Details

analyze43.0ms

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

sample40.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5230	53

prune11.0ms

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: 49.7b

Counts

2 → 2

localize18.0ms

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))
4.2b	(* (* (/ 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))))
48.8b	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

rewrite102.0ms

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))
36.0ms	(* (* (/ 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)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
57.0ms	(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
309.0ms	(* (* (/ 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))))
160.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

simplify74.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5012	5739

prune363.0ms

Filtered

129 candidates to 177 candidates (-37.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	171	6	177
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	173	6	179

Merged error: 36.3b

Counts

179 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ i (+ alpha (+ beta (* i 2.0))))
0.0b	(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
0.1b	(* (* (/ 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)))
41.8b	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
56×	`times-frac`
51×	`add-exp-log` `add-cbrt-cube`
48×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
25×	`distribute-lft-out`
18×	`associate-r` `prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `div-exp`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`pow1`
8×	`associate-/r/`
7×	`difference-of-squares`
5×	`frac-times` `associate-*l/`
4×	`flip3-+` `flip-+` `div-inv` `associate-/l/` `add-log-exp`
3×	`frac-2neg` `associate-*r/` `pow-prod-down` `clear-num`
2×	`flip3--` `flip--`
1×	`associate-l` `*-commutative`

Counts

4 → 169

Calls

4 calls:

6.0ms	(/ i (+ alpha (+ beta (* i 2.0))))
12.0ms	(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
36.0ms	(* (* (/ 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)))
21.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

series387.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ i (+ alpha (+ beta (* i 2.0))))
13.0ms	(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
312.0ms	(* (* (/ 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)))
48.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5036	5620

prune308.0ms

Filtered

117 candidates to 181 candidates (-54.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	177	4	181
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	180	7	187

Merged error: 34.9b

Counts

187 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ 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 (+ 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))))))
36.2b	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))

rewrite120.0ms

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:

10.0ms	(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
42.0ms	(* (* (/ 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)))))))
35.0ms	(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
16.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))

series510.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
386.0ms	(* (* (/ 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)))))))
82.0ms	(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0))))))
29.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (- (* i 2.0) (sqrt 1.0)))))

simplify81.0ms

Algorithm

egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5082	10440

prune397.0ms

Filtered

124 candidates to 267 candidates (-115.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	265	2	267
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	268	6	274

Merged error: 6.9b

Counts

274 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))
0.0b	(/ (+ 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) (+ (* (sqrt 1.0) 0.25) (* 0.125 (/ 1.0 i))))))
0.2b	(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (+ (* i 0.5) (+ (* (sqrt 1.0) 0.25) (* 0.125 (/ 1.0 i)))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-exp-log`
108×	`*-un-lft-identity`
82×	`add-cbrt-cube`
69×	`prod-exp`
52×	`times-frac`
42×	`add-sqr-sqrt` `distribute-lft-out`
39×	`cbrt-unprod`
35×	`add-cube-cbrt` `div-exp`
31×	`frac-times`
22×	`associate-l`
21×	`associate-*r/`
20×	`cbrt-undiv`
19×	`pow1`
14×	`flip3-+` `associate-*l/` `flip-+`
9×	`pow-prod-down` `associate-/r*`
8×	`associate-/l*`
7×	`rec-exp` `1-exp`
6×	`associate-/r/`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 216

Calls

4 calls:

9.0ms	(/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))
11.0ms	(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
36.0ms	(* (* (/ 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) (+ (* (sqrt 1.0) 0.25) (* 0.125 (/ 1.0 i))))))
18.0ms	(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (+ (* i 0.5) (+ (* (sqrt 1.0) 0.25) (* 0.125 (/ 1.0 i)))))

series144.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))
13.0ms	(/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))
62.0ms	(* (* (/ 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) (+ (* (sqrt 1.0) 0.25) (* 0.125 (/ 1.0 i))))))
54.0ms	(* (/ 1 (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (+ (* i 0.5) (+ (* (sqrt 1.0) 0.25) (* 0.125 (/ 1.0 i)))))

simplify81.0ms

Algorithm

egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5017	7554

prune419.0ms

Filtered

118 candidates to 228 candidates (-93.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	216	12	228
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	217	17	234

Merged error: 6.9b

Counts

234 → 17

regimes390.0ms

Accuracy

49.9% (2.9b remaining)

Error of 10.3b against oracle of 7.4b and baseline of 13.2b

bsearch8.0ms

Steps

Iters	Range		Point
2	2.324065703597001e+133	2.8654911335723583e+133	2.6624565973315987e+133

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	112
1	73	112

end0.0ms

sample1.0s

Algorithm

intervals

Results

662.0ms	8000×	body	80	valid
178.0ms	8000×	pre	80	true

Details

analyze43.0ms

sample40.0ms

simplify26.0ms

prune11.0ms

localize18.0ms

rewrite102.0ms

series542.0ms

simplify74.0ms

prune363.0ms

localize18.0ms

rewrite81.0ms

series387.0ms

simplify55.0ms

prune308.0ms

localize25.0ms

rewrite120.0ms

series510.0ms

simplify81.0ms

prune397.0ms

localize25.0ms

rewrite84.0ms

series144.0ms

simplify81.0ms

prune419.0ms

regimes390.0ms

bsearch8.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling