Details

sample1.5s

Algorithm

intervals

Results

1.3s	124×	body	10240	exit
56.0ms	51×	body	1280	nan
46.0ms	261×	body	80	valid
33.0ms	49×	body	640	nan
10.0ms	21×	body	320	nan
4.0ms	12×	body	160	nan
1.0ms	7×	body	80	nan

simplify1.0s

Counts

1 → 1

Iterations

Useful iterations: 3 (201.0ms)

Iter	Nodes	Cost
0	60	123
1	148	123
2	594	121
3	3686	88
done	5000	88

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize55.0ms

Local error

Found 4 expressions with local error:

6.3b	(- (- 1.0 z) 1.0)
6.3b	(- (- 1.0 z) 1.0)
6.3b	(- (- 1.0 z) 1.0)
6.3b	(- (- 1.0 z) 1.0)

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

116×	`*-un-lft-identity`
104×	`add-sqr-sqrt`
96×	`prod-diff`
64×	`add-cube-cbrt`
44×	`associate--l+`
28×	`distribute-lft-out--`
24×	`add-log-exp`
20×	`fma-neg` `difference-of-squares`
12×	`diff-log`
8×	`sub-neg`
4×	`pow1` `add-exp-log` `associate--l-` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

4 → 200

Calls

4 calls:

22.0ms	(- (- 1.0 z) 1.0)
21.0ms	(- (- 1.0 z) 1.0)
22.0ms	(- (- 1.0 z) 1.0)
26.0ms	(- (- 1.0 z) 1.0)

series45.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (- 1.0 z) 1.0)
11.0ms	(- (- 1.0 z) 1.0)
11.0ms	(- (- 1.0 z) 1.0)
12.0ms	(- (- 1.0 z) 1.0)

simplify1.5s

Counts

212 → 212

Iterations

Useful iterations: 3 (288.0ms)

Iter	Nodes	Cost
0	84	2848
1	178	2152
2	525	1500
3	2322	1012
done	5000	1012

prune1.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.3b

localize51.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099))
1.0b	(sqrt (* PI 2.0))
1.1b	(* (* (sqrt (* PI 2.0)) (/ (pow (+ 0.5 (+ (- z) 7.0)) (+ 0.5 (- z))) (exp (+ 0.5 (+ (- z) 7.0))))) (* (/ PI (sin (* PI z))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -1259.1392167224028 (+ (- z) 2.0))) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099))) (/ -176.6150291621406 (+ (- z) 4.0))) (+ (/ 1.5056327351493116e-07 (+ (- z) 8.0)) (/ 9.984369578019572e-06 (+ (- z) 7.0)))))))
1.5b	(+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -1259.1392167224028 (+ (- z) 2.0))) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)))

rewrite1.2m

Algorithm

rewrite-expression-head

Rules

912×	`frac-add`
315×	`associate-*r/`
229×	`flip3-+` `flip-+`
209×	`frac-times`
96×	`*-un-lft-identity`
58×	`add-exp-log`
40×	`add-cbrt-cube` `distribute-lft-out`
37×	`prod-exp`
34×	`fma-def`
33×	`times-frac`
30×	`add-log-exp`
21×	`cbrt-unprod`
20×	`add-sqr-sqrt`
19×	`pow1`
18×	`sum-log`
14×	`add-cube-cbrt` `div-exp`
9×	`pow-prod-down`
6×	`cbrt-undiv` `distribute-rgt-neg-in`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `log1p-expm1-u`
3×	`pow-to-exp` `associate-*l/` `pow-exp` `distribute-lft-out--` `difference-of-squares`
2×	`+-commutative` `associate-+r+` `sqrt-pow1` `associate-/r/`
1×	`associate-+l+` `flip3--` `pow1/2` `associate-r` `associate-l` `sqrt-prod` `*-commutative` `flip--` `div-inv`

Counts

4 → 359

Calls

4 calls:

116.0ms	(+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099))
2.0ms	(sqrt (* PI 2.0))
1.2m	(* (* (sqrt (* PI 2.0)) (/ (pow (+ 0.5 (+ (- z) 7.0)) (+ 0.5 (- z))) (exp (+ 0.5 (+ (- z) 7.0))))) (* (/ PI (sin (* PI z))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -1259.1392167224028 (+ (- z) 2.0))) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099))) (/ -176.6150291621406 (+ (- z) 4.0))) (+ (/ 1.5056327351493116e-07 (+ (- z) 8.0)) (/ 9.984369578019572e-06 (+ (- z) 7.0)))))))
694.0ms	(+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -1259.1392167224028 (+ (- z) 2.0))) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)))

series907.0ms

Counts

4 → 10

Calls

4 calls:

54.0ms	(+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099))
0.0ms	(sqrt (* PI 2.0))
750.0ms	(* (* (sqrt (* PI 2.0)) (/ (pow (+ 0.5 (+ (- z) 7.0)) (+ 0.5 (- z))) (exp (+ 0.5 (+ (- z) 7.0))))) (* (/ PI (sin (* PI z))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -1259.1392167224028 (+ (- z) 2.0))) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099))) (/ -176.6150291621406 (+ (- z) 4.0))) (+ (/ 1.5056327351493116e-07 (+ (- z) 8.0)) (/ 9.984369578019572e-06 (+ (- z) 7.0)))))))
103.0ms	(+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ -1259.1392167224028 (+ (- z) 2.0))) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ 771.3234287776531 (+ 3.0 (- z))) 0.9999999999998099)))

simplify619.0ms

Counts

369 → 369

Iterations

Useful iterations: done (524.0ms)

