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

simplify104.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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

prune9.0ms

Filtered

1 candidates to 1 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: 11.1b

Counts

2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
3.7b	(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:

10.0ms	(/ (- y z) (- a z))
1.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series183.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- y z) (- a z))
130.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify81.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	263	450
1	726	425
2	2550	423
3	5003	421

prune146.0ms

Filtered

70 candidates to 51 candidates (27.1%)

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: 4.0b

Counts

72 → 9

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

160×	`add-sqr-sqrt`
154×	`*-un-lft-identity`
77×	`times-frac`
70×	`add-cube-cbrt`
63×	`associate-l`
43×	`fma-def`
40×	`distribute-lft-out--` `difference-of-squares`
36×	`prod-diff`
30×	`frac-times`
23×	`flip3--` `flip--`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
20×	`associate-/r` `associate-/l`
15×	`associate-*l/`
10×	`add-exp-log` `associate-r` `add-cbrt-cube`
8×	`associate-/l/`
6×	`associate-/r/`
5×	`pow1` `add-log-exp`
4×	`sub-neg` `frac-2neg` `clear-num` `unswap-sqr`
3×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
2×	`cbrt-undiv` `associate-r/` `div-exp` `prod-exp` `-commutative` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `flip3-+` `div-sub` `pow-prod-down` `sum-log` `flip-+`

Counts

3 → 256

Calls

3 calls:

9.0ms	(/ (- y z) (- a z))
20.0ms	(* (/ (- y z) (- a z)) (- t x))
38.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)

series588.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ (- y z) (- a z))
332.0ms	(* (/ (- y z) (- a z)) (- t x))
198.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)

simplify150.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	944	1911
1	4528	1669
2	5001	1669

prune497.0ms

Filtered

265 candidates to 183 candidates (30.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	257	8	265
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	263	11	274

Merged error: 3.5b

Counts

274 → 11

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
2.5b	(/ (- t x) (/ (- a z) (- y z)))
2.7b	(+ (/ (- t x) (/ (- a z) (- y z))) x)

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

610×	`times-frac`
584×	`*-un-lft-identity`
582×	`add-sqr-sqrt`
204×	`add-cube-cbrt`
189×	`distribute-lft-out--` `difference-of-squares`
174×	`fma-def`
54×	`associate-/r/`
46×	`associate-/r*`
20×	`associate-/l*`
16×	`flip3--` `flip--`
14×	`div-inv`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l/`
5×	`add-log-exp`
4×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u`
1×	`+-commutative` `associate-+l-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 468

Calls

3 calls:

9.0ms	(/ (- a z) (- y z))
19.0ms	(/ (- t x) (/ (- a z) (- y z)))
73.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)

series448.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ (- a z) (- y z))
230.0ms	(/ (- t x) (/ (- a z) (- y z)))
160.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)

simplify152.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 2 (117.0ms)

Iter	Nodes	Cost
0	1084	3151
1	4439	3075
2	5002	3073

prune837.0ms

Filtered

477 candidates to 293 candidates (38.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	470	7	477
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	477	11	488

Merged error: 3.5b

Counts

488 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

136×	`add-sqr-sqrt` `*-un-lft-identity`
77×	`times-frac`
62×	`associate-r`
46×	`add-cube-cbrt`
43×	`fma-def`
42×	`distribute-lft-out--`
40×	`difference-of-squares`
30×	`frac-times`
23×	`flip3--` `flip--`
22×	`associate-/l*`
20×	`associate-/r*`
15×	`associate-*r/`
12×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l/`
6×	`associate-/r/`
5×	`pow1` `clear-num` `add-log-exp`
4×	`frac-2neg` `unswap-sqr`
3×	`expm1-log1p-u` `un-div-inv` `log1p-expm1-u` `div-inv` `distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod`
1×	`+-commutative` `flip3-+` `div-sub` `pow-prod-down` `sum-log` `flip-+`

Counts

3 → 216

Calls

3 calls:

12.0ms	(/ (- y z) (- a z))
21.0ms	(* (- t x) (/ (- y z) (- a z)))
35.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

series361.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ (- y z) (- a z))
128.0ms	(* (- t x) (/ (- y z) (- a z)))
175.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

simplify116.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	647	1324
1	3253	1274
2	5001	1272

prune388.0ms

Filtered

225 candidates to 157 candidates (30.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	225	11	236

Merged error: 3.5b

Counts

236 → 11

regimes304.0ms

Accuracy

-3.3% (8.7b remaining)

Error of 12.1b against oracle of 3.4b and baseline of 11.8b

bsearch96.0ms

Steps

Iters	Range		Point
6	6.205046733010805e-06	3.0981377036179784e-05	6.276232023584138e-06
9	-5.075255642507074e-86	-2.48737230382698e-95	-1.128219015475836e-90

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	12
1	31	12

end0.0ms

sample696.0ms

Algorithm

intervals

Results

260.0ms	7787×	body	80	valid
66.0ms	518×	body	640	valid
39.0ms	258×	body	1280	valid
34.0ms	376×	body	320	valid
20.0ms	320×	body	160	valid
4.0ms	21×	body	2560	valid