Details

sample1.6s

Algorithm

intervals

Results

1.4s	124×	body	10240	exit
53.0ms	261×	body	80	valid
53.0ms	51×	body	1280	nan
36.0ms	49×	body	640	nan
11.0ms	21×	body	320	nan
4.0ms	12×	body	160	nan
1.0ms	7×	body	80	nan

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	60	123
1	148	123
2	594	121
3	3633	88
done	5000	78

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize53.0ms

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)

rewrite103.0ms

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)
23.0ms	(- (- 1.0 z) 1.0)
22.0ms	(- (- 1.0 z) 1.0)
25.0ms	(- (- 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)

simplify1.2s

Counts

212 → 212

Iterations

Useful iterations: 3 (274.0ms)

Iter	Nodes	Cost
0	84	2848
1	164	2152
2	437	1500
3	2077	1012
done	5001	1012

prune1.7s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize50.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z)))))
1.0b	(+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))))))
1.0b	(sqrt (* PI 2.0))
1.3b	(/ (* (* (* (/ PI (sin (* PI z))) (sqrt (* PI 2.0))) (pow (+ 0.5 (- 7.0 z)) (- 0.5 z))) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))))))) (exp (+ 0.5 (- 7.0 z))))

rewrite2.3m

Algorithm

rewrite-expression-head

Rules

296×	`frac-add`
163×	`*-un-lft-identity`
131×	`add-log-exp`
104×	`sum-log` `distribute-lft-out`
77×	`flip3-+` `flip-+`
75×	`associate-/l/`
73×	`frac-times`
60×	`associate-*l/`
42×	`fma-def`
40×	`add-exp-log`
38×	`pow-sub`
37×	`associate-*r/`
36×	`add-sqr-sqrt`
34×	`times-frac`
25×	`prod-exp`
24×	`add-cube-cbrt` `add-cbrt-cube`
14×	`div-exp`
9×	`cbrt-unprod`
7×	`pow1`
6×	`cbrt-undiv` `distribute-lft-out--` `difference-of-squares`
5×	`associate-/r/`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`pow-to-exp` `pow-exp` `div-inv`
2×	`+-commutative` `associate-+r+` `flip3--` `sqrt-pow1` `exp-sum` `flip--`
1×	`associate-+r-` `frac-2neg` `pow1/2` `exp-diff` `pow-prod-down` `clear-num` `sqrt-prod` `associate-/l*`

Counts

4 → 270

Calls

4 calls:

23.3s	(+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z)))))
59.6s	(+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))))))
2.0ms	(sqrt (* PI 2.0))
53.6s	(/ (* (* (* (/ PI (sin (* PI z))) (sqrt (* PI 2.0))) (pow (+ 0.5 (- 7.0 z)) (- 0.5 z))) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))))))) (exp (+ 0.5 (- 7.0 z))))

series1.1s

Counts

4 → 10

Calls

4 calls:

173.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z)))))
195.0ms	(+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))))))
0.0ms	(sqrt (* PI 2.0))
706.0ms	(/ (* (* (* (/ PI (sin (* PI z))) (sqrt (* PI 2.0))) (pow (+ 0.5 (- 7.0 z)) (- 0.5 z))) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))))))) (exp (+ 0.5 (- 7.0 z))))

simplify601.0ms

Counts

280 → 280

Iterations

Useful iterations: done (564.0ms)

Iter	Nodes	Cost
0	736	24708
1	2602	21937
done	5000	21920

prune3.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.3m

Algorithm

rewrite-expression-head

Rules

163×	`*-un-lft-identity`
131×	`add-log-exp`
104×	`sum-log` `distribute-lft-out`
88×	`frac-add`
42×	`fma-def`
38×	`add-sqr-sqrt`
30×	`times-frac`
25×	`flip3-+` `flip-+`
24×	`add-cube-cbrt`
9×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `associate-r` `associate-/r/` `log1p-expm1-u`
3×	`associate-l`
2×	`+-commutative` `associate-+r+` `flip3--` `sqrt-pow1` `pow-prod-down` `sqrt-prod` `flip--` `div-inv`
1×	`pow1/2` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 178

Calls

4 calls:

22.8s	(+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z)))))
56.7s	(+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))))))
2.0ms	(sqrt (* PI 2.0))
7.0ms	(* PI (sqrt (* PI 2.0)))

series359.0ms

Counts

4 → 8

Calls

4 calls:

167.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z)))))
192.0ms	(+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))))))
0.0ms	(sqrt (* PI 2.0))
0.0ms	(* PI (sqrt (* PI 2.0)))

simplify393.0ms

Counts

186 → 186

Iterations

Useful iterations: 1 (119.0ms)

Iter	Nodes	Cost
0	444	13812
1	1614	12124
done	5002	12124

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite4.4m

Algorithm

rewrite-expression-head

Rules

1338×	`*-un-lft-identity`
974×	`distribute-lft-out`
240×	`times-frac`
176×	`exp-sum`
161×	`add-sqr-sqrt`
149×	`add-cube-cbrt`
144×	`prod-diff`
140×	`frac-add`
131×	`add-log-exp`
104×	`sum-log`
42×	`fma-def`
38×	`flip3-+` `flip-+`
18×	`associate-/l/`
16×	`sub-neg`
15×	`associate-/l*`
14×	`associate-/r*`
7×	`pow1`
6×	`add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
5×	`add-exp-log` `associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`div-inv`
2×	`+-commutative` `associate-+r+` `flip3--` `sqrt-pow1` `flip--`
1×	`cbrt-undiv` `frac-2neg` `pow1/2` `exp-diff` `div-exp` `pow-prod-down` `clear-num` `sqrt-prod`

Counts

4 → 429

Calls

4 calls:

22.4s	(+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z)))))
55.9s	(+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))))))
2.0ms	(sqrt (* PI 2.0))
3.1m	(/ (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z)))))) (exp (- 7.0 z)))

series573.0ms

Counts

4 → 10

Calls

4 calls:

164.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z)))))
186.0ms	(+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))))))
0.0ms	(sqrt (* PI 2.0))
223.0ms	(/ (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z)))))) (exp (- 7.0 z)))

simplify501.0ms

Counts

439 → 439

Iterations

Useful iterations: done (451.0ms)

Iter	Nodes	Cost
0	597	35038
1	1918	31687
done	5001	31648

prune2.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes197.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	84
1	74	84
done	74	84

end0.0ms

sample42.2s

Algorithm

intervals

Results

37.7s	3835×	body	10240	exit
1.5s	1525×	body	1280	nan
1.3s	8100×	body	80	valid
1.0s	1275×	body	640	nan
283.0ms	597×	body	320	nan
103.0ms	328×	body	160	nan
47.0ms	304×	body	80	nan