Details

sample1.8s

Algorithm

intervals

Results

1.6s	146×	body	10240	exit
58.0ms	258×	body	80	valid
52.0ms	50×	body	1280	nan
37.0ms	50×	body	640	nan
8.0ms	16×	body	320	nan
3.0ms	7×	body	160	nan
2.0ms	10×	body	80	nan

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	60	123
1	148	123
2	594	121
3	3627	88
done	5001	78

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize52.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
0.9b	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
0.9b	(/ (pow (+ 0.5 (- 7.0 z)) (- 0.5 z)) (exp (+ 0.5 (- 7.0 z))))
1.0b	(sqrt (* PI 2.0))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

207×	`*-un-lft-identity`
142×	`times-frac`
95×	`add-sqr-sqrt`
83×	`add-cube-cbrt`
55×	`unpow-prod-up`
45×	`prod-diff`
42×	`fma-def`
34×	`distribute-lft-out`
27×	`distribute-lft-out--`
25×	`unpow-prod-down`
21×	`exp-sum`
20×	`associate-/l*`
11×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`sub-neg` `frac-add` `associate-/r/` `sqr-pow`
4×	`expm1-log1p-u` `associate-/r*` `sum-log` `log1p-expm1-u`
3×	`flip3-+` `div-exp` `flip-+` `div-inv`
2×	`+-commutative` `flip3--` `sqrt-pow1` `flip--`
1×	`cbrt-undiv` `pow-to-exp` `associate-+r-` `associate-+r+` `frac-2neg` `pow1/2` `exp-diff` `pow-prod-down` `pow-exp` `clear-num` `sqrt-prod` `associate-/l/` `pow-sub`

Counts

4 → 224

Calls

4 calls:

148.0ms	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
48.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
83.0ms	(/ (pow (+ 0.5 (- 7.0 z)) (- 0.5 z)) (exp (+ 0.5 (- 7.0 z))))
2.0ms	(sqrt (* PI 2.0))

series343.0ms

Counts

4 → 10

Calls

4 calls:

110.0ms	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
72.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
160.0ms	(/ (pow (+ 0.5 (- 7.0 z)) (- 0.5 z)) (exp (+ 0.5 (- 7.0 z))))
0.0ms	(sqrt (* PI 2.0))

simplify960.0ms

Counts

234 → 234

Iterations

Useful iterations: done (947.0ms)

Iter	Nodes	Cost
0	415	5509
1	945	4937
2	2950	4618
done	5001	4573

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ PI (sin (* PI z))) (sqrt (* PI 2.0)))
0.9b	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
0.9b	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
1.0b	(sqrt (* PI 2.0))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

129×	`*-un-lft-identity`
72×	`times-frac`
47×	`add-sqr-sqrt`
42×	`fma-def`
30×	`add-cube-cbrt`
24×	`distribute-lft-out`
22×	`distribute-lft-out--`
13×	`associate-l`
11×	`add-log-exp`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`difference-of-squares`
5×	`frac-add`
4×	`expm1-log1p-u` `associate-r` `sum-log` `associate-/r/` `log1p-expm1-u`
3×	`flip3-+` `flip-+` `div-inv`
2×	`+-commutative` `flip3--` `sqrt-pow1` `pow-prod-down` `prod-exp` `sqrt-prod` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate-+r+` `pow1/2` `div-exp` `associate-l/` `-commutative`

Counts

4 → 137

Calls

4 calls:

14.0ms	(* (/ PI (sin (* PI z))) (sqrt (* PI 2.0)))
149.0ms	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
49.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
5.0ms	(sqrt (* PI 2.0))

series351.0ms

Counts

4 → 10

Calls

4 calls:

169.0ms	(* (/ PI (sin (* PI z))) (sqrt (* PI 2.0)))
109.0ms	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
74.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
0.0ms	(sqrt (* PI 2.0))

simplify797.0ms

Counts

147 → 147

Iterations

Useful iterations: done (793.0ms)

Iter	Nodes	Cost
0	225	1859
1	594	1745
2	1793	1645
done	5002	1633

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
0.9b	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
1.0b	(sqrt (* PI 2.0))
1.0b	(* PI (sqrt (* PI 2.0)))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

151.0ms	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
49.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
2.0ms	(sqrt (* PI 2.0))
7.0ms	(* PI (sqrt (* PI 2.0)))

series178.0ms

Counts

4 → 8

Calls

4 calls:

106.0ms	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
72.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
0.0ms	(sqrt (* PI 2.0))
0.0ms	(* PI (sqrt (* PI 2.0)))

simplify1.3s

Counts

131 → 131

Iterations

Useful iterations: 3 (566.0ms)

Iter	Nodes	Cost
0	154	1435
1	418	1333
2	1301	1269
3	4307	1258
done	5001	1258

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
0.9b	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
0.9b	(/ (pow (+ 0.5 (- 7.0 z)) (- 0.5 z)) (exp (+ 0.5 7.0)))
1.0b	(sqrt (* PI 2.0))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

207×	`*-un-lft-identity`
142×	`times-frac`
95×	`add-sqr-sqrt`
83×	`add-cube-cbrt`
55×	`unpow-prod-up`
45×	`prod-diff`
42×	`fma-def`
34×	`distribute-lft-out`
27×	`distribute-lft-out--`
25×	`unpow-prod-down`
21×	`exp-sum`
20×	`associate-/l*`
11×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`sub-neg` `frac-add` `sqr-pow`
4×	`expm1-log1p-u` `associate-/r*` `sum-log` `associate-/r/` `log1p-expm1-u`
3×	`flip3-+` `div-exp` `flip-+` `div-inv`
2×	`+-commutative` `flip3--` `sqrt-pow1` `flip--`
1×	`cbrt-undiv` `pow-to-exp` `associate-+r+` `frac-2neg` `pow1/2` `pow-prod-down` `pow-exp` `clear-num` `sqrt-prod` `associate-/l/` `pow-sub`

Counts

4 → 223

Calls

4 calls:

147.0ms	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
48.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
57.0ms	(/ (pow (+ 0.5 (- 7.0 z)) (- 0.5 z)) (exp (+ 0.5 7.0)))
2.0ms	(sqrt (* PI 2.0))

series364.0ms

Counts

4 → 10

Calls

4 calls:

105.0ms	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
72.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
187.0ms	(/ (pow (+ 0.5 (- 7.0 z)) (- 0.5 z)) (exp (+ 0.5 7.0)))
0.0ms	(sqrt (* PI 2.0))

simplify921.0ms

Counts

233 → 233

Iterations

Useful iterations: done (912.0ms)

Iter	Nodes	Cost
0	382	5057
1	866	4485
2	2607	4178
done	5000	4133

prune2.0s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes333.0ms

Accuracy

0% (1.1b remaining)

Error of 1.2b against oracle of 0.1b and baseline of 1.2b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	107
1	77	107
done	77	107

end0.0ms

sample47.9s

Algorithm

intervals

Results

42.8s	4054×	body	10240	exit
1.7s	1530×	body	1280	nan
1.5s	8094×	body	80	valid
919.0ms	1245×	body	640	nan
324.0ms	623×	body	320	nan
108.0ms	301×	body	160	nan
59.0ms	332×	body	80	nan