Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	248×	body	80	valid
2.0ms	18×	body	320	valid
2.0ms	13×	body	640	valid
2.0ms	10×	body	1280	valid
0.0ms	1×	body	2560	valid
0.0ms	3×	body	160	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

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: 15.7b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.6b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.8b	(* (- y z) (/ (- t x) (- a z)))

rewrite32.0ms

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))))
16.0ms	(* (- y z) (/ (- t x) (- a z)))

series328.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (- t x) (- a z))
145.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
130.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify55.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (12.0ms)

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

prune309.0ms

Filtered

128 candidates to 88 candidates (68.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	116	12	128
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	116	13	129

Merged error: 4.2b

Counts

129 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.9b	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
7.7b	(+ 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 (- a z))
3.0ms	(cbrt (- a z))
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)))))

series727.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (- a z))
151.0ms	(cbrt (- a z))
273.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
154.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify70.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	668	1363
1	2615	1151
2	5001	1129

prune338.0ms

Filtered

97 candidates to 74 candidates (76.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	98	12	110

Merged error: 4.2b

Counts

110 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

1.2b	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
1.2b	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
1.2b	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
7.7b	(+ x (* (* (* (- y z) (* (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod` `cbrt-div`
24×	`associate-/r/`
18×	`flip3--` `flip--`
12×	`frac-times`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r/` `associate-l/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`times-frac` `pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

17.0ms	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
17.0ms	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
17.0ms	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
3.0ms	(+ x (* (* (* (- y z) (* (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series734.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
194.0ms	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
193.0ms	(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
155.0ms	(+ x (* (* (* (- y z) (* (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	372	2240
1	1002	2012
2	5001	1948

prune429.0ms

Filtered

89 candidates to 75 candidates (84.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	9	9
Picked	0	1	1
Done	1	1	2
Total	88	13	101

Merged error: 3.5b

Counts

101 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.2b	(/ 1 (/ (- a z) (- t x)))
3.8b	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
6.8b	(* (- y z) (/ 1 (/ (- a z) (- t x))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

392×	`times-frac`
338×	`add-sqr-sqrt`
326×	`*-un-lft-identity`
158×	`add-cube-cbrt`
98×	`associate-r`
83×	`distribute-lft-out--` `difference-of-squares`
36×	`add-exp-log` `associate-/r*`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
11×	`flip3--` `flip--`
10×	`div-inv`
8×	`associate-/l*`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`add-log-exp`
5×	`associate-l` `unswap-sqr`
4×	`rec-exp` `1-exp`
3×	`cbrt-unprod`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `flip-+` `inv-pow`

Counts

4 → 344

Calls

4 calls:

8.0ms	(/ (- a z) (- t x))
12.0ms	(/ 1 (/ (- a z) (- t x)))
3.0ms	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
40.0ms	(* (- y z) (/ 1 (/ (- a z) (- t x))))

series710.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (- a z) (- t x))
201.0ms	(/ 1 (/ (- a z) (- t x)))
153.0ms	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
307.0ms	(* (- y z) (/ 1 (/ (- a z) (- t x))))

simplify66.0ms

Algorithm

egg-herbie

Counts

356 → 356

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1010	3037
1	5002	2740

prune670.0ms

Filtered

356 candidates to 208 candidates (58.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	355	1	356
Fresh	1	9	10
Picked	1	0	1
Done	1	1	2
Total	358	11	369

Merged error: 3.5b

Counts

369 → 11

regimes261.0ms

Accuracy

21% (6.8b remaining)

Error of 10.0b against oracle of 3.2b and baseline of 11.8b

bsearch115.0ms

Steps

Iters	Range		Point
8	2.7754957924394407e-157	4.426179654126689e-153	4.1983362121842287e-156
10	-3.607687969514871e-118	-2.2872698318815147e-131	-1.133677899711763e-127

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	11
1	29	11

end0.0ms

sample799.0ms

Algorithm

intervals

Results

308.0ms	7757×	body	80	valid
70.0ms	486×	body	640	valid
54.0ms	265×	body	1280	valid
50.0ms	443×	body	320	valid
20.0ms	268×	body	160	valid
2.0ms	11×	body	2560	valid

Details

sample32.0ms

simplify74.0ms

prune2.0ms

localize9.0ms

rewrite32.0ms

series328.0ms

simplify55.0ms

prune309.0ms

localize17.0ms

rewrite41.0ms

series727.0ms

simplify70.0ms

prune338.0ms

localize27.0ms

rewrite57.0ms

series734.0ms

simplify48.0ms

prune429.0ms

localize11.0ms

rewrite84.0ms

series710.0ms

simplify66.0ms

prune670.0ms

regimes261.0ms

bsearch115.0ms

simplify1.0ms

end0.0ms

sample799.0ms

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