Details

analyze122.0ms

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

sample39.0ms

Algorithm

intervals

Results

15.0ms	217×	body	80	valid
6.0ms	256×	pre	80	true
4.0ms	15×	body	1280	valid
2.0ms	11×	body	640	valid
2.0ms	11×	body	320	valid
0.0ms	2×	body	160	valid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

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: 18.6b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
1.7b	(* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))))
2.5b	(+ (* (+ alpha beta) (/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))) 1.0)
17.9b	(/ (- beta alpha) (* (+ alpha (+ beta (* 2.0 i))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))

rewrite82.0ms

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:

14.0ms	(* (+ 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)))))))
24.0ms	(+ (* (+ 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))))))

series209.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ 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)))))))
84.0ms	(+ (* (+ 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))))))

simplify53.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5522	3306

prune271.0ms

Filtered

106 candidates to 132 candidates (-24.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	125	7	132
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	127	7	134

Merged error: 3.4b

Counts

134 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ beta (+ alpha (* 2.0 i))))
0.1b	(/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
1.7b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
2.5b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

667×	`*-un-lft-identity`
503×	`times-frac`
287×	`add-sqr-sqrt`
221×	`distribute-lft-out`
180×	`add-cube-cbrt`
136×	`associate-r`
49×	`distribute-lft-out--` `difference-of-squares`
31×	`associate-/l*`
28×	`associate-/r/`
20×	`add-exp-log` `add-cbrt-cube`
17×	`flip3-+` `flip-+`
14×	`div-inv`
9×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
4×	`associate-l`
3×	`div-sub` `prod-exp` `cbrt-unprod` `associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num`
1×	`+-commutative` `flip3--` `associate-r/` `pow-prod-down` `sum-log` `-commutative` `flip--`

Counts

4 → 399

Calls

4 calls:

9.0ms	(/ (- beta alpha) (+ beta (+ alpha (* 2.0 i))))
23.0ms	(/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
49.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
31.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

series206.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- beta alpha) (+ beta (+ alpha (* 2.0 i))))
38.0ms	(/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))
65.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i))))))
86.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)

simplify112.0ms

Algorithm

egg-herbie

Counts

411 → 411

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4997	11341
1	4997	11341

prune642.0ms

Filtered

207 candidates to 411 candidates (-98.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	408	3	411
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	411	7	418

Merged error: 3.4b

Counts

418 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

2.5b	(+ (* (* (+ alpha beta) (* (cbrt (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))) (cbrt (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))))) (/ (cbrt (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i))))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)
5.5b	(cbrt (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i)))))
5.5b	(cbrt (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i)))))
5.5b	(cbrt (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

88×	`*-un-lft-identity`
78×	`cbrt-prod`
60×	`times-frac`
58×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
15×	`distribute-lft-out`
12×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`+-commutative` `sum-log`

Counts

4 → 116

Calls

4 calls:

55.0ms	(+ (* (* (+ alpha beta) (* (cbrt (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))) (cbrt (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))))) (/ (cbrt (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i))))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)
9.0ms	(cbrt (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i)))))
9.0ms	(cbrt (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i)))))
11.0ms	(cbrt (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (* (* (+ alpha beta) (* (cbrt (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))) (cbrt (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i))))))) (/ (cbrt (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i))))) (+ alpha (+ beta (+ 2.0 (* 2.0 i)))))) 1.0)
78.0ms	(cbrt (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i)))))
78.0ms	(cbrt (/ (- beta alpha) (+ alpha (+ beta (* 2.0 i)))))
80.0ms	(cbrt (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4989	2793
1	4989	2793

prune339.0ms

Filtered

96 candidates to 128 candidates (-33.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	128	7	135

Merged error: 3.4b

Counts

135 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
0.1b	(cbrt (pow (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0) 3))
1.7b	(* (+ beta alpha) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
2.5b	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

637×	`*-un-lft-identity`
483×	`times-frac`
269×	`add-sqr-sqrt`
215×	`distribute-lft-out`
172×	`add-cube-cbrt`
136×	`associate-r`
44×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/r/` `associate-/l*`
18×	`add-exp-log` `add-cbrt-cube`
17×	`flip3-+` `flip-+`
13×	`div-inv`
12×	`cbrt-prod`
6×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
5×	`associate-/r*`
4×	`associate-l`
3×	`unpow-prod-down` `cube-prod` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cube-div` `frac-times` `cbrt-div` `div-sub` `associate-*l/`
1×	`+-commutative` `cube-mult` `frac-2neg` `pow1/3` `unpow3` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `rem-cbrt-cube` `associate-/l/` `sqr-pow`

Counts

4 → 376

Calls

4 calls:

22.0ms	(/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
30.0ms	(cbrt (pow (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0) 3))
52.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
28.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)

series224.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))
58.0ms	(cbrt (pow (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0) 3))
64.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ beta (+ alpha (+ 2.0 (* 2.0 i))))))
62.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ beta (+ alpha (* 2.0 i)))) (+ beta (+ alpha (+ 2.0 (* 2.0 i)))))) 1.0)

simplify98.0ms

Algorithm

egg-herbie

Counts

388 → 388

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5118	11561

prune719.0ms

Filtered

190 candidates to 388 candidates (-104.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	384	4	388
Fresh	4	1	5
Picked	0	1	1
Done	0	1	1
Total	388	7	395

Merged error: 3.4b

Counts

395 → 7

regimes276.0ms

Accuracy

16.4% (5.3b remaining)

Error of 11.0b against oracle of 5.8b and baseline of 12.1b

bsearch50.0ms

Steps

Iters	Range		Point
10	9.340254950034806e+218	1.9940823317305303e+236	2.632083162561644e+221

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	77	77
1	77	77

end0.0ms

sample1.1s

Algorithm

intervals

Results

354.0ms	6389×	body	80	valid
184.0ms	8000×	pre	80	true
146.0ms	509×	body	1280	valid
128.0ms	568×	body	640	valid
56.0ms	345×	body	320	valid
21.0ms	189×	body	160	valid

Details

analyze122.0ms

sample39.0ms

simplify45.0ms

prune11.0ms

localize16.0ms

rewrite82.0ms

series209.0ms

simplify53.0ms

prune271.0ms

localize15.0ms

rewrite143.0ms

series206.0ms

simplify112.0ms

prune642.0ms

localize24.0ms

rewrite89.0ms

series325.0ms

simplify53.0ms

prune339.0ms

localize18.0ms

rewrite164.0ms

series224.0ms

simplify98.0ms

prune719.0ms

regimes276.0ms

bsearch50.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling