Details

sample2.3s

Algorithm

intervals

Results

1.8s	116×	body	10240	exit
151.0ms	256×	body	80	valid
106.0ms	31×	body	1280	nan
62.0ms	39×	body	640	nan
10.0ms	10×	body	320	nan
10.0ms	13×	body	160	nan
4.0ms	9×	body	80	nan

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 3 (798.0ms)

Iter	Nodes	Cost
0	60	123
1	148	123
2	609	121
3	3846	88
done	5001	88

prune70.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize135.0ms

Local error

Found 4 expressions with local error:

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

rewrite4.0m

Algorithm

rewrite-expression-head

Rules

534×	`frac-add`
137×	`frac-times` `associate-*r/`
127×	`*-un-lft-identity`
111×	`flip3-+` `flip-+`
88×	`times-frac`
54×	`unpow-prod-down`
51×	`associate-l` `distribute-lft-out`
46×	`add-sqr-sqrt` `add-cube-cbrt`
39×	`add-exp-log`
27×	`add-cbrt-cube`
23×	`exp-sum`
20×	`prod-exp`
16×	`div-exp`
13×	`add-log-exp`
12×	`pow1`
11×	`associate-/l*`
10×	`cbrt-unprod`
9×	`unpow-prod-up` `distribute-rgt-neg-in` `sqr-pow`
8×	`associate-+r-`
6×	`cbrt-undiv` `exp-diff` `sum-log` `associate-/r/`
4×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-prod-down` `pow-exp` `associate-/r*`
3×	`neg-sub0` `associate-*l/`
2×	`sqrt-pow1` `unsub-neg` `div-inv`
1×	`+-commutative` `associate-+l-` `associate-+r+` `frac-2neg` `pow1/2` `associate-r` `clear-num` `sqrt-prod` `*-commutative` `associate-/l/` `pow-sub`

Counts

4 → 332

Calls

4 calls:

374.0ms	(+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))
232.0ms	(/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z)))))
4.0m	(* (/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z))))) (* (/ PI (sin (* PI z))) (+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z))))))))
4.0ms	(sqrt (* PI 2.0))

series813.0ms

Counts

4 → 10

Calls

4 calls:

81.0ms	(+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))
172.0ms	(/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z)))))
560.0ms	(* (/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z))))) (* (/ PI (sin (* PI z))) (+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z))))))))
0.0ms	(sqrt (* PI 2.0))

simplify1.4s

Counts

342 → 342

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	1133	59239
1	4387	50432
done	5001	49380

prune5.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize213.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z))))
1.0b	(sqrt (* PI 2.0))
1.5b	(pow (/ 12.507343278686905 (- 5.0 z)) 3)
1.5b	(pow (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))) 3)

rewrite8.4s

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
53×	`add-sqr-sqrt`
46×	`times-frac`
36×	`add-cube-cbrt` `frac-add` `distribute-lft-out`
28×	`unpow-prod-down` `cube-prod`
21×	`associate-r`
13×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
11×	`pow1`
9×	`cube-div`
8×	`frac-times` `associate-*l/`
7×	`associate-l`
6×	`pow-unpow` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
4×	`add-log-exp`
3×	`distribute-rgt-neg-in` `pow-exp` `div-inv` `rem-cube-cbrt`
2×	`cbrt-undiv` `cube-mult` `pow-to-exp` `flip3--` `pow-pow` `sqrt-pow1` `unpow3` `div-exp` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `unswap-sqr` `sqr-pow`
1×	`pow1/2` `associate-r/` `sqrt-prod` `-commutative`

Counts

4 → 172

Calls

4 calls:

6.5s	(* (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z))))
3.0ms	(sqrt (* PI 2.0))
13.0ms	(pow (/ 12.507343278686905 (- 5.0 z)) 3)
1.9s	(pow (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))) 3)

series322.0ms

Counts

4 → 10

Calls

4 calls:

139.0ms	(* (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z))))
0.0ms	(sqrt (* PI 2.0))
53.0ms	(pow (/ 12.507343278686905 (- 5.0 z)) 3)
129.0ms	(pow (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))) 3)

simplify628.0ms

Counts

182 → 182

Iterations

Useful iterations: done (615.0ms)

