
17×	`flip3--` `flip--`
13×	`prod-exp`
12×	`pow1`
10×	`associate-r/` `associate-l` `associate-l/`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`div-exp` `add-log-exp`
5×	`associate-/r*`
4×	`pow-prod-down` `associate-/r/` `un-div-inv`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 146

Calls

4 calls:

6.0ms	(/ 1 (- a z))
14.0ms	(* (- t x) (/ 1 (- a z)))
7.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
16.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

series361.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (- a z))
53.0ms	(* (- t x) (/ 1 (- a z)))
151.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
124.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

simplify74.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	585	1027
1	2810	910
2	5003	865

prune275.0ms

Filtered

158 candidates to 99 candidates (62.7%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	0	12	12
Picked	0	1	1
Done	0	2	2
Total	157	16	173

Merged error: 3.5b

Counts

173 → 16

regimes639.0ms

Accuracy

52.4% (3.8b remaining)

Error of 8.1b against oracle of 4.3b and baseline of 12.3b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	38
1	43	38

end0.0ms

sample675.0ms

Algorithm

intervals

Results

251.0ms	7702×	body	80	valid
59.0ms	512×	body	640	valid
42.0ms	269×	body	1280	valid
34.0ms	395×	body	320	valid
17.0ms	284×	body	160	valid
3.0ms	15×	body	2560	valid