Iter	Nodes	Cost
0	1377	88631
done	5002	77828

prune6.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize149.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (+ (pow (/ -1259.1392167224028 (+ (- z) 2.0)) 3) (pow (/ -0.13857109526572012 (- 6.0 z)) 3)) (- 1.0 z)) (+ (/ (* 771.3234287776531 (/ 771.3234287776531 (- 3.0 z))) (- 3.0 z)) (* 0.9999999999998099 (- 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))))))
1.0b	(pow (/ 771.3234287776531 (- 3.0 z)) 3)
1.0b	(pow (/ -0.13857109526572012 (- 6.0 z)) 3)
1.0b	(sqrt (* PI 2.0))

rewrite732.0ms

Algorithm

rewrite-expression-head

Rules

74×	`frac-times`
67×	`add-sqr-sqrt` `*-un-lft-identity`
60×	`times-frac`
43×	`add-cube-cbrt`
42×	`unpow-prod-down` `cube-prod`
39×	`frac-add`
38×	`associate-*r/`
36×	`flip3--` `flip--`
32×	`cube-div`
27×	`flip3-+` `flip-+`
26×	`associate-*l/`
15×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
12×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/`
6×	`pow-unpow`
4×	`expm1-log1p-u` `pow-prod-down` `pow-exp` `log1p-expm1-u` `div-inv` `add-log-exp` `rem-cube-cbrt`
3×	`associate-r` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `cube-mult` `pow-to-exp` `pow-pow` `sqrt-pow1` `unpow3` `div-exp` `sqr-pow`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/2` `associate-l` `sqrt-prod` `*-commutative`

Counts

4 → 222

Calls

4 calls:

702.0ms	(* (* (+ (pow (/ -1259.1392167224028 (+ (- z) 2.0)) 3) (pow (/ -0.13857109526572012 (- 6.0 z)) 3)) (- 1.0 z)) (+ (/ (* 771.3234287776531 (/ 771.3234287776531 (- 3.0 z))) (- 3.0 z)) (* 0.9999999999998099 (- 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))))))
8.0ms	(pow (/ 771.3234287776531 (- 3.0 z)) 3)
8.0ms	(pow (/ -0.13857109526572012 (- 6.0 z)) 3)
2.0ms	(sqrt (* PI 2.0))

series306.0ms

Counts

4 → 10

Calls

4 calls:

204.0ms	(* (* (+ (pow (/ -1259.1392167224028 (+ (- z) 2.0)) 3) (pow (/ -0.13857109526572012 (- 6.0 z)) 3)) (- 1.0 z)) (+ (/ (* 771.3234287776531 (/ 771.3234287776531 (- 3.0 z))) (- 3.0 z)) (* 0.9999999999998099 (- 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))))))
49.0ms	(pow (/ 771.3234287776531 (- 3.0 z)) 3)
53.0ms	(pow (/ -0.13857109526572012 (- 6.0 z)) 3)
0.0ms	(sqrt (* PI 2.0))

simplify669.0ms

Counts

232 → 232

Iterations

Useful iterations: done (650.0ms)

Iter	Nodes	Cost
0	595	10350
1	2379	9228
done	5001	8853

prune7.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize89.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 771.3234287776531 (- 3.0 z)) 0.9999999999998099)
1.0b	(+ (/ 771.3234287776531 (- 3.0 z)) 0.9999999999998099)
1.0b	(+ (* -176.6150291621406 (* (* (+ (- z) 2.0) (- 6.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) 0.9999999999998099)))) (* (+ (- z) 4.0) (+ (* (- (* (/ 676.5203681218851 (- 1.0 z)) (/ 676.5203681218851 (- 1.0 z))) (* (+ (/ 771.3234287776531 (- 3.0 z)) 0.9999999999998099) (+ (/ 771.3234287776531 (- 3.0 z)) 0.9999999999998099))) (* (+ (- z) 2.0) (- 6.0 z))) (* (+ (* -1259.1392167224028 (- 6.0 z)) (* -0.13857109526572012 (+ (- z) 2.0))) (- (/ 676.5203681218851 (- 1.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) 0.9999999999998099))))))
1.0b	(sqrt (* PI 2.0))

rewrite8.6m

Algorithm

rewrite-expression-head

Calls

4 calls:

24.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) 0.9999999999998099)
47.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) 0.9999999999998099)
29.0s	(+ (* -176.6150291621406 (* (* (+ (- z) 2.0) (- 6.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) 0.9999999999998099)))) (* (+ (- z) 4.0) (+ (* (- (* (/ 676.5203681218851 (- 1.0 z)) (/ 676.5203681218851 (- 1.0 z))) (* (+ (/ 771.3234287776531 (- 3.0 z)) 0.9999999999998099) (+ (/ 771.3234287776531 (- 3.0 z)) 0.9999999999998099))) (* (+ (- z) 2.0) (- 6.0 z))) (* (+ (* -1259.1392167224028 (- 6.0 z)) (* -0.13857109526572012 (+ (- z) 2.0))) (- (/ 676.5203681218851 (- 1.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) 0.9999999999998099))))))
2.0ms	(sqrt (* PI 2.0))