Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

sample32.0ms (1.3%)

Algorithm

1×

intervals

Results

9.0ms	256×	pre	80	true
5.0ms	176×	body	80	valid
5.0ms	31×	body	1280	valid
4.0ms	30×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	5×	body	160	valid

simplify55.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5002	13

prune5.0ms (0.2%)

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: 18.9b

Counts

2 → 1

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.3b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite30.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 65

Calls

2 calls:

17.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series19.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

12.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
7.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify49.0ms (2%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5370	1005

prune143.0ms (5.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 18.1b

Counts

72 → 10

localize14.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ beta (+ alpha 2.0)))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.3b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite56.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
32×	`times-frac`
24×	`add-cube-cbrt` `distribute-lft-out`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv`
1×	`associate--r+` `associate--r-`

Counts

4 → 108

Calls

4 calls:

26.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
13.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ beta (+ alpha 2.0)))

series38.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
11.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)
6.0ms	(/ alpha (+ beta (+ alpha 2.0)))
6.0ms	(/ beta (+ (+ alpha beta) 2.0))

simplify45.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	6016	1670

prune235.0ms (9.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	122	8	130

Merged error: 3.1b

Counts

130 → 8

localize20.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ alpha (+ beta 2.0)))
0.7b	(cbrt (+ alpha (+ beta 2.0)))
0.7b	(cbrt (+ alpha (+ beta 2.0)))
1.3b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite29.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`cbrt-prod`
12×	`add-sqr-sqrt`
9×	`distribute-lft-out`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 59

Calls

4 calls:

13.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)
5.0ms	(cbrt (+ alpha (+ beta 2.0)))
5.0ms	(cbrt (+ alpha (+ beta 2.0)))
5.0ms	(cbrt (+ alpha (+ beta 2.0)))

series64.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(cbrt (+ alpha (+ beta 2.0)))
17.0ms	(cbrt (+ alpha (+ beta 2.0)))
17.0ms	(cbrt (+ alpha (+ beta 2.0)))
12.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify27.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5240	838

prune226.0ms (9.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	71	8	79

Merged error: 3.1b

Counts

79 → 8

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ beta (+ alpha 2.0)))
0.0b	(exp (+ (/ (- beta alpha) (+ beta (+ alpha 2.0))) 1.0))
1.3b	(+ (/ (- beta alpha) (+ beta (+ alpha 2.0))) 1.0)
1.3b	(log (exp (+ (/ (- beta alpha) (+ beta (+ alpha 2.0))) 1.0)))

rewrite68.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
25×	`times-frac`
21×	`distribute-lft-out`
19×	`add-cube-cbrt`
9×	`add-log-exp`
8×	`exp-prod`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
5×	`pow1` `associate-/r` `log-pow` `associate-/l`
4×	`log-prod` `div-sub`
3×	`associate-+l-`
2×	`flip3-+` `exp-diff` `exp-sum` `sum-log` `associate-/r/` `flip-+` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `log-div` `flip3--` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 98

Calls

4 calls:

19.0ms	(exp (+ (/ (- beta alpha) (+ beta (+ alpha 2.0))) 1.0))
18.0ms	(+ (/ (- beta alpha) (+ beta (+ alpha 2.0))) 1.0)
18.0ms	(log (exp (+ (/ (- beta alpha) (+ beta (+ alpha 2.0))) 1.0)))
10.0ms	(/ (- beta alpha) (+ beta (+ alpha 2.0)))

series51.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(exp (+ (/ (- beta alpha) (+ beta (+ alpha 2.0))) 1.0))
12.0ms	(log (exp (+ (/ (- beta alpha) (+ beta (+ alpha 2.0))) 1.0)))
12.0ms	(+ (/ (- beta alpha) (+ beta (+ alpha 2.0))) 1.0)
11.0ms	(/ (- beta alpha) (+ beta (+ alpha 2.0)))

simplify69.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4954	1491
1	4954	1491

prune195.0ms (8.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	110	8	118

Merged error: 3.1b

Counts

118 → 8

regimes192.0ms (8%)

Accuracy

Total 3.8b remaining (57.1%)

Threshold costs 0b (0%)

bsearch14.0ms (0.6%)

Steps

Iters	Range		Point
6	8.586352624315138e+40	6.075077405479101e+41	8.680683382301839e+40

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	289	44
1	289	44

end0.0ms (0%)

sample710.0ms (29.4%)

Algorithm

1×

intervals

Results

178.0ms	5794×	body	80	valid
130.0ms	8000×	pre	80	true
124.0ms	806×	body	1280	valid
95.0ms	782×	body	640	valid
34.0ms	381×	body	320	valid
14.0ms	237×	body	160	valid

Details

analyze2.0ms (0.1%)

sample32.0ms (1.3%)

simplify55.0ms (2.3%)

prune5.0ms (0.2%)

localize8.0ms (0.3%)

rewrite30.0ms (1.2%)

series19.0ms (0.8%)

simplify49.0ms (2%)

prune143.0ms (5.9%)

localize14.0ms (0.6%)

rewrite56.0ms (2.3%)

series38.0ms (1.6%)

simplify45.0ms (1.9%)

prune235.0ms (9.7%)

localize20.0ms (0.8%)

rewrite29.0ms (1.2%)

series64.0ms (2.7%)

simplify27.0ms (1.1%)

prune226.0ms (9.4%)

localize12.0ms (0.5%)

rewrite68.0ms (2.8%)

series51.0ms (2.1%)

simplify69.0ms (2.8%)

prune195.0ms (8.1%)

regimes192.0ms (8%)

bsearch14.0ms (0.6%)

simplify6.0ms (0.3%)

end0.0ms (0%)

sample710.0ms (29.4%)

Profiling