Details

analyze3.0ms (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 (1.2%)

Algorithm

1×

intervals

Results

6.0ms	32×	body	1280	valid
6.0ms	180×	body	80	valid
5.0ms	9×	body	320	valid
4.0ms	256×	pre	80	true
3.0ms	28×	body	640	valid
0.0ms	7×	body	160	valid

simplify65.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

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: 17.8b

Counts

2 → 1

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.9b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite28.0ms (1.1%)

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:

16.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
9.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series21.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

12.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify47.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5370	1005

prune141.0ms (5.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 17.0b

Counts

72 → 11

localize14.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ beta alpha) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ beta alpha) 2.0))
1.9b	(- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)

rewrite55.0ms (2.2%)

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:

25.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ beta alpha) 2.0)) 1.0))
13.0ms	(- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)
7.0ms	(/ alpha (+ (+ beta alpha) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))

series38.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)
11.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ beta alpha) 2.0)) 1.0))
9.0ms	(/ beta (+ (+ alpha beta) 2.0))
6.0ms	(/ alpha (+ (+ beta alpha) 2.0))

simplify30.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	4978	1670
1	4978	1670

prune233.0ms (9.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	123	8	131

Merged error: 3.5b

Counts

131 → 8

localize16.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.9b	(- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)
6.6b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.6b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.6b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite39.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity`
63×	`cbrt-prod`
46×	`times-frac`
36×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
27×	`distribute-lft-out`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 104

Calls

4 calls:

12.0ms	(- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)
9.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series77.0ms (3%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
21.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
21.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
11.0ms	(- (/ alpha (+ (+ beta alpha) 2.0)) 1.0)

simplify82.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4937	1711
1	4937	1711

prune341.0ms (13.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	116	8	124

Merged error: 3.5b

Counts

124 → 8

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ beta alpha) 2.0))
0.1b	(exp (log (+ (/ (- beta alpha) (+ (+ beta alpha) 2.0)) 1.0)))
1.9b	(+ (/ (- beta alpha) (+ (+ beta alpha) 2.0)) 1.0)
4.6b	(log (+ (/ (- beta alpha) (+ (+ beta alpha) 2.0)) 1.0))

rewrite65.0ms (2.5%)

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`
8×	`log-prod`
7×	`add-exp-log`
6×	`pow1` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`log-div` `exp-prod` `flip3-+` `exp-sum` `flip-+`
2×	`exp-diff` `div-sub` `associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `sum-log` `flip--` `div-inv` `rem-exp-log`

Counts

4 → 98

Calls

4 calls:

19.0ms	(+ (/ (- beta alpha) (+ (+ beta alpha) 2.0)) 1.0)
17.0ms	(exp (log (+ (/ (- beta alpha) (+ (+ beta alpha) 2.0)) 1.0)))
16.0ms	(log (+ (/ (- beta alpha) (+ (+ beta alpha) 2.0)) 1.0))
9.0ms	(/ (- beta alpha) (+ (+ beta alpha) 2.0))

series48.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(log (+ (/ (- beta alpha) (+ (+ beta alpha) 2.0)) 1.0))
11.0ms	(exp (log (+ (/ (- beta alpha) (+ (+ beta alpha) 2.0)) 1.0)))
11.0ms	(+ (/ (- beta alpha) (+ (+ beta alpha) 2.0)) 1.0)
7.0ms	(/ (- beta alpha) (+ (+ beta alpha) 2.0))

simplify56.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	6180	1610

prune188.0ms (7.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	110	8	118

Merged error: 3.5b

Counts

118 → 8

regimes161.0ms (6.3%)

Accuracy

Total 3.1b remaining (51%)

Threshold costs 0b (0%)

bsearch17.0ms (0.7%)

Steps

Iters	Range		Point
9	0.5900090070486723	45029.78694382322	44511.573118962006

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	325	69
1	325	69

end0.0ms (0%)

sample719.0ms (28.2%)

Algorithm

1×

intervals

Results

185.0ms	5823×	body	80	valid
127.0ms	821×	body	1280	valid
127.0ms	8000×	pre	80	true
91.0ms	731×	body	640	valid
39.0ms	405×	body	320	valid
13.0ms	220×	body	160	valid

Details

analyze3.0ms (0.1%)

sample32.0ms (1.2%)

simplify65.0ms (2.5%)

prune5.0ms (0.2%)

localize8.0ms (0.3%)

rewrite28.0ms (1.1%)

series21.0ms (0.8%)

simplify47.0ms (1.8%)

prune141.0ms (5.6%)

localize14.0ms (0.6%)

rewrite55.0ms (2.2%)

series38.0ms (1.5%)

simplify30.0ms (1.2%)

prune233.0ms (9.2%)

localize16.0ms (0.6%)

rewrite39.0ms (1.5%)

series77.0ms (3%)

simplify82.0ms (3.2%)

prune341.0ms (13.4%)

localize11.0ms (0.5%)

rewrite65.0ms (2.5%)

series48.0ms (1.9%)

simplify56.0ms (2.2%)

prune188.0ms (7.4%)

regimes161.0ms (6.3%)

bsearch17.0ms (0.7%)

simplify7.0ms (0.3%)

end0.0ms (0%)

sample719.0ms (28.2%)

Profiling