Details

sample23.0ms

Algorithm

intervals

Results

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

simplify81.0ms

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

prune7.0ms

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: 3.1b

Counts

2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.0b	(+ (+ alpha beta) (* beta alpha))
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))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite117.0ms

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`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
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 → 475

Calls

4 calls:

20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
6.0ms	(+ (+ alpha beta) (* beta alpha))
41.0ms	(/ (/ (/ (+ (+ (+ 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)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
17.0ms	(+ (+ alpha beta) (* beta alpha))
164.0ms	(/ (/ (/ (+ (+ (+ 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))
98.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify137.0ms

Algorithm

egg-herbie

Counts

487 → 487

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1534	13079
1	5001	12129

prune1.1s

Filtered

487 candidates to 297 candidates (61.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	480	7	487
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	482	7	489

Merged error: 0.7b

Counts

489 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

210×	`times-frac`
160×	`*-un-lft-identity`
120×	`add-sqr-sqrt` `sqrt-prod`
108×	`add-cube-cbrt`
26×	`distribute-lft-out`
20×	`associate-/r/`
12×	`flip3-+` `flip-+`
10×	`div-inv`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
6×	`pow1` `rem-sqrt-square` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

4 → 224

Calls

4 calls:

21.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
24.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
15.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
15.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series540.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
193.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
80.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify95.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	644	4874
1	2380	4546
2	5001	4384

prune857.0ms

Filtered

236 candidates to 168 candidates (71.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	236	0	236
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	236	7	243

Merged error: 0.7b

Counts

243 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

1.6b	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.1b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.1b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.1b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
17×	`*-un-lft-identity`
12×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`flip3-+` `flip-+`
9×	`add-exp-log`
8×	`associate-/l/`
7×	`add-cbrt-cube`
6×	`times-frac` `associate-/r*` `sqrt-prod`
4×	`pow1` `expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
2×	`cbrt-undiv` `sqrt-div` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 87

Calls

4 calls:

26.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series427.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
61.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
65.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
65.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	524	1497
1	1755	1376
2	5001	1341

prune501.0ms

Filtered

99 candidates to 87 candidates (87.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	99	7	106

Merged error: 0.7b

Counts

106 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
1.2b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 142

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* beta alpha))
8.0ms	(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
21.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ alpha beta) (* beta alpha))
42.0ms	(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
179.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify103.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	708	2094
1	3754	1752
2	5001	1749

prune449.0ms

Filtered

154 candidates to 113 candidates (73.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	154	7	161

Merged error: 0.7b

Counts

161 → 7

regimes77.0ms

Accuracy

40.6% (1.6b remaining)

Error of 2.8b against oracle of 1.2b and baseline of 3.9b

bsearch52.0ms

Steps

Iters	Range		Point
6	4.909214320538352e+91	3.7507584931071266e+92	7.929088531646719e+91

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	46
1	44	46

end0.0ms

sample535.0ms

Algorithm

intervals

Results

299.0ms	8000×	body	80	valid
96.0ms	8000×	pre	80	true