Details

analyze125.0ms

Algorithm

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

sample40.0ms

Algorithm

intervals

Results

11.0ms	205×	body	80	valid
7.0ms	16×	body	1280	valid
5.0ms	256×	pre	80	true
5.0ms	23×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5446	29

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: 17.7b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
1.5b	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
2.6b	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
17.3b	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
22×	`associate-r`
21×	`add-sqr-sqrt` `flip3-+` `flip-+`
20×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/r/`
14×	`frac-times`
11×	`add-cube-cbrt`
10×	`times-frac`
8×	`pow1` `associate-l` `associate-*l/`
7×	`associate-*r/`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`distribute-lft-out` `associate-/l*`
4×	`cbrt-undiv` `div-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow-prod-down` `*-commutative` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `div-sub` `clear-num` `associate-/r*` `sum-log` `flip--`

Counts

4 → 120

Calls

4 calls:

13.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
22.0ms	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
23.0ms	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
16.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

series205.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
62.0ms	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
85.0ms	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
38.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5522	3306

prune271.0ms

Filtered

106 candidates to 132 candidates (-24.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	126	6	132
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	128	6	134

Merged error: 5.1b

Counts

134 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
0.1b	(* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
1.5b	(* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
2.6b	(+ (* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

123×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
69×	`times-frac`
60×	`add-exp-log`
37×	`distribute-lft-out`
36×	`add-cube-cbrt` `add-cbrt-cube`
32×	`associate-r`
25×	`prod-exp`
22×	`associate-l`
17×	`div-exp`
13×	`cbrt-unprod`
11×	`pow1` `distribute-lft-out--` `difference-of-squares`
10×	`frac-times`
9×	`cbrt-undiv`
8×	`flip3-+` `flip-+`
7×	`associate-*r/`
6×	`associate-*l/` `associate-/r/` `add-log-exp` `unswap-sqr`
5×	`associate-/r` `associate-/l`
4×	`rec-exp` `1-exp` `pow-prod-down`
3×	`div-inv`
2×	`*-commutative` `associate-/l/`
1×	`+-commutative` `flip3--` `frac-2neg` `div-sub` `clear-num` `sum-log` `flip--`

Counts

4 → 182

Calls

4 calls:

13.0ms	(/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
27.0ms	(* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
22.0ms	(* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
25.0ms	(+ (* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

series206.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
40.0ms	(* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
65.0ms	(* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
83.0ms	(+ (* (+ alpha beta) (* (/ 1 (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

simplify67.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5143	4381

prune258.0ms

Filtered

120 candidates to 194 candidates (-61.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	194	6	200

Merged error: 5.1b

Counts

200 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i))))
0.0b	(/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
0.1b	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
1.2b	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

159×	`*-un-lft-identity`
86×	`times-frac`
80×	`add-sqr-sqrt`
51×	`distribute-lft-out`
46×	`add-cube-cbrt`
31×	`associate-r`
22×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`associate-/r` `associate-/l`
8×	`associate-/r/`
6×	`pow1` `cbrt-undiv` `flip3-+` `div-exp` `flip-+` `add-log-exp`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `frac-times` `flip3--` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative` `flip--`

Counts

4 → 180

Calls

4 calls:

8.0ms	(/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i))))
10.0ms	(/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
32.0ms	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
20.0ms	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

series153.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i))))
17.0ms	(/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
62.0ms	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
58.0ms	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

simplify62.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5223	4158

prune266.0ms

Filtered

122 candidates to 192 candidates (-57.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	190	2	192
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	192	6	198

Merged error: 5.1b

Counts

198 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
0.1b	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
1.2b	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)
1.2b	(log (exp (+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

131×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
70×	`times-frac`
41×	`distribute-lft-out`
38×	`add-cube-cbrt`
31×	`associate-r`
22×	`associate-l`
18×	`add-exp-log` `add-cbrt-cube`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`pow1`
6×	`associate-/r/` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l`
4×	`log-prod` `flip3-+` `prod-exp` `log-pow` `cbrt-unprod` `flip-+` `unswap-sqr`
3×	`exp-prod` `div-inv`
2×	`associate-/l/`
1×	`+-commutative` `frac-times` `flip3--` `frac-2neg` `div-sub` `associate-r/` `rem-log-exp` `exp-sum` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `*-commutative` `flip--`

Counts

4 → 156

Calls

4 calls:

10.0ms	(/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
30.0ms	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
20.0ms	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)
24.0ms	(log (exp (+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)))

series197.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
62.0ms	(* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
58.0ms	(+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)
58.0ms	(log (exp (+ (* (/ (+ beta alpha) (+ beta (+ alpha (* 2.0 i)))) (/ (- beta alpha) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5269	4042

prune260.0ms

Filtered

107 candidates to 168 candidates (-57.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	167	7	174

Merged error: 5.1b

Counts

174 → 7

regimes267.0ms

Accuracy

2.8% (6.1b remaining)

Error of 11.9b against oracle of 5.8b and baseline of 12.1b

bsearch108.0ms

Steps

Iters	Range		Point
9	3.842360551475222e+277	5.322702157156398e+283	3.9128100197110995e+277
8	4.920411161038839e+221	2.0827765457677008e+226	1.7621934558652523e+226
6	1.5946941152322766e+96	2.2857458408513704e+97	2.657257095770849e+96

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	86	61
1	86	61

end0.0ms

sample1.0s

Algorithm

intervals

Results

350.0ms	6384×	body	80	valid
170.0ms	8000×	pre	80	true
138.0ms	494×	body	1280	valid
135.0ms	602×	body	640	valid
51.0ms	318×	body	320	valid
22.0ms	202×	body	160	valid

Details

analyze125.0ms

sample40.0ms

simplify46.0ms

prune11.0ms

localize17.0ms

rewrite78.0ms

series205.0ms

simplify49.0ms

prune271.0ms

localize21.0ms

rewrite95.0ms

series206.0ms

simplify67.0ms

prune258.0ms

localize16.0ms

rewrite78.0ms

series153.0ms

simplify62.0ms

prune266.0ms

localize20.0ms

rewrite92.0ms

series197.0ms

simplify47.0ms

prune260.0ms

regimes267.0ms

bsearch108.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling