Details

analyze35.0ms

Algorithm

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

sample22.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true
0.0ms	4×	pre	80	false

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5165	11

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 12.5b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (- 1 (* b (/ b (* a a))))))
0.0b	(- 1 (* b (/ b (* a a))))
0.2b	(* b (/ b (* a a)))
12.7b	(/ b (* a a))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
15×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1` `times-frac` `associate-r`
6×	`add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp`
3×	`associate-l` `sqrt-prod` `associate-/l*`
2×	`div-inv` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `*-commutative` `flip--`

Counts

4 → 73

Calls

4 calls:

1.0ms	(sqrt (fabs (- 1 (* b (/ b (* a a))))))
3.0ms	(- 1 (* b (/ b (* a a))))
7.0ms	(* b (/ b (* a a)))
5.0ms	(/ b (* a a))

series25.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(sqrt (fabs (- 1 (* b (/ b (* a a))))))
6.0ms	(- 1 (* b (/ b (* a a))))
5.0ms	(* b (/ b (* a a)))
5.0ms	(/ b (* a a))

simplify33.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4973	710
1	4973	710

prune102.0ms

Filtered

54 candidates to 85 candidates (-57.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	1	86

Merged error: 0.0b

Counts

86 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (- 1 (cbrt (pow (/ b a) 6)))))
0.0b	(- 1 (cbrt (pow (/ b a) 6)))
0.4b	(pow (/ b a) 6)
29.4b	(cbrt (pow (/ b a) 6))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
30×	`unpow-prod-down`
28×	`*-un-lft-identity`
25×	`cbrt-prod`
21×	`add-cube-cbrt`
20×	`times-frac`
10×	`difference-of-squares`
7×	`add-exp-log`
6×	`pow1` `add-log-exp`
4×	`add-cbrt-cube` `sqr-pow`
3×	`pow-unpow` `sqrt-prod`
2×	`pow-exp` `div-inv`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `flip3--` `pow-pow` `sqrt-pow1` `pow1/2` `pow1/3` `diff-log` `div-exp` `flip--` `distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

1.0ms	(sqrt (fabs (- 1 (cbrt (pow (/ b a) 6)))))
10.0ms	(- 1 (cbrt (pow (/ b a) 6)))
5.0ms	(pow (/ b a) 6)
4.0ms	(cbrt (pow (/ b a) 6))

series30.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt (fabs (- 1 (cbrt (pow (/ b a) 6)))))
6.0ms	(- 1 (cbrt (pow (/ b a) 6)))
8.0ms	(pow (/ b a) 6)
5.0ms	(cbrt (pow (/ b a) 6))

simplify60.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5315	903

prune139.0ms

Filtered

61 candidates to 100 candidates (-63.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	1	101

Merged error: 0b

Counts

101 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1 (log (exp (pow (/ b a) 2))))
0.0b	(exp (pow (/ b a) 2))
0.4b	(pow (/ b a) 2)
5.1b	(log (exp (pow (/ b a) 2)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

39×	`unpow-prod-down`
36×	`exp-prod`
34×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
27×	`times-frac`
20×	`log-pow`
7×	`pow1` `add-exp-log`
6×	`log-prod` `add-log-exp`
4×	`add-cbrt-cube`
3×	`pow-unpow` `div-inv` `associate--r+` `unpow2` `sqr-pow`
2×	`pow-exp` `distribute-lft-out--` `difference-of-squares`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `div-exp` `rem-log-exp` `flip--` `rem-exp-log`

Counts

4 → 103

Calls

4 calls:

13.0ms	(- 1 (log (exp (pow (/ b a) 2))))
6.0ms	(exp (pow (/ b a) 2))
4.0ms	(pow (/ b a) 2)
6.0ms	(log (exp (pow (/ b a) 2)))

series22.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- 1 (log (exp (pow (/ b a) 2))))
9.0ms	(exp (pow (/ b a) 2))
3.0ms	(pow (/ b a) 2)
4.0ms	(log (exp (pow (/ b a) 2)))

simplify51.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5483	778

prune188.0ms

Filtered

85 candidates to 115 candidates (-35.3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	115	1	116

Merged error: 0b

Counts

116 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	11
1	21	11

end0.0ms

sample573.0ms

Algorithm

intervals

Results

280.0ms	8000×	body	80	valid
152.0ms	8000×	pre	80	true
2.0ms	121×	pre	80	false

Details

analyze35.0ms

sample22.0ms

simplify52.0ms

prune8.0ms

localize12.0ms

rewrite18.0ms

series25.0ms

simplify33.0ms

prune102.0ms

localize9.0ms

rewrite23.0ms

series30.0ms

simplify60.0ms

prune139.0ms

localize10.0ms

rewrite33.0ms

series22.0ms

simplify51.0ms

prune188.0ms

simplify1.0ms

end0.0ms

sample573.0ms

Profiling