Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify87.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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: 5.6b

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))
5.3b	(/ (+ (+ (+ 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)))
39.0ms	(/ (/ (/ (+ (+ (+ 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)))

series371.0ms

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))
72.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify146.0ms

Algorithm

egg-herbie

Counts

488 → 488

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1513	12983
1	5002	12137

prune1.0s

Filtered

488 candidates to 299 candidates (61.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	479	9	488
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	481	9	490

Merged error: 1.5b

Counts

490 → 9

localize25.0ms

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))))
5.2b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.2b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite51.0ms

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))))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series415.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
110.0ms	(/ (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))

simplify72.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (47.0ms)

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

prune504.0ms

Filtered

189 candidates to 109 candidates (57.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	189	9	198

Merged error: 1.5b

Counts

198 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
5.2b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.2b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
11.1b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (fma 1.0 2.0 (+ alpha beta))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

88×	`times-frac`
74×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
48×	`sqrt-prod`
36×	`add-exp-log`
28×	`associate-/l*`
27×	`add-cbrt-cube`
19×	`div-exp`
12×	`cbrt-undiv` `distribute-lft-out`
8×	`associate-/r*`
6×	`pow1` `sqrt-div` `prod-exp`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3-+` `1-exp` `associate-/r/` `flip-+`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `hypot-def`
1×	`associate-*l/` `associate-/l/`

Counts

4 → 165

Calls

4 calls:

14.0ms	(/ (fma 1.0 2.0 (+ alpha beta)) (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))
22.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (fma 1.0 2.0 (+ alpha beta))))

series490.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
45.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
51.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
141.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (fma 1.0 2.0 (+ alpha beta))))

simplify93.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	676	2861
1	3075	2427
2	5001	2287

prune395.0ms

Filtered

177 candidates to 105 candidates (59.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	177	9	186

Merged error: 1.5b

Counts

186 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
5.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
30×	`cbrt-div`
27×	`associate-r`
26×	`add-sqr-sqrt`
25×	`cbrt-prod`
23×	`times-frac`
21×	`add-cube-cbrt`
16×	`add-exp-log` `frac-times` `flip3-+` `flip-+`
12×	`associate-*l/`
10×	`add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod` `distribute-lft-out`
5×	`associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `pow-prod-down` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`associate-l` `*-commutative` `div-inv`

Counts

4 → 116

Calls

4 calls:

33.0ms	(* (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ 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))

series266.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
58.0ms	(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))

simplify91.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	675	2478
1	2766	2233
2	5001	2128

prune380.0ms

Filtered

128 candidates to 104 candidates (81.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	128	9	137

Merged error: 1.5b

Counts

137 → 9

regimes93.0ms

Accuracy

56.9% (1.2b remaining)

Error of 2.2b against oracle of 1.1b and baseline of 3.7b

bsearch68.0ms

Steps

Iters	Range		Point
9	1.007730983848284e+158	5.015723311903944e+163	1.7419001788956927e+160

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	28
1	32	28

end0.0ms

sample639.0ms

Algorithm

intervals

Results

367.0ms	8000×	body	80	valid
127.0ms	8000×	pre	80	true