Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	248×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	6×	body	1280	valid
1.0ms	12×	body	160	valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1498	6
6	3410	6
7	5001	6

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 27.1b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.7b	(+ x (/ (* (- y z) (- t x)) (- a z)))
19.3b	(/ (* (- y z) (- t x)) (- a z))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-sqr-sqrt`
104×	`*-un-lft-identity`
80×	`times-frac`
40×	`add-cube-cbrt`
35×	`associate-r` `associate-l`
31×	`distribute-lft-out--` `difference-of-squares`
16×	`associate-/l*`
13×	`flip3--` `flip--`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `associate-/l/`
7×	`*-commutative` `unswap-sqr`
5×	`pow1` `associate-/r*` `add-log-exp`
4×	`associate-r/` `associate-l/`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `flip-+` `div-inv` `distribute-lft-out`

Counts

3 → 171

Calls

3 calls:

9.0ms	(* (- y z) (- t x))
31.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
17.0ms	(/ (* (- y z) (- t x)) (- a z))

series333.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* (- y z) (- t x))
155.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
138.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify83.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	726	1523
1	3249	1474
2	5001	1474

prune319.0ms

Filtered

180 candidates to 121 candidates (32.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	168	12	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	169	12	181

Merged error: 4.2b

Counts

181 → 12

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.2b	(* (- t x) (/ (- y z) (- a z)))
2.7b	(+ x (* (- t x) (/ (- y z) (- a z))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
96×	`add-sqr-sqrt`
51×	`times-frac`
33×	`add-cube-cbrt`
31×	`associate-r` `distribute-lft-out--`
30×	`frac-times`
29×	`difference-of-squares`
22×	`flip3--` `flip--` `associate-/l*`
20×	`associate-/r*`
15×	`associate-*r/`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l/`
7×	`associate-l`
5×	`pow1` `clear-num` `add-log-exp`
4×	`frac-2neg` `associate-/r/`
3×	`un-div-inv` `distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `flip3-+` `div-sub` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

3 → 167

Calls

3 calls:

10.0ms	(/ (- y z) (- a z))
21.0ms	(* (- t x) (/ (- y z) (- a z)))
23.0ms	(+ x (* (- t x) (/ (- y z) (- a z))))

series346.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(/ (- y z) (- a z))
122.0ms	(* (- t x) (/ (- y z) (- a z)))
167.0ms	(+ x (* (- t x) (/ (- y z) (- a z))))

simplify93.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	631	1308
1	3251	1259
2	5002	1259

prune370.0ms

Filtered

176 candidates to 116 candidates (34.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	167	9	176
Fresh	9	2	11
Picked	0	1	1
Done	0	0	0
Total	176	12	188

Merged error: 4.2b

Counts

188 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

3.1b	(cbrt (* (- t x) (/ (- y z) (- a z))))
3.1b	(cbrt (* (- t x) (/ (- y z) (- a z))))
3.1b	(cbrt (* (- t x) (/ (- y z) (- a z))))
8.5b	(+ x (* (* (cbrt (* (- t x) (/ (- y z) (- a z)))) (cbrt (* (- t x) (/ (- y z) (- a z))))) (cbrt (* (- t x) (/ (- y z) (- a z))))))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

178×	`add-sqr-sqrt` `*-un-lft-identity`
150×	`cbrt-div`
129×	`cbrt-prod`
93×	`associate-r`
90×	`frac-times`
78×	`times-frac`
61×	`add-cube-cbrt`
60×	`flip3--` `flip--`
54×	`distribute-lft-out--`
51×	`associate-/l*` `difference-of-squares`
45×	`associate-r/` `associate-/r`
18×	`associate-l` `associate-/l/`
12×	`clear-num`
9×	`frac-2neg` `un-div-inv`
6×	`associate-*l/` `associate-/r/` `add-log-exp` `unswap-sqr`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3` `*-commutative` `div-inv` `distribute-lft-out`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 317

Calls

4 calls:

24.0ms	(cbrt (* (- t x) (/ (- y z) (- a z))))
26.0ms	(cbrt (* (- t x) (/ (- y z) (- a z))))
24.0ms	(cbrt (* (- t x) (/ (- y z) (- a z))))
253.0ms	(+ x (* (* (cbrt (* (- t x) (/ (- y z) (- a z)))) (cbrt (* (- t x) (/ (- y z) (- a z))))) (cbrt (* (- t x) (/ (- y z) (- a z))))))

series3.3s

Counts

4 → 12

Calls

4 calls:

1.1s	(cbrt (* (- t x) (/ (- y z) (- a z))))
1.0s	(cbrt (* (- t x) (/ (- y z) (- a z))))
1.0s	(cbrt (* (- t x) (/ (- y z) (- a z))))
173.0ms	(+ x (* (* (cbrt (* (- t x) (/ (- y z) (- a z)))) (cbrt (* (- t x) (/ (- y z) (- a z))))) (cbrt (* (- t x) (/ (- y z) (- a z))))))

simplify110.0ms

Algorithm

egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	788	4258
1	3197	4164
2	5002	4158

prune962.0ms

Filtered

329 candidates to 236 candidates (28.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	329	0	329
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	329	12	341

Merged error: 4.2b

Counts

341 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y z))
0.5b	(cbrt (- y z))
2.2b	(* (- t x) (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))))
8.2b	(+ x (* (- t x) (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z))))))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

3175×	`times-frac`
3069×	`add-sqr-sqrt`
2867×	`*-un-lft-identity`
2364×	`cbrt-prod`
2024×	`associate-r`
1174×	`add-cube-cbrt`
794×	`distribute-lft-out--`
695×	`difference-of-squares`
496×	`swap-sqr`
400×	`associate-l`
236×	`unswap-sqr`
196×	`frac-times`
152×	`flip3--` `flip--`
146×	`associate-/r*`
116×	`cbrt-div`
112×	`associate-/l*`
98×	`associate-*r/`
94×	`associate-/r/`
56×	`add-cbrt-cube`
53×	`*-commutative`
39×	`div-inv`
28×	`cbrt-unprod`
26×	`associate-/l/`
25×	`cbrt-undiv`
22×	`add-exp-log`
8×	`associate-*l/`
7×	`prod-exp`
6×	`pow1` `div-exp` `add-log-exp`
5×	`clear-num`
4×	`frac-2neg`
3×	`un-div-inv` `distribute-lft-out`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `flip-+`

Counts

4 → 2020

Calls

4 calls:

3.0ms	(cbrt (- y z))
3.0ms	(cbrt (- y z))
621.0ms	(* (- t x) (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))))
623.0ms	(+ x (* (- t x) (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z))))))

series603.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt (- y z))
156.0ms	(cbrt (- y z))
118.0ms	(* (- t x) (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))))
170.0ms	(+ x (* (- t x) (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z))))))

simplify306.0ms

Algorithm

egg-herbie

Counts

2032 → 2032

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5001	29717

prune4.6s

Filtered

2032 candidates to 1083 candidates (46.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	2031	1	2032
Fresh	2	7	9
Picked	0	1	1
Done	1	1	2
Total	2034	10	2044

Merged error: 4.2b

Counts

2044 → 10

regimes292.0ms

Accuracy

44.8% (4.2b remaining)

Error of 8.5b against oracle of 4.3b and baseline of 11.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	24
1	36	24

end0.0ms

sample698.0ms

Algorithm

intervals

Results

257.0ms	7787×	body	80	valid
63.0ms	518×	body	640	valid
40.0ms	258×	body	1280	valid
33.0ms	376×	body	320	valid
19.0ms	320×	body	160	valid
4.0ms	21×	body	2560	valid