Details

sample24.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify82.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	33	17
1	122	15
2	598	13
3	4475	13
4	5001	13

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: 3.9b

Counts

2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
587×	`*-un-lft-identity`
341×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sum-log`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`fma-def` `frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 476

Calls

4 calls:

8.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
19.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
40.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
140.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
150.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
79.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify147.0ms

Algorithm

egg-herbie

Counts

488 → 488

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1513	12983
1	5002	12137

prune1.0s

Filtered

488 candidates to 299 candidates (61.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	480	8	488
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	482	8	490

Merged error: 1.3b

Counts

490 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
831×	`*-un-lft-identity`
384×	`add-sqr-sqrt` `add-cube-cbrt`
254×	`distribute-lft-out`
82×	`associate-/l*`
62×	`associate-/r/`
33×	`flip3-+` `flip-+`
31×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 536

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* beta alpha))
19.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
41.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ alpha beta) (* beta alpha))
147.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
155.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
82.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify154.0ms

Algorithm

egg-herbie

Counts

548 → 548

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1549	13893
1	5001	12967

prune1.0s

Filtered

548 candidates to 297 candidates (54.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	544	4	548
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	548	8	556

Merged error: 1.3b

Counts

556 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.5b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.5b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

126×	`*-un-lft-identity`
84×	`sqrt-prod`
77×	`times-frac`
62×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
39×	`distribute-lft-out`
13×	`associate-/r*`
12×	`associate-/l*`
10×	`sqrt-div`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `flip3-+` `flip-+`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `hypot-def` `div-inv`
1×	`sqrt-undiv`

Counts

4 → 177

Calls

4 calls:

15.0ms	(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
15.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
8.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series429.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
106.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
47.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
53.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify71.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	527	2718
1	1940	2545
2	5001	2473

prune506.0ms

Filtered

189 candidates to 109 candidates (57.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	189	8	197

Merged error: 1.3b

Counts

197 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta)))
1.9b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
52×	`times-frac`
34×	`add-sqr-sqrt`
32×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
14×	`distribute-lft-out`
9×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
5×	`associate-l`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `associate-l/` `associate-/r` `flip-+` `log1p-expm1-u` `div-inv`
3×	`associate-r` `prod-exp` `sum-log` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `clear-num` `associate-/r/` `fma-udef`
1×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 136

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* beta alpha))
8.0ms	(* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta)))
17.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))))
11.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (+ alpha beta) (* beta alpha))
36.0ms	(* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta)))
167.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))))
83.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify84.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	600	1864
1	2980	1619
2	5002	1609

prune334.0ms

Filtered

148 candidates to 106 candidates (71.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	148	8	156

Merged error: 1.3b

Counts

156 → 8

regimes79.0ms

Accuracy

54.2% (1.3b remaining)

Error of 2.3b against oracle of 1.0b and baseline of 3.9b

bsearch76.0ms

Steps

Iters	Range		Point
9	3.500794972217022e+132	6.485357508963688e+139	6.14863726142867e+139

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	28
1	40	28

end0.0ms

sample527.0ms

Algorithm

intervals

Results

294.0ms	8000×	body	80	valid
93.0ms	8000×	pre	80	true