Details

analyze127.0ms

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

sample63.0ms

Algorithm

intervals

Results

10.0ms	198×	body	80	valid
4.0ms	18×	body	640	valid
4.0ms	14×	body	1280	valid
2.0ms	14×	body	320	valid
1.0ms	12×	body	160	valid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5446	29

prune14.0ms

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: 19.7b

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)))))
2.1b	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
13.6b	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
15.0b	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

rewrite80.0ms

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:

16.0ms	(* (+ 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)))))))
21.0ms	(+ (* (+ 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))))))

series212.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
66.0ms	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
86.0ms	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
39.0ms	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5522	3306

prune313.0ms

Filtered

106 candidates to 132 candidates (-24.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	122	10	132
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	124	10	134

Merged error: 6.2b

Counts

134 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
0.3b	(/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
2.1b	(* (+ alpha beta) (/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
13.6b	(+ (* (+ alpha beta) (/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-exp-log`
45×	`*-un-lft-identity`
35×	`add-sqr-sqrt`
32×	`add-cbrt-cube`
30×	`associate-l`
27×	`times-frac`
24×	`prod-exp`
20×	`add-cube-cbrt`
19×	`div-exp`
17×	`associate-r`
12×	`associate-/r/`
11×	`pow1`
10×	`cbrt-unprod`
9×	`cbrt-undiv` `flip3-+` `flip-+` `distribute-lft-out`
8×	`frac-times`
7×	`associate-*r/`
6×	`rec-exp` `1-exp` `add-log-exp`
5×	`associate-*l/`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`pow-prod-down` `div-inv` `associate-/l*` `unswap-sqr`
2×	`pow-flip` `*-commutative`
1×	`+-commutative` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r*` `sum-log` `un-div-inv` `flip--` `inv-pow`

Counts

4 → 147

Calls

4 calls:

20.0ms	(* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
20.0ms	(/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
24.0ms	(* (+ alpha beta) (/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
24.0ms	(+ (* (+ alpha beta) (/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

series227.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
39.0ms	(/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
67.0ms	(* (+ alpha beta) (/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
87.0ms	(+ (* (+ alpha beta) (/ 1 (* (/ (+ beta (+ alpha (* 2.0 i))) (- beta alpha)) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

simplify80.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5057	3746

prune270.0ms

Filtered

104 candidates to 159 candidates (-52.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	153	6	159
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	159	10	169

Merged error: 6.2b

Counts

169 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
0.1b	(* (+ alpha beta) (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i)))))
0.1b	(* (* (+ alpha beta) (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))) (/ 1 (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
13.6b	(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))) (/ 1 (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
52×	`add-exp-log`
51×	`times-frac`
47×	`add-sqr-sqrt` `associate-r`
34×	`add-cube-cbrt`
32×	`add-cbrt-cube`
27×	`distribute-lft-out`
22×	`prod-exp`
13×	`div-exp`
12×	`pow1` `cbrt-unprod`
11×	`frac-times` `associate-*l/`
10×	`flip3-+` `flip-+`
7×	`cbrt-undiv`
6×	`associate-/r/` `add-log-exp`
5×	`associate-l` `associate-/r*`
4×	`rec-exp` `1-exp` `associate-*r/` `pow-prod-down` `distribute-lft-out--` `difference-of-squares`
3×	`div-inv` `associate-/l*`
2×	`*-commutative` `unswap-sqr`
1×	`+-commutative` `pow-flip` `frac-2neg` `clear-num` `sum-log` `un-div-inv` `inv-pow`

Counts

4 → 164

Calls

4 calls:

8.0ms	(/ 1 (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
17.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i)))))
25.0ms	(* (* (+ alpha beta) (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))) (/ 1 (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
28.0ms	(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))) (/ 1 (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)

series185.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ 1 (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
17.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i)))))
67.0ms	(* (* (+ alpha beta) (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))) (/ 1 (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
88.0ms	(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))) (/ 1 (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5246	3465

prune276.0ms

Filtered

103 candidates to 176 candidates (-70.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	172	4	176
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	176	10	186

Merged error: 6.2b

Counts

186 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (+ alpha beta) (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))) (/ (/ 1 (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
0.3b	(/ (/ 1 (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
0.4b	(/ 1 (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
13.6b	(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))) (/ (/ 1 (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

979×	`*-un-lft-identity`
912×	`times-frac`
580×	`sqrt-prod`
399×	`add-sqr-sqrt` `add-cube-cbrt`
348×	`distribute-lft-out`
246×	`associate-r`
77×	`add-exp-log`
47×	`add-cbrt-cube`
40×	`sqrt-div` `associate-/r/`
33×	`associate-/l*`
31×	`div-exp`
25×	`flip3-+` `prod-exp` `flip-+`
20×	`div-inv`
16×	`cbrt-undiv` `associate-/r*`
15×	`cbrt-unprod`
11×	`pow1`
9×	`frac-times` `associate-*l/`
6×	`add-log-exp`
5×	`rec-exp` `1-exp`
3×	`pow-flip` `associate-*r/` `pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `sqrt-pow1` `pow1/2` `associate-l` `sum-log` `*-commutative` `associate-/l/` `inv-pow`

Counts

4 → 655

Calls

4 calls:

70.0ms	(* (* (+ alpha beta) (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))) (/ (/ 1 (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
24.0ms	(/ (/ 1 (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
10.0ms	(/ 1 (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
48.0ms	(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))) (/ (/ 1 (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

series744.0ms

Counts

4 → 12

Calls

4 calls:

450.0ms	(* (* (+ alpha beta) (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))) (/ (/ 1 (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))))
21.0ms	(/ (/ 1 (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
34.0ms	(/ 1 (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
238.0ms	(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))) (/ (/ 1 (sqrt (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) (sqrt (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))) 1.0)

simplify184.0ms

Algorithm

egg-herbie

Counts

667 → 667

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4985	20163
1	4985	20163

prune885.0ms

Filtered

198 candidates to 667 candidates (-236.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	665	2	667
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	667	10	677

Merged error: 6.2b

Counts

677 → 10

regimes359.0ms

Accuracy

21% (5.5b remaining)

Error of 11.3b against oracle of 5.8b and baseline of 12.8b

bsearch42.0ms

Steps

Iters	Range		Point
8	5.819642507927184e+169	5.887895675558121e+172	5.996138338071563e+169

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	77	64
1	77	64

end0.0ms

sample1.7s

Algorithm

intervals

Results

341.0ms	6310×	body	80	valid
151.0ms	543×	body	1280	valid
130.0ms	584×	body	640	valid
61.0ms	368×	body	320	valid
21.0ms	195×	body	160	valid

Details

analyze127.0ms

sample63.0ms

simplify44.0ms

prune14.0ms

localize17.0ms

rewrite80.0ms

series212.0ms

simplify51.0ms

prune313.0ms

localize18.0ms

rewrite94.0ms

series227.0ms

simplify80.0ms

prune270.0ms

localize18.0ms

rewrite85.0ms

series185.0ms

simplify65.0ms

prune276.0ms

localize24.0ms

rewrite212.0ms

series744.0ms

simplify184.0ms

prune885.0ms

regimes359.0ms

bsearch42.0ms

simplify2.0ms

end0.0ms

sample1.7s

Profiling