Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample38.0ms (1.1%)

Algorithm

1×

intervals

Results

19.0ms	80×	body	1280	valid
5.0ms	132×	body	80	valid
5.0ms	25×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	9×	body	160	valid

simplify21.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	442	12
1	442	12

prune6.0ms (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: 16.6b

Counts

2 → 1

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.9b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `sqrt-prod` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 65

Calls

4 calls:

7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
3.0ms	(/ 1.0 (hypot 1.0 x))

series41.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
14.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.0ms	(/ 1.0 (hypot 1.0 x))

simplify84.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4844	870
1	4844	870

prune188.0ms (5.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	4	78

Merged error: 16.1b

Counts

78 → 4

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.4b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite23.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out`
4×	`associate-/r*`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`flip3--` `sqrt-pow1` `sqrt-div` `associate-*r/` `associate-/r/` `flip--` `associate-/l/` `associate--r+`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `pow1/2` `diff-log` `div-sub` `div-exp` `pow-prod-down` `clear-num` `sum-log` `sqrt-prod` `div-inv`

Counts

4 → 74

Calls

4 calls:

8.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
4.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series67.0ms (2%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
15.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
14.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify54.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5642	1860

prune298.0ms (8.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	84	6	90

Merged error: 16.1b

Counts

90 → 6

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.3b	(- 0.5 (/ 0.5 (hypot 1.0 x)))

rewrite33.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
30×	`times-frac`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
8×	`distribute-lft-out` `add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `distribute-lft-out--`
4×	`associate-/r*`
3×	`flip3-+` `flip-+`
2×	`flip3--` `sqrt-pow1` `sqrt-div` `associate-*r/` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `pow1/2` `diff-log` `div-sub` `div-exp` `pow-prod-down` `clear-num` `sum-log` `sqrt-prod` `div-inv`

Counts

4 → 90

Calls

4 calls:

10.0ms	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
7.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series67.0ms (2%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
14.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

simplify74.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4949	2224
1	4949	2224

prune366.0ms (10.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	96	6	102
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	101	7	108

Merged error: 16.1b

Counts

108 → 7

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 1.0 (log (exp (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
0.0b	(log (exp (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.3b	(- 0.5 (/ 0.5 (hypot 1.0 x)))

rewrite31.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt` `*-un-lft-identity`
37×	`times-frac`
19×	`add-cube-cbrt`
15×	`pow1`
14×	`distribute-lft-out` `difference-of-squares`
12×	`log-pow`
7×	`distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
5×	`associate-/r*`
4×	`exp-prod`
3×	`log-prod`
2×	`flip3--` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `sqrt-prod` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `pow1/2` `diff-log` `div-sub` `div-exp` `rem-log-exp` `pow-prod-down` `clear-num` `div-inv`

Counts

4 → 101

Calls

4 calls:

12.0ms	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 1.0 (log (exp (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))
2.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

series67.0ms (2%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 1.0 (log (exp (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
15.0ms	(log (exp (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

simplify65.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5744	2409

prune389.0ms (11.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	113	7	120

Merged error: 16.1b

Counts

120 → 7

regimes234.0ms (7%)

Accuracy

Total 0.0b remaining (0.1%)

Threshold costs 0.0b (0.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	22
1	34	22

end0.0ms (0%)

sample1.1s (33.8%)

Algorithm

1×

intervals

Results

682.0ms	2876×	body	1280	valid
165.0ms	4019×	body	80	valid
120.0ms	639×	body	640	valid
38.0ms	300×	body	320	valid
16.0ms	166×	body	160	valid

Details

analyze1.0ms (0%)

sample38.0ms (1.1%)

simplify21.0ms (0.6%)

prune6.0ms (0.2%)

localize9.0ms (0.3%)

rewrite21.0ms (0.6%)

series41.0ms (1.2%)

simplify84.0ms (2.5%)

prune188.0ms (5.6%)

localize13.0ms (0.4%)

rewrite23.0ms (0.7%)

series67.0ms (2%)

simplify54.0ms (1.6%)

prune298.0ms (8.9%)

localize13.0ms (0.4%)

rewrite33.0ms (1%)

series67.0ms (2%)

simplify74.0ms (2.2%)

prune366.0ms (10.9%)

localize17.0ms (0.5%)

rewrite31.0ms (0.9%)

series67.0ms (2%)

simplify65.0ms (1.9%)

prune389.0ms (11.6%)

regimes234.0ms (7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.1s (33.8%)

Profiling