Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	252×	body	80	valid
2.0ms	16×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	5×	body	1280	valid
1.0ms	10×	body	160	valid

simplify88.0ms

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	1907	5
6	4560	5
7	5001	5

prune9.0ms

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: 10.4b

Counts

2 → 2

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
13.5b	(fma (/ (- y x) (- a t)) (- z t) 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 x) (- a t))
1.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series147.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- y x) (- a t))
94.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify68.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	269	450
1	734	425
2	2488	423
3	5002	423

prune223.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 5.5b

Counts

72 → 10

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.3b	(* (- y x) (/ 1 (- a t)))
13.4b	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

rewrite26.0ms

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 t))
15.0ms	(* (- y x) (/ 1 (- a t)))
1.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

series191.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ 1 (- a t))
52.0ms	(* (- y x) (/ 1 (- a t)))
97.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

simplify50.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	351	602
1	1495	525
2	5001	481

prune244.0ms

Filtered

114 candidates to 68 candidates (59.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	113	11	124

Merged error: 5.5b

Counts

124 → 11

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- y x))
0.5b	(/ 1 (/ (- a t) (- y x)))
13.4b	(fma (/ 1 (/ (- a t) (- y x))) (- z t) x)

rewrite34.0ms

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:

9.0ms	(/ (- a t) (- y x))
13.0ms	(/ 1 (/ (- a t) (- y x)))
1.0ms	(fma (/ 1 (/ (- a t) (- y x))) (- z t) x)

series435.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(/ (- a t) (- y x))
243.0ms	(/ 1 (/ (- a t) (- y x)))
132.0ms	(fma (/ 1 (/ (- a t) (- y x))) (- z t) x)

simplify83.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	633	1907
1	2810	1722
2	5002	1551

prune405.0ms

Filtered

223 candidates to 104 candidates (46.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	219	4	223
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	220	14	234

Merged error: 5.4b

Counts

234 → 14

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- y x))
2.9b	(+ (/ (- z t) (/ (- a t) (- y x))) x)
4.8b	(/ (- z t) (/ (- a t) (- y x)))

rewrite135.0ms

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

series838.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ (- a t) (- y x))
436.0ms	(+ (/ (- z t) (/ (- a t) (- y x))) x)
343.0ms	(/ (- z t) (/ (- a t) (- y x)))

simplify134.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	1036	3079
1	4296	3003
2	5002	3001

prune1.0s

Filtered

449 candidates to 270 candidates (60.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	437	12	449
Fresh	9	2	11
Picked	1	0	1
Done	1	1	2
Total	448	15	463

Merged error: 3.3b

Counts

463 → 15

regimes382.0ms

Accuracy

8.6% (7.2b remaining)

Error of 10.9b against oracle of 3.7b and baseline of 11.6b

bsearch66.0ms

Steps

Iters	Range		Point
7	2.624083394351866e-144	1.499003438552207e-142	4.809187786061145e-143
3	-2.59558649177248e+233	-1.8773957778754964e+233	-2.543835360887081e+233

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	20
1	27	20

end0.0ms

sample734.0ms

Algorithm

intervals

Results

278.0ms	7791×	body	80	valid
67.0ms	481×	body	640	valid
45.0ms	282×	body	1280	valid
37.0ms	384×	body	320	valid
18.0ms	271×	body	160	valid
5.0ms	23×	body	2560	valid