Details

sample33.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	60	25
1	296	23
2	1711	23
3	5001	23

prune12.0ms

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: 51.1b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
0.1b	(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
40.6b	(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
41.0b	(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log` `add-cbrt-cube`
17×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt` `times-frac`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
10×	`associate-l/` `associate-/r`
6×	`associate-r`
5×	`associate-l`
4×	`expm1-log1p-u` `pow-prod-down` `fma-udef` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
3×	`flip3--` `flip--`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-r/` `clear-num` `-commutative` `associate-/l*`
1×	`flip3-+` `associate-/r/` `flip-+` `difference-of-squares` `unswap-sqr`

Counts

4 → 122

Calls

4 calls:

17.0ms	(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
16.0ms	(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
21.0ms	(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
18.0ms	(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series3.4s

Counts

4 → 12

Calls

4 calls:

508.0ms	(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
268.0ms	(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
755.0ms	(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
1.9s	(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify56.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	794	3237
1	5002	2435

prune449.0ms

Filtered

134 candidates to 97 candidates (72.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	126	8	134
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	127	9	136

Merged error: 44.1b

Counts

136 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ (+ alpha beta) (* 2.0 i)) 3)
0.8b	(/ 1 (fma beta alpha (* i (+ (+ alpha beta) i))))
5.7b	(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
40.2b	(/ (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

261×	`times-frac`
115×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
78×	`add-exp-log`
48×	`add-cbrt-cube`
46×	`div-exp`
31×	`associate-/r/`
27×	`div-inv`
25×	`cbrt-undiv`
19×	`associate-/r*`
16×	`flip3-+` `flip-+`
13×	`associate-/l*`
10×	`prod-exp`
6×	`pow1` `cbrt-unprod`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `frac-2neg` `cube-prod` `clear-num`
2×	`cube-div` `associate-/l/`
1×	`cube-mult` `pow-to-exp` `pow-flip` `pow-pow` `unpow3` `associate-*r/` `pow-exp` `inv-pow` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 265

Calls

4 calls:

7.0ms	(pow (+ (+ alpha beta) (* 2.0 i)) 3)
3.0ms	(/ 1 (fma beta alpha (* i (+ (+ alpha beta) i))))
20.0ms	(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
28.0ms	(/ (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

168.0ms	(pow (+ (+ alpha beta) (* 2.0 i)) 3)
123.0ms	(/ 1 (fma beta alpha (* i (+ (+ alpha beta) i))))
375.0ms	(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
979.0ms	(/ (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))

simplify110.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1528	8113
1	5001	7082

prune710.0ms

Filtered

277 candidates to 144 candidates (52.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	273	4	277
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	276	10	286

Merged error: 44.1b

Counts

286 → 10

localize32.0ms

Local error

Found 4 expressions with local error:

5.7b	(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
5.7b	(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
40.2b	(/ (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))
40.2b	(/ (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

504×	`times-frac`
204×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
142×	`add-exp-log`
88×	`div-exp`
86×	`add-cbrt-cube`
62×	`associate-/r/`
52×	`div-inv`
48×	`cbrt-undiv`
32×	`associate-/r*`
30×	`flip3-+` `flip-+`
20×	`prod-exp` `associate-/l*`
12×	`cbrt-unprod`
8×	`rec-exp` `1-exp`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`associate-*r/`

Counts

4 → 410

Calls

4 calls:

20.0ms	(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
25.0ms	(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
30.0ms	(/ (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))
29.0ms	(/ (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))

series2.7s

Counts

4 → 12

Calls

4 calls:

365.0ms	(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
363.0ms	(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
977.0ms	(/ (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))
963.0ms	(/ (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))

simplify162.0ms

Algorithm

egg-herbie

Counts

422 → 422

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1321	15324
1	5001	13472

prune1.7s

Filtered

422 candidates to 258 candidates (61.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	422	0	422
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	422	10	432

Merged error: 44.1b

Counts

432 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

35.1b	(sqrt (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))
35.1b	(sqrt (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))
36.2b	(sqrt (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))
36.2b	(sqrt (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

44×	`sqrt-prod`
32×	`add-sqr-sqrt`
28×	`times-frac`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
10×	`pow1`
8×	`rem-sqrt-square` `sqrt-pow1`
4×	`add-exp-log` `expm1-log1p-u` `pow1/2` `sqrt-div` `associate-/r/` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow-flip` `flip3-+` `flip-+` `inv-pow`

Counts

4 → 104

Calls

4 calls:

18.0ms	(sqrt (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))
19.0ms	(sqrt (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))
3.0ms	(sqrt (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))
3.0ms	(sqrt (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

699.0ms	(sqrt (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))
694.0ms	(sqrt (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))
82.0ms	(sqrt (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))
83.0ms	(sqrt (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	266	1548
1	961	1478
2	5001	1448

prune504.0ms

Filtered

116 candidates to 88 candidates (75.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	116	10	126

Merged error: 44.1b

Counts

126 → 10

regimes252.0ms

Accuracy

38.7% (2.5b remaining)

Error of 47.3b against oracle of 44.8b and baseline of 48.8b

bsearch253.0ms

Steps

Iters	Range		Point
8	2.728125315629635e+100	1.6606524682588424e+103	1.1017636739463882e+101

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	47
1	44	47
2	45	47
3	45	47

end0.0ms

sample795.0ms

Algorithm

intervals

Results

422.0ms	8000×	body	80	valid
175.0ms	8000×	pre	80	true