Details

sample3.1s

Algorithm

intervals

Results

2.4s	123×	body	10240	exit
173.0ms	259×	body	80	valid
149.0ms	47×	body	1280	nan
147.0ms	37×	body	640	nan
69.0ms	20×	body	320	nan
10.0ms	8×	body	160	nan
4.0ms	7×	body	80	nan

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
3	3482
2	615
1	154
0	60

prune92.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize161.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (* 2 PI)) (/ PI (sin (* PI z))))
1.0b	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
1.0b	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))
1.0b	(sqrt (* 2 PI))

rewrite339.0ms

Algorithm

rewrite-expression-head

Rules

414×	`*-un-lft-identity`
372×	`add-sqr-sqrt`
269×	`times-frac`
250×	`unpow-prod-up`
225×	`prod-diff`
181×	`add-cube-cbrt`
123×	`difference-of-squares`
72×	`distribute-lft-out--`
60×	`exp-sum`
59×	`associate-/l*`
55×	`associate--l+`
25×	`unpow-prod-down`
21×	`fma-def`
15×	`distribute-lft-out`
13×	`associate-r`
11×	`add-cbrt-cube` `add-exp-log`
10×	`sub-neg`
9×	`pow1`
6×	`add-log-exp`
5×	`associate--r-` `sqr-pow`
4×	`expm1-log1p-u` `associate-/r` `div-exp` `associate-l*` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r/` `div-inv`
2×	`cbrt-undiv` `sqrt-pow1` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `unswap-sqr`
1×	`pow-to-exp` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `flip3--` `pow1/2` `exp-diff` `frac-add` `pow-exp` `associate-r/` `-commutative` `associate-+l-` `flip-+` `flip--` `pow-sub` `associate-/l/`

Counts

4 → 409

Calls

4 calls:

48.0ms	(* (sqrt (* 2 PI)) (/ PI (sin (* PI z))))
58.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
214.0ms	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))
7.0ms	(sqrt (* 2 PI))

series515.0ms

Counts

4 → 10

Calls

4 calls:

223.0ms	(* (sqrt (* 2 PI)) (/ PI (sin (* PI z))))
71.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
221.0ms	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))
0.0ms	(sqrt (* 2 PI))

simplify2.1s

Counts

419 → 419

Iterations

Iter	Nodes
2	4083
1	1492
0	696

prune18.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize205.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
1.0b	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))
1.0b	(sqrt (* 2 PI))
1.0b	(* (sqrt (* 2 PI)) PI)

rewrite284.0ms

Algorithm

rewrite-expression-head

Rules

408×	`*-un-lft-identity`
363×	`add-sqr-sqrt`
259×	`times-frac`
250×	`unpow-prod-up`
225×	`prod-diff`
175×	`add-cube-cbrt`
123×	`difference-of-squares`
72×	`distribute-lft-out--`
60×	`exp-sum`
59×	`associate-/l*`
55×	`associate--l+`
25×	`unpow-prod-down`
21×	`fma-def`
15×	`distribute-lft-out`
10×	`sub-neg`
9×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`associate--r-` `sqr-pow`
4×	`expm1-log1p-u` `associate-/r` `associate-l*` `insert-posit16` `log1p-expm1-u`
3×	`div-exp` `associate-r` `associate-/r/`
2×	`sqrt-pow1` `pow-prod-down` `sqrt-prod` `div-inv`
1×	`pow-to-exp` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `flip3--` `pow1/2` `exp-diff` `frac-add` `pow-exp` `prod-exp` `*-commutative` `associate-+l-` `cbrt-unprod` `flip-+` `flip--` `pow-sub` `unswap-sqr` `associate-/l/`

Counts

4 → 395

Calls

4 calls:

62.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
186.0ms	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))
4.0ms	(sqrt (* 2 PI))
20.0ms	(* (sqrt (* 2 PI)) PI)

series270.0ms

Counts

4 → 8

Calls

4 calls:

83.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
187.0ms	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))
0.0ms	(sqrt (* 2 PI))
0.0ms	(* (sqrt (* 2 PI)) PI)

simplify2.1s

Counts

403 → 403

Iterations

Iter	Nodes
2	3214
1	1248
0	605

prune18.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize191.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (* 2 PI)) (/ PI (sin (* PI z))))
1.0b	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
1.0b	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))
1.0b	(sqrt (* 2 PI))

rewrite353.0ms

Algorithm

rewrite-expression-head

Rules

414×	`*-un-lft-identity`
372×	`add-sqr-sqrt`
269×	`times-frac`
250×	`unpow-prod-up`
225×	`prod-diff`
181×	`add-cube-cbrt`
123×	`difference-of-squares`
72×	`distribute-lft-out--`
60×	`exp-sum`
59×	`associate-/l*`
55×	`associate--l+`
25×	`unpow-prod-down`
21×	`fma-def`
15×	`distribute-lft-out`
13×	`associate-r`
11×	`add-cbrt-cube` `add-exp-log`
10×	`sub-neg`
9×	`pow1`
6×	`add-log-exp`
5×	`associate--r-` `sqr-pow`
4×	`expm1-log1p-u` `associate-/r` `div-exp` `associate-l*` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r/` `div-inv`
2×	`cbrt-undiv` `sqrt-pow1` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `unswap-sqr`
1×	`pow-to-exp` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `flip3--` `pow1/2` `exp-diff` `frac-add` `pow-exp` `associate-r/` `-commutative` `associate-+l-` `flip-+` `flip--` `pow-sub` `associate-/l/`

