Details

analyze78.0ms (2.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	80	valid
0.0ms	9×	body	80	invalid
0.0ms	9×	body	80	nan

simplify172.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (170.0ms)

Iter	Nodes	Cost
0	4908	20
1	4908	20

prune7.0ms (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: 0.2b

Counts

2 → 1

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
1.3b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite47.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `times-frac`
24×	`add-cube-cbrt` `associate-l`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
8×	`associate-*r/` `sqrt-prod`
6×	`flip3--` `sqrt-div` `associate-r` `flip--`
4×	`frac-times` `associate-/r*` `associate-/r/` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `associate-l/` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `sqrt-pow1` `div-exp` `*-commutative` `div-inv` `difference-of-squares`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 114

Calls

4 calls:

14.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
12.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series54.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
17.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
9.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify52.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4974	2418
1	4974	2418

prune437.0ms (13.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	116	10	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	10	127

Merged error: 0.0b

Counts

127 → 10

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(* 9.0 (- a (/ 1.0 3.0)))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
0.2b	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
1.3b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

rewrite41.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`add-cube-cbrt`
14×	`times-frac`
11×	`pow1`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-r` `associate-l`
8×	`associate-*r/`
6×	`flip3--` `flip--`
5×	`sqrt-prod`
4×	`frac-times` `sqrt-div` `associate-/r*` `add-log-exp` `difference-of-squares`
3×	`flip3-+` `pow-prod-down` `flip-+` `associate-/l*`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-pow1` `associate-l/` `prod-exp` `associate-/r/` `-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `frac-2neg` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 102

Calls

4 calls:

12.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
9.0ms	(* 9.0 (- a (/ 1.0 3.0)))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series39.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
15.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* 1.0 (/ rand (sqrt (* 9.0 (- a (/ 1.0 3.0))))))))
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
3.0ms	(* 9.0 (- a (/ 1.0 3.0)))

simplify37.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5053	2006

prune307.0ms (9.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	115	9	124

Merged error: 0.0b

Counts

124 → 9

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
1.3b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
8.7b	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite54.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
24×	`associate-l`
23×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
8×	`sqrt-prod`
7×	`associate-*r/` `prod-exp` `cbrt-unprod`
6×	`sqrt-div` `associate-*l/`
5×	`flip3--` `pow-prod-down` `flip--`
4×	`associate-r` `associate-/r*` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`frac-times` `sqrt-pow1` `*-commutative` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 111

Calls

4 calls:

19.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))
14.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

series55.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
19.0ms	(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
6.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))

simplify38.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5182	2263

prune356.0ms (11.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	123	9	132

Merged error: 0.0b

Counts

132 → 9

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0)))) rand)
0.3b	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0))))
0.3b	(/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
1.3b	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

rewrite60.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`times-frac`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
15×	`associate-*l/`
14×	`pow1`
8×	`sqrt-prod`
7×	`flip3--` `associate-l` `prod-exp` `flip--` `cbrt-unprod`
6×	`sqrt-div`
5×	`pow-prod-down`
4×	`frac-times` `associate-/r*` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`sqrt-pow1` `associate-r/` `-commutative` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 115

Calls

4 calls:

20.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0))))
19.0ms	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0)))) rand)
10.0ms	(/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
8.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

series46.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0)))) rand)
12.0ms	(/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0)))
9.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* (- a (/ 1.0 3.0)) 9.0))))
6.0ms	(sqrt (* (- a (/ 1.0 3.0)) 9.0))

simplify39.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5545	2434

prune365.0ms (11.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	2	4	6
Picked	0	1	1
Done	1	1	2
Total	129	7	136

Merged error: 0.0b

Counts

136 → 7

regimes173.0ms (5.4%)

Accuracy

Total 0.1b remaining (89.3%)

Threshold costs 0.1b (89.3%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	26
1	36	26

end0.0ms (0%)

sample658.0ms (20.6%)

Algorithm

1×

intervals

Results

479.0ms	8000×	body	80	valid
17.0ms	283×	body	80	invalid
13.0ms	245×	body	80	nan

Details

analyze78.0ms (2.5%)

sample24.0ms (0.7%)

simplify172.0ms (5.4%)

prune7.0ms (0.2%)

localize10.0ms (0.3%)

rewrite47.0ms (1.5%)

series54.0ms (1.7%)

simplify52.0ms (1.6%)

prune437.0ms (13.7%)

localize10.0ms (0.3%)

rewrite41.0ms (1.3%)

series39.0ms (1.2%)

simplify37.0ms (1.2%)

prune307.0ms (9.6%)

localize11.0ms (0.4%)

rewrite54.0ms (1.7%)

series55.0ms (1.7%)

simplify38.0ms (1.2%)

prune356.0ms (11.2%)

localize14.0ms (0.4%)

rewrite60.0ms (1.9%)

series46.0ms (1.5%)

simplify39.0ms (1.2%)

prune365.0ms (11.5%)

regimes173.0ms (5.4%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample658.0ms (20.6%)

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