Details

analyze1.7s (2.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
0%	74.9%	25.1%	2
18.7%	56.2%	25.1%	3
37.5%	37.5%	25.1%	4
42.1%	32.8%	25.1%	5
46.8%	28.1%	25.1%	6
48%	26.9%	25.1%	7
49.2%	25.8%	25.1%	8
49.5%	25.5%	25.1%	9
49.8%	25.2%	25.1%	10
49.8%	25.2%	25.1%	11
49.8%	25.1%	25.1%	12
49.9%	25%	25.1%	13
49.9%	25%	25.1%	14

sample1.6s (2.3%)

Algorithm

1×

intervals

Results

1.5s	123×	body	5120	exit
76.0ms	256×	body	80	valid
6.0ms	380×	pre	80	true
0.0ms	1×	body	80	invalid

simplify38.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5022	78

prune17.0ms (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: 1.8b

Counts

2 → 2

localize48.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z))) (/ 771.3234287776531 (- 3.0 z))) (/ -176.6150291621406 (- 4.0 z)))
1.0b	(+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z))) (/ 771.3234287776531 (- 3.0 z)))
1.0b	(sqrt (* PI 2.0))
2.6b	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))

rewrite98.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity` `add-log-exp`
20×	`frac-add`
19×	`sum-log` `distribute-lft-out`
9×	`flip3-+` `flip-+`
7×	`pow1`
4×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `add-cbrt-cube`
3×	`+-commutative` `associate-+l+`
2×	`sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 74

Calls

4 calls:

44.0ms	(+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z))) (/ 771.3234287776531 (- 3.0 z))) (/ -176.6150291621406 (- 4.0 z)))
28.0ms	(+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z))) (/ 771.3234287776531 (- 3.0 z)))
21.0ms	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))
2.0ms	(sqrt (* PI 2.0))

series18.0ms (0%)

Counts

4 → 10

Calls

4 calls:

8.0ms	(+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z))) (/ 771.3234287776531 (- 3.0 z))) (/ -176.6150291621406 (- 4.0 z)))
6.0ms	(+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z))) (/ 771.3234287776531 (- 3.0 z)))
4.0ms	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))
0.0ms	(sqrt (* PI 2.0))

simplify33.0ms (0%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	4983	2481
1	4983	2481

prune546.0ms (0.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	81	5	86

Merged error: 0.3b

Counts

86 → 5

localize80.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(* (+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))))) (- 3.0 z))
1.0b	(* (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))) (* (- 2.0 z) (* (- 3.0 z) -176.6150291621406)))
1.0b	(sqrt (* PI 2.0))
2.6b	(+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)))))

rewrite124.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`frac-times` `associate-*r/`
69×	`flip3-+` `flip-+`
64×	`frac-add`
61×	`flip3--` `flip--`
60×	`associate-*l/`
18×	`pow1`
15×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`pow-prod-down`
7×	`add-cube-cbrt` `prod-exp` `cbrt-unprod`
6×	`associate-r` `associate-l` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`sub-neg` `associate-+l+` `associate-+r+` `sqrt-pow1` `*-commutative`
1×	`+-commutative` `pow1/2` `sum-log` `sqrt-prod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 167

Calls

4 calls:

49.0ms	(* (+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))))) (- 3.0 z))
43.0ms	(+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)))))
17.0ms	(* (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))) (* (- 2.0 z) (* (- 3.0 z) -176.6150291621406)))
2.0ms	(sqrt (* PI 2.0))

series29.0ms (0%)

Counts

4 → 10

Calls

4 calls:

11.0ms	(* (+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))))) (- 3.0 z))
10.0ms	(+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)))))
7.0ms	(* (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))) (* (- 2.0 z) (* (- 3.0 z) -176.6150291621406)))
0.0ms	(sqrt (* PI 2.0))

simplify122.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5006	13521

prune6.4s (9.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	177	5	182

Merged error: 0.3b

Counts

182 → 5

localize68.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+ (/ (+ (* (+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))))) (- 3.0 z)) (* (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))) (* (- 2.0 z) 771.3234287776531))) (* (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))) (* (- 2.0 z) (- 3.0 z)))) (/ -176.6150291621406 (- 4.0 z)))
1.0b	(* (+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))))) (- 3.0 z))
1.0b	(sqrt (* PI 2.0))
2.6b	(+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)))))

rewrite187.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`associate-*r/`
68×	`frac-times`
65×	`frac-add`
61×	`flip3-+` `flip-+`
43×	`flip3--` `flip--`
34×	`associate-*l/`
10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`pow1`
8×	`add-log-exp`
6×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`associate-r`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
2×	`+-commutative` `sub-neg` `associate-+l+` `associate-+r+` `sqrt-pow1` `pow-prod-down` `sum-log`
1×	`pow1/2` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 133

Calls

4 calls:

84.0ms	(+ (/ (+ (* (+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))))) (- 3.0 z)) (* (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))) (* (- 2.0 z) 771.3234287776531))) (* (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))) (* (- 2.0 z) (- 3.0 z)))) (/ -176.6150291621406 (- 4.0 z)))
49.0ms	(* (+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))))) (- 3.0 z))
42.0ms	(+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)))))
2.0ms	(sqrt (* PI 2.0))

series112.0ms (0.2%)

Counts

4 → 10

Calls

4 calls:

85.0ms	(+ (/ (+ (* (+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))))) (- 3.0 z)) (* (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))) (* (- 2.0 z) 771.3234287776531))) (* (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))) (* (- 2.0 z) (- 3.0 z)))) (/ -176.6150291621406 (- 4.0 z)))
16.0ms	(* (+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))))) (- 3.0 z))
10.0ms	(+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)))))
0.0ms	(sqrt (* PI 2.0))

simplify80.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5668	13085

prune4.0s (5.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	142	6	148

Merged error: 0.3b

Counts

148 → 6

localize80.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt (* PI 2.0))
2.6b	(+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)))))
2.6b	(+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)))))
2.6b	(+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)))))

rewrite129.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`associate-*r/`
48×	`frac-add`
45×	`flip3-+` `flip-+`
24×	`frac-times`
18×	`flip3--` `flip--`
12×	`associate-*l/`
10×	`add-log-exp`
7×	`pow1`
6×	`distribute-rgt-in` `associate-+l+` `associate-+r+` `distribute-lft-in`
4×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`+-commutative` `sum-log`
2×	`sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 104

Calls

4 calls:

42.0ms	(+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)))))
41.0ms	(+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)))))
38.0ms	(+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)))))
2.0ms	(sqrt (* PI 2.0))

series30.0ms (0%)

Counts

4 → 10

Calls

4 calls:

10.0ms	(+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)))))
10.0ms	(+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)))))
10.0ms	(+ (* (- 2.0 z) (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3))) (* -1259.1392167224028 (+ (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)))))
0.0ms	(sqrt (* PI 2.0))

simplify74.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4986	8458
1	4986	8458

prune4.2s (6.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	114	6	120

Merged error: 0.3b

Counts

120 → 6

regimes124.0ms (0.2%)

Accuracy

Total 0.1b remaining (35.2%)

Threshold costs 0.1b (35.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	136	178
1	136	178

end0.0ms (0%)

sample48.8s (71%)

Algorithm

1×

intervals

Results

45.9s	3859×	body	5120	exit
2.3s	8000×	body	80	valid
190.0ms	11938×	pre	80	true
25.0ms	79×	body	80	invalid

Details

analyze1.7s (2.5%)

sample1.6s (2.3%)

simplify38.0ms (0.1%)

prune17.0ms (0%)

localize48.0ms (0.1%)

rewrite98.0ms (0.1%)

series18.0ms (0%)

simplify33.0ms (0%)

prune546.0ms (0.8%)

localize80.0ms (0.1%)

rewrite124.0ms (0.2%)

series29.0ms (0%)

simplify122.0ms (0.2%)

prune6.4s (9.3%)

localize68.0ms (0.1%)

rewrite187.0ms (0.3%)

series112.0ms (0.2%)

simplify80.0ms (0.1%)

prune4.0s (5.8%)

localize80.0ms (0.1%)

rewrite129.0ms (0.2%)

series30.0ms (0%)

simplify74.0ms (0.1%)

prune4.2s (6.1%)

regimes124.0ms (0.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample48.8s (71%)

Profiling