Counts

4 → 409

Calls

4 calls:

39.0ms	(* (sqrt (* 2 PI)) (/ PI (sin (* PI z))))
50.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
234.0ms	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))
8.0ms	(sqrt (* 2 PI))

series568.0ms

Counts

4 → 10

Calls

4 calls:

234.0ms	(* (sqrt (* 2 PI)) (/ PI (sin (* PI z))))
70.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
264.0ms	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))
0.0ms	(sqrt (* 2 PI))

simplify2.8s

Counts

419 → 419

Iterations

Iter	Nodes
2	3867
1	1421
0	667

prune19.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize231.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (sqrt (* 2 PI)) (/ PI (sin (* PI z)))) (expm1 (log1p (* (pow (+ (- 7 z) 0.5) (- 1 z)) (/ (pow (+ (- 7 z) 0.5) (- (- 1 0.5))) (exp (+ (- 7 z) 0.5))))))) (+ (+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z))) (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (+ (/ -176.6150291621406 (- 4 z)) 0.9999999999998099) (+ (/ 771.3234287776531 (+ 2 (- 1 z))) (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))))
0.5b	(* (sqrt (* 2 PI)) (/ PI (sin (* PI z))))
1.0b	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
1.0b	(sqrt (* 2 PI))

rewrite1.0m

Algorithm

rewrite-expression-head

Rules

393×	`frac-add`
155×	`*-un-lft-identity`
107×	`flip3-+` `flip-+`
102×	`associate-*r/`
92×	`distribute-lft-out`
52×	`associate-*l/`
50×	`frac-times`
34×	`associate-r`
33×	`add-sqr-sqrt` `times-frac`
23×	`add-cbrt-cube` `add-exp-log`
22×	`add-cube-cbrt`
21×	`fma-def`
18×	`pow1`
11×	`prod-exp` `cbrt-unprod`
8×	`pow-prod-down`
7×	`distribute-lft-out--`
6×	`add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`cbrt-undiv` `sqrt-pow1` `div-exp` `associate-/r/` `*-commutative` `sqrt-prod` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `flip3--` `pow1/2` `flip--`

Counts

4 → 238

Calls

4 calls:

1.0m	(* (* (* (sqrt (* 2 PI)) (/ PI (sin (* PI z)))) (expm1 (log1p (* (pow (+ (- 7 z) 0.5) (- 1 z)) (/ (pow (+ (- 7 z) 0.5) (- (- 1 0.5))) (exp (+ (- 7 z) 0.5))))))) (+ (+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z))) (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (+ (/ -176.6150291621406 (- 4 z)) 0.9999999999998099) (+ (/ 771.3234287776531 (+ 2 (- 1 z))) (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))))
57.0ms	(* (sqrt (* 2 PI)) (/ PI (sin (* PI z))))
40.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
7.0ms	(sqrt (* 2 PI))

series5.9s

Counts

4 → 10

Calls

4 calls:

5.6s	(* (* (* (sqrt (* 2 PI)) (/ PI (sin (* PI z)))) (expm1 (log1p (* (pow (+ (- 7 z) 0.5) (- 1 z)) (/ (pow (+ (- 7 z) 0.5) (- (- 1 0.5))) (exp (+ (- 7 z) 0.5))))))) (+ (+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z))) (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (+ (+ (/ -176.6150291621406 (- 4 z)) 0.9999999999998099) (+ (/ 771.3234287776531 (+ 2 (- 1 z))) (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z)))))) (/ 12.507343278686905 (- 5 z)))))
222.0ms	(* (sqrt (* 2 PI)) (/ PI (sin (* PI z))))
75.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
0.0ms	(sqrt (* 2 PI))

simplify9.7s

Counts

248 → 248

Iterations

Iter	Nodes
1	4326
0	994

prune13.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes666.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify47.0ms

Iterations

Iter	Nodes
2	108
1	108
0	81

end0.0ms

sample1.4m

Algorithm

intervals

Results

1.1m	3892×	body	10240	exit
5.5s	1489×	body	1280	nan
5.3s	8087×	body	80	valid
3.6s	1257×	body	640	nan
1.5s	610×	body	320	nan
397.0ms	302×	body	160	nan
163.0ms	255×	body	80	nan