Details

sample441.0ms

Algorithm

intervals

Results

130.0ms	120×	body	10240	exit
100.0ms	106×	body	1280	valid
63.0ms	80×	body	640	valid
40.0ms	53×	body	1280	nan
24.0ms	39×	body	640	nan
19.0ms	34×	body	320	valid
8.0ms	27×	body	160	valid
6.0ms	14×	body	320	nan
2.0ms	9×	body	160	nan
1.0ms	10×	body	80	valid
1.0ms	7×	body	80	nan

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	133	48
1	455	48
2	2797	47
3	5001	47

prune28.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 61.1b

Counts

2 → 2

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
1.0b	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b	(sqrt (* PI 2.0))
7.5b	(+ (- z 1.0) 1.0)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
62×	`add-sqr-sqrt`
46×	`associate-+l+`
35×	`add-cube-cbrt`
30×	`sqrt-prod`
29×	`associate-r`
27×	`prod-diff`
21×	`associate-l`
20×	`add-log-exp`
17×	`distribute-lft-out`
16×	`exp-prod`
15×	`distribute-neg-in` `exp-sum` `unswap-sqr`
13×	`unpow-prod-up`
9×	`pow1` `add-exp-log` `unpow-prod-down`
7×	`sum-log`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `add-cbrt-cube`
5×	`fma-def` `rem-exp-log` `distribute-lft-out--`
4×	`+-commutative` `expm1-log1p-u` `neg-log` `log1p-expm1-u` `sqr-pow`
3×	`sub-neg` `prod-exp` `*-commutative`
2×	`associate-+l-` `rem-sqrt-square` `sqrt-pow1` `diff-log` `pow-prod-down`
1×	`neg-sub0` `exp-neg` `pow-to-exp` `neg-mul-1` `flip3-+` `pow1/2` `exp-diff` `associate-*r/` `pow-exp` `cbrt-unprod` `flip-+` `pow-sub` `difference-of-squares`

Counts

4 → 169

Calls

4 calls:

15.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
36.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
5.0ms	(sqrt (* PI 2.0))
8.0ms	(+ (- z 1.0) 1.0)

series351.0ms

Counts

4 → 10

Calls

4 calls:

19.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
319.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))
12.0ms	(+ (- z 1.0) 1.0)

simplify96.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	835	1446
1	3101	1188
2	5002	1179

prune1.4s

Filtered

179 candidates to 123 candidates (68.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	174	5	179
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	176	5	181

Merged error: 0.7b

Counts

181 → 5

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
0.7b	(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
1.0b	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b	(sqrt (* PI 2.0))

rewrite10.0m

Algorithm

rewrite-expression-head

Calls

2 calls:

30.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
5.0ms	(sqrt (* PI 2.0))