Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	248×	body	80	valid
2.0ms	15×	body	640	valid
1.0ms	16×	body	320	valid
1.0ms	8×	body	1280	valid
0.0ms	8×	body	160	valid

simplify89.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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

prune10.0ms

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: 11.0b

Counts

2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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)

series179.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- y z) (- a z))
129.0ms	(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

prune226.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	10	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 3.6b

Counts

72 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- y z) (/ 1 (- a z)))
4.2b	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-l` `associate-/r*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 105

Calls

3 calls:

6.0ms	(/ 1 (- a z))
13.0ms	(* (- y z) (/ 1 (- a z)))
1.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

series216.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ 1 (- a z))
56.0ms	(* (- y z) (/ 1 (- a z)))
123.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify50.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	340	602
1	1472	525
2	5002	481

prune257.0ms

Filtered

114 candidates to 71 candidates (62.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	114	11	125

Merged error: 3.6b

Counts

125 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
0.4b	(/ 1 (/ (- a z) (- y z)))
2.5b	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

rewrite37.0ms

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:

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

series328.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- a z) (- y z))
149.0ms	(/ 1 (/ (- a z) (- y z)))
127.0ms	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

simplify88.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (61.0ms)

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

prune398.0ms

Filtered

223 candidates to 107 candidates (48.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	219	4	223
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	223	11	234

Merged error: 3.5b

Counts

234 → 11

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
1.6b	(/ (- t x) (/ (- a z) (- y z)))
1.9b	(+ (/ (- t x) (/ (- a z) (- y z))) x)

rewrite128.0ms

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))
22.0ms	(/ (- t x) (/ (- a z) (- y z)))
65.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)

series448.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ (- a z) (- y z))
221.0ms	(/ (- t x) (/ (- a z) (- y z)))
168.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)

simplify116.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 2 (83.0ms)

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

prune991.0ms

Filtered

449 candidates to 271 candidates (60.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	442	7	449
Fresh	6	3	9
Picked	0	1	1
Done	1	0	1
Total	449	11	460

Merged error: 3.5b

Counts

460 → 11

regimes355.0ms

Accuracy

23.9% (6.4b remaining)

Error of 10.0b against oracle of 3.6b and baseline of 12.0b

bsearch70.0ms

Steps

Iters	Range		Point
7	3.0056805004922944e+190	1.625455215461017e+192	9.100194368894704e+191
4	-3.542713222812643e+246	-2.135390510436753e+246	-3.216598382673023e+246

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	10
1	25	10

end0.0ms

sample707.0ms

Algorithm

intervals

Results

264.0ms	7827×	body	80	valid
58.0ms	462×	body	640	valid
47.0ms	292×	body	1280	valid
39.0ms	427×	body	320	valid
17.0ms	266×	body	160	valid
4.0ms	20×	body	2560	valid