Details

sample26.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify79.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	17
1	114	17
2	563	17
3	4164	17
4	5002	17

prune2.0ms

Filtered

1 candidates to 0 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: 2.2b

Counts

2 → 1

localize13.0ms

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))
2.0b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
586×	`*-un-lft-identity`
340×	`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` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

8.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
22.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
37.0ms	(/ (/ (/ (+ (+ (+ 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)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
137.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
148.0ms	(/ (/ (/ (+ (+ (+ 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))
81.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify138.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune952.0ms

Filtered

477 candidates to 281 candidates (58.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	471	6	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	472	6	478

Merged error: 0.7b

Counts

478 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.4b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
1.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
80×	`sqrt-prod`
70×	`times-frac`
56×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
22×	`distribute-lft-out`
13×	`associate-/r*`
11×	`associate-/l*`
10×	`sqrt-div`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`
1×	`sqrt-undiv`

Counts

4 → 159

Calls

4 calls:

17.0ms	(/ (+ (+ (+ alpha beta) (* 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))))
10.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series415.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(/ (+ (+ (+ alpha beta) (* 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))))
46.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
52.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	507	2617
1	1942	2448
2	5003	2394

prune447.0ms

Filtered

171 candidates to 99 candidates (57.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	171	6	177

Merged error: 0.6b

Counts

177 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
1.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
1.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

64×	`sqrt-prod`
57×	`*-un-lft-identity`
42×	`times-frac`
40×	`add-sqr-sqrt`
37×	`add-cube-cbrt`
10×	`sqrt-div` `distribute-lft-out`
7×	`pow1` `associate-/l*`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 120

Calls

4 calls:

16.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
8.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series253.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
45.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
51.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
50.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify105.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	325	1790
1	1021	1680
2	4270	1636
3	5001	1636

prune423.0ms

Filtered

132 candidates to 81 candidates (61.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	132	6	138

Merged error: 0.6b

Counts

138 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.1b	(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
17.3b	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

171×	`times-frac`
109×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
96×	`add-cube-cbrt`
54×	`add-exp-log`
51×	`associate-r`
34×	`add-cbrt-cube`
26×	`div-exp`
22×	`associate-/r/`
19×	`associate-/l*`
15×	`flip3-+` `flip-+`
14×	`cbrt-undiv`
12×	`div-inv`
10×	`pow1` `prod-exp` `associate-/r*`
6×	`cbrt-unprod` `associate-/l/`
5×	`unswap-sqr`
4×	`frac-times` `rec-exp` `1-exp` `associate-l` `associate-*l/` `add-log-exp`
3×	`frac-2neg` `clear-num` `distribute-lft-out`
2×	`pow-flip` `associate-*r/` `inv-pow` `pow-div`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 235

Calls

4 calls:

7.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
34.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
15.0ms	(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
32.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
158.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
54.0ms	(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
149.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

simplify60.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	968	3787
1	5001	3271

prune563.0ms

Filtered

247 candidates to 166 candidates (67.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	247	6	253

Merged error: 0.6b

Counts

253 → 6

regimes65.0ms

Accuracy

56.3% (1.1b remaining)

Error of 2.4b against oracle of 1.3b and baseline of 3.9b

bsearch66.0ms

Steps

Iters	Range		Point
8	1.0440787543218478e+182	9.521274526809212e+185	1.1295199514491574e+182

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	44
1	37	44

end0.0ms

sample547.0ms

Algorithm

intervals

Results

302.0ms	8000×	body	80	valid
95.0ms	8000×	pre	80	true