Details

sample43.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4954	53
1	4954	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: 46.6b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
0.1b	(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
4.1b	(* (* (/ 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)))

rewrite97.0ms

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-rgt-in` `distribute-lft-in` `distribute-lft-out`
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 → 167

Calls

4 calls:

16.0ms	(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
14.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
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))))
24.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
15.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (+ i (+ alpha beta)))
307.0ms	(* (* (/ 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))))
162.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))

simplify65.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5011	5777

prune422.0ms

Filtered

129 candidates to 179 candidates (-38.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	171	8	179
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	172	9	181

Merged error: 33.9b

Counts

181 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 192

Calls

4 calls:

24.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
6.0ms	(/ i (+ alpha (+ beta (* i 2.0))))
39.0ms	(* (* (/ 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)))
19.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

series389.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
12.0ms	(/ i (+ alpha (+ beta (* i 2.0))))
301.0ms	(* (* (/ 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)))
52.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

simplify87.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4968	6381
1	4968	6381

prune370.0ms

Filtered

131 candidates to 204 candidates (-55.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	197	7	204
Fresh	4	3	7
Picked	1	0	1
Done	1	0	1
Total	203	10	213

Merged error: 31.3b

Counts

213 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ i (+ alpha (+ beta (* i 2.0))))
0.0b	(/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))
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) (sqrt 1.0))))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))
34.1b	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

670×	`*-un-lft-identity`
546×	`times-frac`
374×	`add-sqr-sqrt`
202×	`add-cube-cbrt`
194×	`distribute-lft-out`
153×	`associate-r`
86×	`distribute-lft-out--` `difference-of-squares`
82×	`add-exp-log` `add-cbrt-cube`
43×	`sqrt-prod`
38×	`associate-/r/`
32×	`cbrt-undiv` `div-exp`
27×	`prod-exp` `cbrt-unprod` `associate-/l*`
19×	`div-inv`
18×	`flip3-+` `flip-+`
16×	`associate-/r*`
9×	`pow1`
5×	`frac-times` `associate-*l/`
4×	`add-log-exp`
3×	`frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `associate-/l/`
2×	`flip3--` `flip--`
1×	`associate-l` `*-commutative`

Counts

4 → 465

Calls

4 calls:

6.0ms	(/ i (+ alpha (+ beta (* i 2.0))))
25.0ms	(/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))
62.0ms	(* (* (/ 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) (sqrt 1.0))))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))
16.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

series464.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ i (+ alpha (+ beta (* i 2.0))))
44.0ms	(/ (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0))))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))
380.0ms	(* (* (/ 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) (sqrt 1.0))))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))
27.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (+ alpha (+ beta (+ (* i 2.0) (sqrt 1.0)))))

simplify156.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4998	23070
1	4998	23070

prune1.2s

Filtered

215 candidates to 477 candidates (-121.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	472	5	477
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	476	11	487

Merged error: 7.9b

Counts

487 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
0.0b	(/ i (+ alpha (+ beta (* i 2.0))))
0.0b	(/ (+ (* i 0.5) (- (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))
0.1b	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 0.5) (- (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

133×	`*-un-lft-identity`
94×	`add-sqr-sqrt`
90×	`times-frac`
61×	`add-exp-log` `add-cbrt-cube`
54×	`add-cube-cbrt`
53×	`associate-r`
31×	`distribute-lft-out`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp` `associate-l`
14×	`distribute-lft-out--` `difference-of-squares`
11×	`pow1` `associate-/r*`
10×	`associate-/r/`
7×	`sqrt-prod`
6×	`frac-times` `associate-l/` `associate-/l`
5×	`div-inv`
4×	`flip3-+` `associate-*r/` `pow-prod-down` `flip-+` `add-log-exp` `unswap-sqr`
2×	`flip3--` `frac-2neg` `clear-num` `*-commutative` `flip--` `associate-/l/`
1×	`associate-+r-` `div-sub`

Counts

4 → 214

Calls

4 calls:

23.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
6.0ms	(/ i (+ alpha (+ beta (* i 2.0))))
15.0ms	(/ (+ (* i 0.5) (- (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))
36.0ms	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 0.5) (- (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))

series124.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0)))))
15.0ms	(/ i (+ alpha (+ beta (* i 2.0))))
21.0ms	(/ (+ (* i 0.5) (- (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0)))
65.0ms	(* (* (/ i (+ alpha (+ beta (* i 2.0)))) (/ (+ i (+ alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 0.5) (- (* 0.125 (/ 1.0 i)) (* (sqrt 1.0) 0.25))) (- (+ alpha (+ beta (* i 2.0))) (sqrt 1.0))))

simplify67.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5264	7111

prune793.0ms

Filtered

134 candidates to 226 candidates (-68.7%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	211	15	226
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	212	25	237

Merged error: 7.9b

Counts

237 → 25

regimes609.0ms

Accuracy

52% (2.9b remaining)

Error of 10.4b against oracle of 7.5b and baseline of 13.5b

bsearch27.0ms

Steps

Iters	Range		Point
8	6.613116010031684e+111	1.803367467110541e+115	1.076042761241928e+115

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	112
1	60	112

end0.0ms

sample1.1s

Algorithm

intervals

Results

621.0ms	8000×	body	80	valid
167.0ms	8000×	pre	80	true

Details

sample43.0ms

simplify26.0ms

prune11.0ms

localize17.0ms

rewrite97.0ms

series539.0ms

simplify65.0ms

prune422.0ms

localize18.0ms

rewrite96.0ms

series389.0ms

simplify87.0ms

prune370.0ms

localize24.0ms

rewrite146.0ms

series464.0ms

simplify156.0ms

prune1.2s

localize20.0ms

rewrite89.0ms

series124.0ms

simplify67.0ms

prune793.0ms

regimes609.0ms

bsearch27.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling