Details

sample1.4s

Algorithm

intervals

Results

403.0ms	114×	body	10240	exit
364.0ms	103×	body	1280	valid
154.0ms	83×	body	640	valid
125.0ms	49×	body	640	nan
81.0ms	37×	body	320	valid
74.0ms	34×	body	1280	nan
63.0ms	18×	body	320	nan
19.0ms	21×	body	160	valid
15.0ms	18×	body	160	nan
6.0ms	15×	body	80	valid
6.0ms	14×	body	80	nan

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
3	2001
2	422
1	140
0	55

prune81.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize172.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
1.0b	(/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5)))
1.0b	(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
1.0b	(sqrt (* PI 2))

rewrite2.4m

Algorithm

rewrite-expression-head

Rules

276×	`frac-add`
94×	`*-un-lft-identity`
65×	`distribute-lft-out`
62×	`flip3-+` `flip-+`
38×	`frac-times` `associate-*r/`
27×	`add-exp-log`
21×	`associate-r`
20×	`add-cbrt-cube`
19×	`add-sqr-sqrt` `associate-l`
14×	`prod-exp`
12×	`add-cube-cbrt`
9×	`pow1`
8×	`times-frac` `div-exp`
6×	`unpow-prod-down` `cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `associate-/r*` `associate-+l-` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `exp-sum` `associate-*l/` `pow-exp`
2×	`sqrt-pow1` `exp-diff` `pow-prod-down` `associate-/r/` `*-commutative` `sqrt-prod` `div-inv` `pow-sub` `sqr-pow`
1×	`distribute-rgt-in` `unpow-prod-up` `clear-num` `frac-2neg` `distribute-lft-in` `pow1/2` `associate-/l*` `distribute-lft-out--` `associate-/l/`

Counts

4 → 203

Calls

4 calls:

2.4m	(* (/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
184.0ms	(/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5)))
138.0ms	(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
8.0ms	(sqrt (* PI 2))

series1.6s

Counts

4 → 10

Calls

4 calls:

718.0ms	(* (/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
525.0ms	(/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5)))
314.0ms	(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))

simplify3.0s

Counts

213 → 213

Iterations

Iter	Nodes
done	2000
1	2000
0	797

prune7.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize115.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6))) (* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))))))
0.4b	(* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
1.0b	(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6)))
1.0b	(sqrt (* PI 2))

rewrite2.9m

Algorithm

rewrite-expression-head

Rules

828×	`frac-add`
441×	`*-un-lft-identity`
293×	`times-frac`
231×	`exp-sum`
224×	`add-sqr-sqrt`
219×	`add-cube-cbrt`
191×	`frac-times` `associate-*r/`
189×	`prod-diff`
186×	`flip3-+` `flip-+`
161×	`associate-l`
145×	`unpow-prod-down`
121×	`distribute-lft-out`
39×	`add-exp-log`
32×	`add-cbrt-cube`
29×	`unpow-prod-up` `distribute-lft-out--` `sqr-pow`
22×	`prod-exp`
21×	`sub-neg`
18×	`associate-r`
17×	`div-exp`
14×	`pow1` `associate-/r*`
12×	`cbrt-unprod`
10×	`associate-/l*`
7×	`cbrt-undiv`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
4×	`expm1-log1p-u` `pow-to-exp` `associate-*l/` `pow-exp` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`sqrt-pow1` `exp-diff` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow1/2` `associate-+l-` `pow-sub` `associate-/l/`

Counts

4 → 663

Calls

4 calls:

1.3m	(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6))) (* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))))))
1.6m	(* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
131.0ms	(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6)))
6.0ms	(sqrt (* PI 2))

series1.2s

Counts

4 → 10

Calls

4 calls:

724.0ms	(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6))) (* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))))))
297.0ms	(* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
181.0ms	(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6)))
0.0ms	(sqrt (* PI 2))

simplify3.3s

Counts

673 → 673

Iterations

Iter	Nodes
done	2001
1	2001
0	1325

prune17.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize112.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6))) (* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))))))
0.4b	(* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
1.0b	(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6)))
1.0b	(sqrt (* PI 2))

rewrite2.8m

Algorithm

rewrite-expression-head

Rules

828×	`frac-add`
191×	`frac-times` `associate-*r/`
186×	`flip3-+` `flip-+`
161×	`*-un-lft-identity`
77×	`distribute-lft-out`
73×	`times-frac`
54×	`add-sqr-sqrt`
52×	`associate-l`
49×	`add-cube-cbrt`
39×	`add-exp-log`
35×	`unpow-prod-down`
32×	`add-cbrt-cube`
22×	`prod-exp`
18×	`associate-r`
17×	`div-exp`
14×	`pow1`
12×	`cbrt-unprod`
10×	`associate-/l*`
7×	`cbrt-undiv` `unpow-prod-up` `distribute-lft-out--` `sqr-pow`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
4×	`expm1-log1p-u` `pow-to-exp` `associate-*l/` `pow-exp` `associate-/r/` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `div-inv`
2×	`neg-sub0` `exp-neg` `sqrt-pow1` `exp-diff` `*-commutative` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow1/2` `associate-+l-` `pow-sub` `associate-/l/`

Counts

4 → 434

Calls

4 calls:

1.2m	(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6))) (* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))))))
1.6m	(* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
77.0ms	(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6)))
4.0ms	(sqrt (* PI 2))

series1.1s

Counts

4 → 10

Calls

4 calls:

655.0ms	(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6))) (* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))))))
288.0ms	(* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))
193.0ms	(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6)))
0.0ms	(sqrt (* PI 2))

simplify2.8s

Counts

444 → 444

Iterations

Iter	Nodes
done	2000
1	2000
0	1139

prune13.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize124.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (pow (sqrt (+ (- z -6) 0.5)) (+ (- z 1) 0.5)) (exp (fma 1 z (- (* -6 1))))) (* (/ (pow (sqrt (+ (- z -6) 0.5)) (+ (- z 1) 0.5)) (exp (fma (- -6) 1 (* -6 1)))) (* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))))
0.5b	(* (/ (pow (sqrt (+ (- z -6) 0.5)) (+ (- z 1) 0.5)) (exp (fma (- -6) 1 (* -6 1)))) (* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6 (- z 1))) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2))) (/ -1259.1392167224028 (+ z 1)))) (/ -176.6150291621406 (- z -3))) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))))))
1.0b	(/ (pow (sqrt (+ (- z -6) 0.5)) (+ (- z 1) 0.5)) (exp (fma 1 z (- (* -6 1)))))
1.0b	(sqrt (* PI 2))

rewrite59.5s

Algorithm

rewrite-expression-head

Calls

2 calls:

66.0ms	(/ (pow (sqrt (+ (- z -6) 0.5)) (+ (- z 1) 0.5)) (exp (fma 1 z (- (* -6 1)))))
4.0ms	(sqrt (* PI 2))