Details

sample3.6s

Algorithm

intervals

Results

3.0s	144×	body	10240	exit
188.0ms	259×	body	80	valid
147.0ms	45×	body	1280	nan
83.0ms	35×	body	640	nan
35.0ms	20×	body	320	nan
10.0ms	9×	body	160	nan
3.0ms	6×	body	80	nan

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
3	3482
2	615
1	154
0	60

prune86.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

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	(sqrt (* 2 PI))
1.2b	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))

rewrite301.0ms

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:

45.0ms	(* (sqrt (* 2 PI)) (/ PI (sin (* PI z))))
46.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
4.0ms	(sqrt (* 2 PI))
195.0ms	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))

series541.0ms

Counts

4 → 10

Calls

4 calls:

250.0ms	(* (sqrt (* 2 PI)) (/ PI (sin (* PI z))))
74.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
0.0ms	(sqrt (* 2 PI))
217.0ms	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))

simplify2.6s

Counts

419 → 419

Iterations

Iter	Nodes
2	4106
1	1492
0	696

prune12.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize190.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
1.0b	(sqrt (* 2 PI))
1.0b	(* (sqrt (* 2 PI)) PI)
1.2b	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))

rewrite285.0ms

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:

59.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
8.0ms	(sqrt (* 2 PI))
21.0ms	(* (sqrt (* 2 PI)) PI)
185.0ms	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))

series282.0ms

Counts

4 → 8

Calls

4 calls:

78.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
0.0ms	(sqrt (* 2 PI))
0.0ms	(* (sqrt (* 2 PI)) PI)
203.0ms	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))

simplify2.0s

Counts

403 → 403

Iterations

Iter	Nodes
2	3246
1	1249
0	605

prune12.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize166.0ms

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))
1.0b	(sqrt (* 2 PI))
1.0b	(* (sqrt (* 2 PI)) PI)

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

347×	`*-un-lft-identity`
307×	`add-sqr-sqrt`
200×	`unpow-prod-up` `times-frac`
180×	`prod-diff`
155×	`add-cube-cbrt`
99×	`difference-of-squares`
59×	`associate-/l*` `distribute-lft-out--`
44×	`associate--l+`
21×	`fma-def`
20×	`unpow-prod-down`
13×	`distribute-lft-out`
9×	`pow1`
8×	`sub-neg` `add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u` `associate--r-` `sqr-pow`
3×	`associate-/r` `div-exp` `associate-r*`
2×	`sqrt-pow1` `pow-prod-down` `associate-/r/` `sqrt-prod` `div-inv`
1×	`pow-to-exp` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `flip3--` `pow1/2` `frac-add` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `flip--` `pow-sub` `unswap-sqr` `associate-/l/`

Counts

4 → 334

Calls

4 calls:

46.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
133.0ms	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp 7))
4.0ms	(sqrt (* 2 PI))
18.0ms	(* (sqrt (* 2 PI)) PI)

series377.0ms

Counts

4 → 8

Calls

4 calls:

100.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
277.0ms	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp 7))
0.0ms	(sqrt (* 2 PI))
0.0ms	(* (sqrt (* 2 PI)) PI)

simplify1.6s

Counts

342 → 342

Iterations

Iter	Nodes
2	2797
1	1163
0	536

prune10.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize201.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt (* 2 PI))
1.0b	(* (sqrt (* 2 PI)) (sqrt PI))
1.0b	(* (* (sqrt (* 2 PI)) (sqrt PI)) (sqrt PI))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1`
16×	`pow-prod-down`
15×	`add-sqr-sqrt`
13×	`sqrt-pow1`
12×	`associate-r` `sqrt-prod`
11×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1/2`
5×	`associate-l`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-unprod`
2×	`*-commutative` `unswap-sqr`
1×	`rem-sqrt-square`

Counts

4 → 88

Calls

4 calls:

2.0ms	(sqrt PI)
7.0ms	(sqrt (* 2 PI))
32.0ms	(* (sqrt (* 2 PI)) (sqrt PI))
102.0ms	(* (* (sqrt (* 2 PI)) (sqrt PI)) (sqrt PI))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(sqrt (* 2 PI))
0.0ms	(* (sqrt (* 2 PI)) (sqrt PI))
0.0ms	(* (* (sqrt (* 2 PI)) (sqrt PI)) (sqrt PI))

simplify3.9s

Counts

92 → 92

Iterations

Iter	Nodes
4	2870
3	1279
2	397
1	161
0	76

prune2.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes263.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify31.0ms

Iterations

Iter	Nodes
2	79
1	79
0	62

end0.0ms

sample1.6m

Algorithm

intervals

Results

1.2m	3879×	body	10240	exit
7.1s	1456×	body	1280	nan
6.2s	8086×	body	80	valid
5.3s	1224×	body	640	nan
1.7s	591×	body	320	nan
870.0ms	314×	body	160	nan
161.0ms	267×	body	80	nan