Details

analyze42.0ms

Algorithm

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

sample39.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify25.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5230	53

prune12.0ms

Filtered

1 candidates to 1 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: 47.4b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
0.0b	(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
2.7b	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))
46.3b	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log` `add-cbrt-cube`
32×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
24×	`associate-r`
23×	`frac-times` `associate-l`
22×	`prod-exp` `cbrt-unprod`
19×	`add-cube-cbrt` `times-frac`
18×	`associate-/r/`
17×	`flip3-+` `flip-+`
14×	`associate-*l/`
13×	`pow1` `associate-*r/`
12×	`cbrt-undiv` `div-exp`
9×	`flip3--` `flip--`
7×	`distribute-lft-out`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`pow-prod-down`
4×	`associate--l+` `add-log-exp`
3×	`-commutative` `div-inv` `associate-/l` `unswap-sqr`
2×	`sub-neg` `associate-/l/`
1×	`frac-2neg` `clear-num` `associate-/r*` `difference-of-squares`

Counts

4 → 165

Calls

4 calls:

17.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
17.0ms	(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
39.0ms	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))
27.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

series573.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
60.0ms	(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
324.0ms	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))
172.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

simplify79.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5012	5739

prune393.0ms

Filtered

129 candidates to 177 candidates (-37.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	170	7	177
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	172	7	179

Merged error: 34.5b

Counts

179 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
0.1b	(* (/ 1 (+ alpha (+ beta (* i 2.0)))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
2.7b	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (* (/ 1 (+ alpha (+ beta (* i 2.0)))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))
39.1b	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

156×	`add-exp-log`
92×	`add-cbrt-cube`
79×	`prod-exp`
67×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
56×	`times-frac`
43×	`div-exp` `cbrt-unprod`
38×	`add-cube-cbrt`
37×	`associate-l`
32×	`frac-times`
24×	`associate-r`
23×	`cbrt-undiv`
20×	`pow1` `associate-*r/`
17×	`associate-*l/`
13×	`flip3-+` `flip-+`
10×	`pow-prod-down`
9×	`distribute-lft-out`
8×	`rec-exp` `1-exp` `associate-/r/` `unswap-sqr`
7×	`difference-of-squares`
4×	`associate-/r*` `div-inv` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 225

Calls

4 calls:

14.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
32.0ms	(* (/ 1 (+ alpha (+ beta (* i 2.0)))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
41.0ms	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (* (/ 1 (+ alpha (+ beta (* i 2.0)))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))
22.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

series450.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
69.0ms	(* (/ 1 (+ alpha (+ beta (* i 2.0)))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
316.0ms	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (* (/ 1 (+ alpha (+ beta (* i 2.0)))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))
48.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

simplify78.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5022	9246

prune410.0ms

Filtered

145 candidates to 237 candidates (-63.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	234	3	237
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	238	6	244

Merged error: 32.5b

Counts

244 → 6

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
2.7b	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (* (/ 1 (+ alpha (+ beta (* i 2.0)))) (* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))))
33.0b	(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
33.0b	(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

376×	`add-exp-log`
217×	`prod-exp`
208×	`add-cbrt-cube`
113×	`cbrt-unprod`
103×	`div-exp`
100×	`*-un-lft-identity`
82×	`frac-times`
72×	`add-sqr-sqrt` `times-frac`
54×	`cbrt-undiv` `associate-*r/`
42×	`sqrt-prod`
40×	`add-cube-cbrt`
37×	`associate-r` `associate-l`
36×	`distribute-lft-out`
32×	`associate-*l/`
29×	`pow1`
20×	`flip3-+` `flip-+`
16×	`pow-prod-down`
15×	`rec-exp` `1-exp`
9×	`unswap-sqr`
4×	`sqrt-div` `associate-/r/` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative` `div-inv`

Counts

4 → 290

Calls

4 calls:

59.0ms	(* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
61.0ms	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (* (/ 1 (+ alpha (+ beta (* i 2.0)))) (* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))))
8.0ms	(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
8.0ms	(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

series512.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
397.0ms	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta))) (* (/ 1 (+ alpha (+ beta (* i 2.0)))) (* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))))
31.0ms	(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
36.0ms	(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

simplify114.0ms

Algorithm

egg-herbie

Counts

302 → 302

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5007	14551

prune488.0ms

Filtered

133 candidates to 302 candidates (-127.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	300	2	302
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	302	6	308

Merged error: 32.0b

Counts

308 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (* (+ i (+ alpha beta)) (/ i (+ alpha (+ beta (* i 2.0))))) (+ alpha (+ beta (* i 2.0)))) (* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))))
0.2b	(* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
33.0b	(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
33.0b	(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-exp-log` `add-cbrt-cube`
104×	`*-un-lft-identity`
76×	`times-frac`
74×	`add-sqr-sqrt`
50×	`prod-exp` `cbrt-unprod`
46×	`associate-l`
42×	`add-cube-cbrt` `sqrt-prod`
40×	`cbrt-undiv` `div-exp`
37×	`associate-r` `distribute-lft-out`
13×	`pow1`
9×	`unswap-sqr`
6×	`frac-times` `associate-*r/` `associate-/r/`
5×	`flip3-+` `flip-+`
4×	`sqrt-div` `pow-prod-down` `associate-*l/` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative`

Counts

4 → 199

Calls

4 calls:

56.0ms	(* (/ (* (+ i (+ alpha beta)) (/ i (+ alpha (+ beta (* i 2.0))))) (+ alpha (+ beta (* i 2.0)))) (* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))))
52.0ms	(* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
8.0ms	(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
8.0ms	(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

series509.0ms

Counts

4 → 12

Calls

4 calls:

396.0ms	(* (/ (* (+ i (+ alpha beta)) (/ i (+ alpha (+ beta (* i 2.0))))) (+ alpha (+ beta (* i 2.0)))) (* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))))
46.0ms	(* (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
36.0ms	(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
30.0ms	(sqrt (+ (* i (+ i (+ alpha beta))) (* alpha beta)))

simplify76.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5296	8955

prune529.0ms

Filtered

112 candidates to 211 candidates (-88.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	209	8	217

Merged error: 32.0b

Counts

217 → 8

regimes225.0ms

Accuracy

32.8% (2.6b remaining)

Error of 36.8b against oracle of 34.2b and baseline of 38.0b

bsearch23.0ms

Steps

Iters	Range		Point
8	6.642975198303638e+193	1.1758257102308071e+198	6.7438209606351525e+193

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	76
1	57	76

end0.0ms

sample1.0s

Algorithm

intervals

Results

651.0ms	8000×	body	80	valid
185.0ms	8000×	pre	80	true

Details

analyze42.0ms

sample39.0ms

simplify25.0ms

prune12.0ms

localize17.0ms

rewrite107.0ms

series573.0ms

simplify79.0ms

prune393.0ms

localize20.0ms

rewrite125.0ms

series450.0ms

simplify78.0ms

prune410.0ms

localize29.0ms

rewrite159.0ms

series512.0ms

simplify114.0ms

prune488.0ms

localize27.0ms

rewrite135.0ms

series509.0ms

simplify76.0ms

prune529.0ms

regimes225.0ms

bsearch23.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling