Details

sample29.0ms

Algorithm

intervals

Results

10.0ms	238×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	10×	body	1280	valid
1.0ms	14×	body	320	valid
0.0ms	8×	body	160	valid

simplify87.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	116	5
3	324	5
4	861	5
5	1912	5
6	4581	5
7	5001	5

prune8.0ms

Filtered

1 candidates to 1 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: 11.8b

Counts

2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.4b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

9.0ms	(/ (- y z) (- a z))
1.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series177.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ (- y z) (- a z))
122.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify71.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	265	450
1	729	425
2	2562	423
3	5002	421

prune201.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	62	8	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	63	9	72

Merged error: 3.8b

Counts

72 → 9

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
0.8b	(/ 1 (/ (- a z) (- y z)))
2.4b	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
195×	`add-sqr-sqrt` `*-un-lft-identity`
91×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`flip3--` `flip--` `div-inv`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `fma-udef` `inv-pow`

Counts

3 → 214

Calls

3 calls:

14.0ms	(/ (- a z) (- y z))
14.0ms	(/ 1 (/ (- a z) (- y z)))
1.0ms	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

series323.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ (- a z) (- y z))
142.0ms	(/ 1 (/ (- a z) (- y z)))
131.0ms	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

simplify91.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	630	1909
1	2802	1724
2	5001	1553

prune387.0ms

Filtered

223 candidates to 108 candidates (48.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	221	2	223
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	224	8	232

Merged error: 3.8b

Counts

232 → 8

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
1.4b	(+ (/ (- t x) (/ (- a z) (- y z))) x)
4.1b	(/ (- t x) (/ (- a z) (- y z)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

610×	`times-frac`
572×	`*-un-lft-identity`
570×	`add-sqr-sqrt`
200×	`add-cube-cbrt`
185×	`distribute-lft-out--` `difference-of-squares`
160×	`fma-def`
36×	`associate-/r*`
26×	`associate-/r/`
14×	`flip3--` `flip--` `div-inv`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 440

Calls

3 calls:

9.0ms	(/ (- a z) (- y z))
68.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)
18.0ms	(/ (- t x) (/ (- a z) (- y z)))

series428.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (- a z) (- y z))
157.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)
218.0ms	(/ (- t x) (/ (- a z) (- y z)))

simplify137.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	1043	3090
1	4307	3014
2	5001	3012

prune1.0s

Filtered

449 candidates to 271 candidates (60.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	442	7	449
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	446	11	457

Merged error: 3.8b

Counts

457 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.8b	(/ (cbrt (- t x)) (/ (cbrt (- a z)) (- y z)))
11.9b	(fma (/ (* (cbrt (- t x)) (cbrt (- t x))) (/ (* (cbrt (- a z)) (cbrt (- a z))) 1)) (/ (cbrt (- t x)) (/ (cbrt (- a z)) (- y z))) x)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

728×	`times-frac`
603×	`add-sqr-sqrt` `*-un-lft-identity`
470×	`cbrt-prod`
271×	`add-cube-cbrt`
166×	`distribute-lft-out--` `difference-of-squares`
46×	`associate-/r*`
19×	`associate-/r/`
12×	`flip3--` `flip--`
10×	`div-inv`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`cbrt-div` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow1/3` `associate-/l/`
1×	`frac-2neg` `clear-num` `fma-udef`

Counts

4 → 485

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
26.0ms	(/ (cbrt (- t x)) (/ (cbrt (- a z)) (- y z)))
1.0ms	(fma (/ (* (cbrt (- t x)) (cbrt (- t x))) (/ (* (cbrt (- a z)) (cbrt (- a z))) 1)) (/ (cbrt (- t x)) (/ (cbrt (- a z)) (- y z))) x)

series1.1s

Counts

4 → 12

Calls

4 calls:

162.0ms	(cbrt (- a z))
159.0ms	(cbrt (- a z))
174.0ms	(/ (cbrt (- t x)) (/ (cbrt (- a z)) (- y z)))
560.0ms	(fma (/ (* (cbrt (- t x)) (cbrt (- t x))) (/ (* (cbrt (- a z)) (cbrt (- a z))) 1)) (/ (cbrt (- t x)) (/ (cbrt (- a z)) (- y z))) x)

simplify122.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	1521	8208
1	5001	8035

prune1.8s

Filtered

497 candidates to 335 candidates (67.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	493	4	497
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	494	14	508

Merged error: 3.8b

Counts

508 → 14

regimes495.0ms

Accuracy

23.8% (6.7b remaining)

Error of 10.3b against oracle of 3.6b and baseline of 12.4b

bsearch215.0ms

Steps

Iters	Range		Point
8	9.287635583578815e+180	8.441796565691108e+183	2.188550894831957e+182
8	-4.493126295006387e+48	-1.376693901545937e+44	-4.407526637118989e+48
10	-3.969499018544341e+93	-3.344898669619616e+83	-1.7008839814515772e+84
9	-2.4597182572382793e+176	-2.2190483476432023e+170	-6.064203325484277e+171

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	37
1	41	37

end0.0ms

sample704.0ms

Algorithm

intervals

Results

270.0ms	7788×	body	80	valid
59.0ms	483×	body	640	valid
41.0ms	258×	body	1280	valid
39.0ms	423×	body	320	valid
17.0ms	277×	body	160	valid
3.0ms	18×	body	2560	valid