Details

sample31.0ms

Algorithm

intervals

Results

9.0ms	251×	body	80	valid
2.0ms	11×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	2×	body	2560	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	6
1	46	5
2	128	5
3	362	5
4	1024	5
5	2296	5
6	5001	5

prune7.0ms

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: 14.1b

Counts

2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
14.2b	(fma (- y z) (/ (- t x) (- a z)) x)

rewrite11.0ms

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:

8.0ms	(/ (- t x) (- a z))
1.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

series137.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- t x) (- a z))
88.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	268	450
1	733	425
2	2490	423
3	5001	421

prune200.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	57	13	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	58	14	72

Merged error: 5.7b

Counts

72 → 14

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.9b	(+ x (* (- y z) (/ (- t x) (- a z))))
4.4b	(* (- y z) (/ (- t x) (- a z)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
28×	`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/`
3×	`expm1-log1p-u` `fma-def` `log1p-expm1-u`
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 → 128

Calls

3 calls:

8.0ms	(/ (- t x) (- a z))
4.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
19.0ms	(* (- y z) (/ (- t x) (- a z)))

series317.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (- t x) (- a z))
143.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
124.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	488	901
1	2066	849
2	5001	847

prune307.0ms

Filtered

137 candidates to 95 candidates (69.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	128	9	137
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	137	14	151

Merged error: 3.4b

Counts

151 → 14

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.6b	(/ 1 (/ (- a z) (- t x)))
14.1b	(fma (- y z) (/ 1 (/ (- a z) (- t x))) x)

rewrite33.0ms

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:

8.0ms	(/ (- a z) (- t x))
12.0ms	(/ 1 (/ (- a z) (- t x)))
1.0ms	(fma (- y z) (/ 1 (/ (- a z) (- t x))) x)

series349.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (- a z) (- t x))
185.0ms	(/ 1 (/ (- a z) (- t x)))
113.0ms	(fma (- y z) (/ 1 (/ (- a z) (- t x))) x)

simplify71.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	632	1907
1	2802	1722
2	5001	1551

prune335.0ms

Filtered

223 candidates to 106 candidates (47.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	221	2	223
Fresh	4	9	13
Picked	0	1	1
Done	0	0	0
Total	225	12	237

Merged error: 3.4b

Counts

237 → 12

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
3.7b	(+ (/ (- y z) (/ (- a z) (- t x))) x)
4.5b	(/ (- y z) (/ (- a z) (- t x)))

rewrite118.0ms

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:

8.0ms	(/ (- a z) (- t x))
61.0ms	(+ (/ (- y z) (/ (- a z) (- t x))) x)
15.0ms	(/ (- y z) (/ (- a z) (- t x)))

series520.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (- a z) (- t x))
171.0ms	(+ (/ (- y z) (/ (- a z) (- t x))) x)
297.0ms	(/ (- y z) (/ (- a z) (- t x)))

simplify112.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	1035	3079
1	4296	3003
2	5001	3001

prune1.1s

Filtered

449 candidates to 270 candidates (60.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	439	10	449
Fresh	5	5	10
Picked	1	0	1
Done	1	0	1
Total	446	15	461

Merged error: 3.4b

Counts

461 → 15

regimes354.0ms

Accuracy

26.4% (6.2b remaining)

Error of 9.3b against oracle of 3.1b and baseline of 11.6b

bsearch58.0ms

Steps

Iters	Range		Point
6	1.2267941376108159e+216	6.778178219820912e+216	1.4177224063350496e+216
4	-2.3151170337336688e+173	-1.3452309363883822e+173	-2.2848080931916287e+173

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	11
1	29	11

end0.0ms

sample788.0ms

Algorithm

intervals

Results

312.0ms	7884×	body	80	valid
67.0ms	456×	body	640	valid
52.0ms	278×	body	1280	valid
42.0ms	396×	body	320	valid
18.0ms	252×	body	160	valid
4.0ms	18×	body	2560	valid