Iter	Nodes	Cost
0	528	7415
1	1790	6597
done	5001	6185

prune4.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize231.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))))
1.0b	(* (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z))))
1.0b	(sqrt (* PI 2.0))
1.5b	(pow (/ 12.507343278686905 (- 5.0 z)) 3)

rewrite19.0s

Algorithm

rewrite-expression-head

Rules

251×	`*-un-lft-identity`
240×	`frac-add`
136×	`distribute-lft-out`
81×	`flip3-+` `flip-+`
72×	`frac-times`
56×	`add-sqr-sqrt`
46×	`times-frac`
37×	`add-cube-cbrt`
28×	`associate-r`
27×	`swap-sqr`
21×	`unpow-prod-down` `cube-prod`
17×	`pow1`
16×	`associate-*l/`
14×	`add-exp-log` `associate-l` `add-cbrt-cube`
9×	`associate-*r/`
6×	`associate-/r/` `distribute-lft-out--` `difference-of-squares`
4×	`add-log-exp`
3×	`pow-unpow` `distribute-rgt-neg-in` `pow-prod-down` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `sqrt-pow1` `div-exp` `pow-exp` `*-commutative` `flip--` `rem-cube-cbrt`
1×	`cube-div` `pow2` `distribute-rgt-in` `cube-mult` `pow-to-exp` `pow-pow` `distribute-lft-in` `pow-plus` `pow1/2` `unpow3` `sqrt-prod` `pow-sqr` `pow-prod-up` `sqr-pow`

Counts

4 → 272

Calls

4 calls:

12.4s	(* (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))))
6.5s	(* (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z))))
3.0ms	(sqrt (* PI 2.0))
14.0ms	(pow (/ 12.507343278686905 (- 5.0 z)) 3)

series322.0ms

Counts

4 → 10

Calls

4 calls:

120.0ms	(* (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))))
145.0ms	(* (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z))))
0.0ms	(sqrt (* PI 2.0))
57.0ms	(pow (/ 12.507343278686905 (- 5.0 z)) 3)

simplify774.0ms

Counts

282 → 282

Iterations

Useful iterations: done (737.0ms)

Iter	Nodes	Cost
0	556	26511
1	2150	23097
done	5002	22527

prune6.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize230.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))))
1.0b	(* (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z))))
1.0b	(sqrt PI)
1.5b	(pow (/ 12.507343278686905 (- 5.0 z)) 3)

rewrite18.9s

Algorithm

rewrite-expression-head

Rules

252×	`*-un-lft-identity`
240×	`frac-add`
136×	`distribute-lft-out`
81×	`flip3-+` `flip-+`
72×	`frac-times`
58×	`add-sqr-sqrt`
46×	`times-frac`
38×	`add-cube-cbrt`
28×	`associate-r`
27×	`swap-sqr`
21×	`unpow-prod-down` `cube-prod`
16×	`associate-*l/`
15×	`pow1`
14×	`add-exp-log` `associate-l` `add-cbrt-cube`
9×	`associate-*r/`
6×	`associate-/r/` `distribute-lft-out--` `difference-of-squares`
4×	`add-log-exp`
3×	`pow-unpow` `distribute-rgt-neg-in` `prod-exp` `sqrt-prod` `cbrt-unprod` `div-inv` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `pow-exp` `*-commutative` `flip--` `rem-cube-cbrt`
1×	`cube-div` `pow2` `distribute-rgt-in` `cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `distribute-lft-in` `sqrt-pow1` `pow-plus` `pow1/2` `unpow3` `pow-sqr` `pow-prod-up` `sqr-pow`

Counts

4 → 274

Calls

4 calls:

12.3s	(* (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))))
6.6s	(* (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z))))
1.0ms	(sqrt PI)
14.0ms	(pow (/ 12.507343278686905 (- 5.0 z)) 3)

series297.0ms

Counts

4 → 10

Calls

4 calls:

113.0ms	(* (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))))
136.0ms	(* (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z))))
0.0ms	(sqrt PI)
48.0ms	(pow (/ 12.507343278686905 (- 5.0 z)) 3)

simplify703.0ms

Counts

284 → 284

Iterations

Useful iterations: done (666.0ms)

Iter	Nodes	Cost
0	551	26449
1	2139	23085
done	5001	22467

prune5.5s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes421.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	98	464
1	133	464
done	133	464

end0.0ms

sample53.8s

Algorithm

intervals

Results

45.7s	3870×	body	10240	exit
2.8s	1474×	body	1280	nan
2.5s	8080×	body	80	valid
1.7s	1269×	body	640	nan
484.0ms	611×	body	320	nan
161.0ms	330×	body	160	nan
83.0ms	329×	body	80	nan