Details

sample45.0ms

Algorithm

intervals

Results

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

simplify22.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4954	53
1	4954	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: 47.7b

Counts

2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ i (+ alpha (+ beta (* i 2.0))))
0.1b	(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
5.6b	(* (* (/ 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))))
47.4b	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log` `add-cbrt-cube`
45×	`*-un-lft-identity`
31×	`add-sqr-sqrt` `times-frac`
26×	`add-cube-cbrt`
21×	`prod-exp` `cbrt-unprod`
20×	`associate-r` `associate-/r/`
19×	`frac-times` `associate-l`
15×	`flip3-+` `flip-+`
13×	`cbrt-undiv` `div-exp`
12×	`associate-*l/`
11×	`pow1` `associate-*r/`
10×	`distribute-lft-out`
6×	`flip3--` `flip--` `associate-/l*`
5×	`associate-/r*`
4×	`pow-prod-down` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative` `associate-/l/` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 164

Calls

4 calls:

7.0ms	(/ i (+ alpha (+ beta (* i 2.0))))
20.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
40.0ms	(* (* (/ 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))))
28.0ms	(/ (+ (* 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:

15.0ms	(/ i (+ alpha (+ beta (* i 2.0))))
18.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
360.0ms	(* (* (/ 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))))
180.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

simplify72.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4998	5111
1	4998	5111

prune395.0ms

Filtered

126 candidates to 176 candidates (-39.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	170	6	176
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	172	6	178

Merged error: 36.2b

Counts

178 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
0.1b	(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
0.2b	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
41.1b	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

123×	`*-un-lft-identity`
80×	`times-frac`
69×	`add-sqr-sqrt`
61×	`add-exp-log` `add-cbrt-cube`
50×	`add-cube-cbrt`
44×	`associate-r`
41×	`distribute-lft-out`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp` `associate-l`
11×	`pow1`
10×	`associate-/r/`
8×	`associate-/r` `associate-/l`
7×	`difference-of-squares`
6×	`frac-times` `associate-*l/`
5×	`flip3-+` `flip-+` `div-inv`
4×	`associate-*r/` `pow-prod-down` `associate-/l/` `add-log-exp` `unswap-sqr`
2×	`flip3--` `frac-2neg` `clear-num` `*-commutative` `flip--`

Counts

4 → 204

Calls

4 calls:

27.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
13.0ms	(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
44.0ms	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ 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))

series466.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
18.0ms	(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
361.0ms	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
61.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

simplify85.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4971	6791
1	4971	6791

prune408.0ms

Filtered

134 candidates to 216 candidates (-61.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	209	7	216
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	213	9	222

Merged error: 34.9b

Counts

222 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
0.2b	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))))
0.2b	(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
35.7b	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

262×	`add-exp-log`
150×	`add-cbrt-cube`
132×	`*-un-lft-identity`
129×	`prod-exp`
86×	`div-exp`
72×	`times-frac`
69×	`cbrt-unprod`
60×	`add-sqr-sqrt`
51×	`distribute-lft-out`
46×	`cbrt-undiv`
43×	`add-cube-cbrt`
22×	`associate-r` `associate-l`
18×	`pow1` `frac-times`
12×	`rec-exp` `1-exp` `associate-r/` `associate-l/`
9×	`pow-prod-down` `associate-/r*`
8×	`associate-/r/` `associate-/l*`
6×	`flip3-+` `flip-+` `unswap-sqr`
4×	`div-inv` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative`

Counts

4 → 255

Calls

4 calls:

13.0ms	(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
50.0ms	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))))
37.0ms	(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
18.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
1.0s	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))))
92.0ms	(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
39.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))

simplify85.0ms

Algorithm

egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5053	10440

prune485.0ms

Filtered

123 candidates to 267 candidates (-117.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	263	4	267
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	266	10	276

Merged error: 9.2b

Counts

276 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
0.1b	(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
0.1b	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (+ (* i 0.5) (+ (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25)))))
0.2b	(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (+ (* i 0.5) (+ (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

142×	`add-exp-log`
132×	`*-un-lft-identity`
92×	`add-cbrt-cube`
73×	`times-frac` `prod-exp`
62×	`add-sqr-sqrt`
50×	`distribute-lft-out`
43×	`add-cube-cbrt` `cbrt-unprod`
40×	`associate-l`
37×	`div-exp`
32×	`frac-times`
30×	`associate-r`
23×	`cbrt-undiv`
22×	`associate-*r/`
20×	`pow1`
15×	`flip3-+` `associate-*l/` `flip-+`
10×	`pow-prod-down`
8×	`associate-/r/`
7×	`unswap-sqr`
6×	`rec-exp` `1-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-/l*`
4×	`associate-/r*` `div-inv` `add-log-exp`
3×	`*-commutative`
2×	`associate-/l/`
1×	`frac-2neg` `clear-num`

Counts

4 → 243

Calls

4 calls:

28.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
13.0ms	(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
45.0ms	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (+ (* i 0.5) (+ (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25)))))
22.0ms	(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (+ (* i 0.5) (+ (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25))))

series175.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
15.0ms	(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
71.0ms	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (+ (* i 0.5) (+ (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25)))))
61.0ms	(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (+ (* i 0.5) (+ (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25))))

simplify75.0ms

Algorithm

egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5002	8579

prune646.0ms

Filtered

142 candidates to 255 candidates (-79.6%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	241	14	255
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	242	23	265

Merged error: 9.2b

Counts

265 → 23

regimes543.0ms

Accuracy

51.9% (2.9b remaining)

Error of 10.1b against oracle of 7.2b and baseline of 13.2b

bsearch24.0ms

Steps

Iters	Range		Point
6	1.825901322534054e+129	1.4822102956726603e+130	9.162949724139249e+129

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	112
1	63	112

end0.0ms

sample1.3s

Algorithm

intervals

Results

748.0ms	8000×	body	80	valid
181.0ms	8000×	pre	80	true

Details

sample45.0ms

simplify22.0ms

prune12.0ms

localize23.0ms

rewrite103.0ms

series573.0ms

simplify72.0ms

prune395.0ms

localize19.0ms

rewrite116.0ms

series466.0ms

simplify85.0ms

prune408.0ms

localize28.0ms

rewrite135.0ms

series1.2s

simplify85.0ms

prune485.0ms

localize27.0ms

rewrite121.0ms

series175.0ms

simplify75.0ms

prune646.0ms

regimes543.0ms

bsearch24.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling