Details

analyze129.0ms (1.2%)

Algorithm

1×

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

sample41.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	202×	body	80	valid
6.0ms	256×	pre	80	true
4.0ms	15×	body	1280	valid
4.0ms	17×	body	640	valid
3.0ms	18×	body	320	valid
0.0ms	4×	body	160	valid

simplify50.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5446	29

prune7.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 24.7b

Counts

2 → 1

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* 2.0 i))
0.1b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.0b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.0b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite79.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac`
48×	`*-un-lft-identity`
26×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/r/`
12×	`flip3-+` `flip-+`
11×	`distribute-lft-out` `add-log-exp`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/r*` `div-inv`
4×	`pow1` `frac-times` `sum-log`
3×	`flip3--` `flip--`
2×	`+-commutative` `frac-2neg` `associate-r/` `associate-l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate-+l+`

Counts

4 → 124

Calls

4 calls:

34.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
14.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))
6.0ms	(+ (+ alpha beta) (* 2.0 i))

series179.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
67.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
18.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))
5.0ms	(+ (+ alpha beta) (* 2.0 i))

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5737	3711

prune332.0ms (3.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	127	9	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	9	137

Merged error: 7.1b

Counts

137 → 9

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i))))
1.3b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i)))))
3.7b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i))))) 1.0)

rewrite112.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

321×	`times-frac`
290×	`*-un-lft-identity`
211×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
31×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/l*`
24×	`associate-/r/`
20×	`add-exp-log` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
12×	`div-inv`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
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 → 295

Calls

4 calls:

39.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i)))))
26.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i))))) 1.0)
19.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i))))
10.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))

series212.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i))))) 1.0)
67.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i)))))
38.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i))))
17.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))

simplify75.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4981	8907
1	4981	8907

prune927.0ms (8.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	302	5	307
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	307	9	316

Merged error: 7.1b

Counts

316 → 9

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 2.0 (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.3b	(/ 1 (/ (+ 2.0 (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
1.3b	(* (+ alpha beta) (/ 1 (/ (+ 2.0 (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
3.7b	(+ (* (+ alpha beta) (/ 1 (/ (+ 2.0 (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

rewrite261.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

1713×	`times-frac`
1199×	`*-un-lft-identity`
879×	`add-sqr-sqrt`
658×	`add-cube-cbrt`
272×	`associate-r`
170×	`distribute-lft-out`
110×	`associate-/r*`
99×	`distribute-lft-out--` `difference-of-squares`
76×	`associate-/r/`
62×	`add-exp-log`
43×	`div-inv`
37×	`flip3-+` `flip-+`
33×	`div-exp`
32×	`add-cbrt-cube`
15×	`cbrt-undiv`
10×	`prod-exp`
7×	`pow1` `associate-/l*` `unswap-sqr`
6×	`rec-exp` `1-exp` `add-log-exp`
4×	`associate-l` `cbrt-unprod`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 833

Calls

4 calls:

83.0ms	(* (+ alpha beta) (/ 1 (/ (+ 2.0 (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
44.0ms	(+ (* (+ alpha beta) (/ 1 (/ (+ 2.0 (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 1.0)
30.0ms	(/ 1 (/ (+ 2.0 (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
23.0ms	(/ (+ 2.0 (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))

series230.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (* (+ alpha beta) (/ 1 (/ (+ 2.0 (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 1.0)
68.0ms	(* (+ alpha beta) (/ 1 (/ (+ 2.0 (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
38.0ms	(/ 1 (/ (+ 2.0 (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
35.0ms	(/ (+ 2.0 (+ (+ alpha beta) (* 2.0 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))

simplify167.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

845 → 845

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5184	28777

prune4.8s (44.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	845	0	845
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	845	9	854

Merged error: 7.1b

Counts

854 → 9

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i))))
0.1b	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i))))) 1.0) 3))
1.3b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i)))))
3.7b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i))))) 1.0)

rewrite130.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

306×	`times-frac`
275×	`*-un-lft-identity`
196×	`add-sqr-sqrt`
133×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
27×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r/`
21×	`associate-/l*`
18×	`add-exp-log` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
12×	`cbrt-prod`
11×	`div-inv`
6×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
4×	`associate-l` `associate-/r*`
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 → 278

Calls

4 calls:

40.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i)))))
27.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i))))) 1.0)
26.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i))))) 1.0) 3))
19.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i))))

series279.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i))))) 1.0)
85.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i))))) 1.0) 3))
67.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i)))))
38.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ 2.0 (+ (+ alpha beta) (* 2.0 i))))

simplify78.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5075	9219

prune1.1s (10.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	282	8	290
Fresh	5	2	7
Picked	0	1	1
Done	1	0	1
Total	288	11	299

Merged error: 7.1b

Counts

299 → 11

regimes385.0ms (3.5%)

Accuracy

Total 5.6b remaining (48.7%)

Threshold costs 0b (0%)

bsearch36.0ms (0.3%)

Steps

Iters	Range		Point
7	2.490290781953067e+179	9.236066902371333e+180	6.636178679578833e+179

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	67
1	68	67

end0.0ms (0%)

sample1.1s (10.2%)

Algorithm

1×

intervals

Results

367.0ms	6345×	body	80	valid
180.0ms	8000×	pre	80	true
150.0ms	514×	body	1280	valid
150.0ms	622×	body	640	valid
59.0ms	337×	body	320	valid
20.0ms	182×	body	160	valid

Details

analyze129.0ms (1.2%)

sample41.0ms (0.4%)

simplify50.0ms (0.5%)

prune7.0ms (0.1%)

localize13.0ms (0.1%)

rewrite79.0ms (0.7%)

series179.0ms (1.7%)

simplify44.0ms (0.4%)

prune332.0ms (3.1%)

localize13.0ms (0.1%)

rewrite112.0ms (1%)

series212.0ms (1.9%)

simplify75.0ms (0.7%)

prune927.0ms (8.5%)

localize15.0ms (0.1%)

rewrite261.0ms (2.4%)

series230.0ms (2.1%)

simplify167.0ms (1.5%)

prune4.8s (44.5%)

localize16.0ms (0.1%)

rewrite130.0ms (1.2%)

series279.0ms (2.6%)

simplify78.0ms (0.7%)

prune1.1s (10.2%)

regimes385.0ms (3.5%)

bsearch36.0ms (0.3%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.1s (10.2%)

Profiling