Details

sample1.0s

Algorithm

intervals

Results

522.0ms	123×	body	10240	exit
192.0ms	59×	body	1280	nan
130.0ms	258×	body	80	valid
58.0ms	32×	body	640	nan
31.0ms	21×	body	320	nan
9.0ms	6×	body	160	nan
2.0ms	5×	body	80	nan

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
3	3482
2	615
1	154
0	60

prune57.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize201.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* (sqrt (* 2 PI)) (/ PI (sin (* PI z)))) (/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5))))
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))

rewrite821.0ms

Algorithm

rewrite-expression-head

Rules

710×	`*-un-lft-identity`
643×	`add-sqr-sqrt`
495×	`times-frac`
450×	`unpow-prod-up`
405×	`prod-diff`
313×	`add-cube-cbrt`
241×	`associate-r`
219×	`difference-of-squares`
124×	`distribute-lft-out--`
119×	`exp-sum`
99×	`associate--l+`
59×	`associate-/l*`
45×	`unpow-prod-down`
39×	`add-exp-log`
27×	`add-cbrt-cube`
23×	`distribute-lft-out`
21×	`fma-def`
20×	`prod-exp`
18×	`sub-neg`
16×	`div-exp`
12×	`pow1`
10×	`cbrt-unprod`
9×	`associate--r-` `sqr-pow`
6×	`cbrt-undiv` `add-log-exp`
4×	`expm1-log1p-u` `pow-to-exp` `associate-/r*` `pow-prod-down` `pow-exp` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`associate-*r/` `div-inv`
2×	`sqrt-pow1` `exp-diff` `associate-+l-`
1×	`frac-times` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `flip3--` `pow1/2` `associate-l` `associate-l/` `frac-add` `-commutative` `sqrt-prod` `flip-+` `flip--` `pow-sub` `associate-/l/`

Counts

4 → 649

Calls

4 calls:

452.0ms	(* (* (sqrt (* 2 PI)) (/ PI (sin (* PI z)))) (/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5))))
59.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
266.0ms	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))
4.0ms	(sqrt (* 2 PI))

series1.1s

Counts

4 → 10

Calls

4 calls:

752.0ms	(* (* (sqrt (* 2 PI)) (/ PI (sin (* PI z)))) (/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5))))
89.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
256.0ms	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))
0.0ms	(sqrt (* 2 PI))

simplify2.3s

Counts

659 → 659

Iterations

Iter	Nodes
1	2506
0	893

prune29.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize232.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (sqrt (* 2 PI)) PI) (/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5))))
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)

rewrite626.0ms

Algorithm

rewrite-expression-head

Rules

675×	`*-un-lft-identity`
632×	`add-sqr-sqrt`
472×	`times-frac`
450×	`unpow-prod-up`
405×	`prod-diff`
306×	`add-cube-cbrt`
244×	`associate-r`
216×	`difference-of-squares`
119×	`exp-sum`
117×	`distribute-lft-out--`
99×	`associate--l+`
59×	`associate-/l*`
45×	`unpow-prod-down`
26×	`add-exp-log`
20×	`add-cbrt-cube`
18×	`sub-neg` `distribute-lft-out`
14×	`pow1`
13×	`prod-exp`
9×	`div-exp` `associate--r-` `sqr-pow`
7×	`cbrt-unprod`
5×	`associate-l` `pow-prod-down`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-exp`
2×	`sqrt-pow1` `exp-diff` `associate-/r/` `*-commutative` `associate-+l-` `sqrt-prod` `div-inv`
1×	`clear-num` `frac-2neg` `pow1/2` `associate-*r/` `pow-sub` `unswap-sqr` `associate-/l/`

Counts

4 → 622

Calls

4 calls:

379.0ms	(* (* (sqrt (* 2 PI)) PI) (/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5))))
161.0ms	(/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5)))
7.0ms	(sqrt (* 2 PI))
28.0ms	(* (sqrt (* 2 PI)) PI)

series891.0ms

Counts

4 → 8

Calls

4 calls:

618.0ms	(* (* (sqrt (* 2 PI)) PI) (/ (pow (+ (- 7 z) 0.5) (- (- 1 z) (- 1 0.5))) (exp (+ (- 7 z) 0.5))))
273.0ms	(/ (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

630 → 630

Iterations

Iter	Nodes
1	2351
0	793

prune29.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize276.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (* (sqrt (* 2 PI)) PI) (/ (pow (+ (- 7 z) 0.5) (- (- 1 z) 1)) (* (cbrt (exp (+ (- 7 z) 0.5))) (cbrt (exp (+ (- 7 z) 0.5)))))) (/ (pow (+ (- 7 z) 0.5) 0.5) (cbrt (exp (+ (- 7 z) 0.5)))))
1.0b	(sqrt (* 2 PI))
1.0b	(* (sqrt (* 2 PI)) PI)
5.7b	(- (- 1 z) 1)

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

297×	`add-exp-log`
169×	`prod-exp`
108×	`*-un-lft-identity`
93×	`div-exp`
73×	`add-sqr-sqrt`
71×	`associate-r`
63×	`times-frac`
56×	`add-cbrt-cube`
55×	`add-cube-cbrt`
37×	`cbrt-unprod`
36×	`cbrt-prod`
35×	`unpow-prod-down`
31×	`pow-to-exp` `pow-exp`
27×	`prod-diff`
18×	`pow1`
15×	`cbrt-undiv`
14×	`distribute-lft-out` `distribute-lft-out--`
11×	`associate--l+`
10×	`difference-of-squares`
9×	`exp-sum` `add-log-exp`
8×	`pow-prod-down`
7×	`sqr-pow`
6×	`fma-neg`
5×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`diff-log` `associate-*r/`
2×	`sub-neg` `sqrt-pow1` `*-commutative` `sqrt-prod`
1×	`associate--l-` `frac-times` `cbrt-div` `expm1-def` `flip3--` `pow1/2` `exp-diff` `difference-of-sqr-1` `associate-*l/` `associate-/r/` `associate-+l-` `div-inv` `flip--` `unswap-sqr`

Counts

4 → 254

Calls

4 calls:

1.1s	(* (* (* (sqrt (* 2 PI)) PI) (/ (pow (+ (- 7 z) 0.5) (- (- 1 z) 1)) (* (cbrt (exp (+ (- 7 z) 0.5))) (cbrt (exp (+ (- 7 z) 0.5)))))) (/ (pow (+ (- 7 z) 0.5) 0.5) (cbrt (exp (+ (- 7 z) 0.5)))))
4.0ms	(sqrt (* 2 PI))
14.0ms	(* (sqrt (* 2 PI)) PI)
30.0ms	(- (- 1 z) 1)

series686.0ms

Counts

4 → 8

Calls

4 calls:

663.0ms	(* (* (* (sqrt (* 2 PI)) PI) (/ (pow (+ (- 7 z) 0.5) (- (- 1 z) 1)) (* (cbrt (exp (+ (- 7 z) 0.5))) (cbrt (exp (+ (- 7 z) 0.5)))))) (/ (pow (+ (- 7 z) 0.5) 0.5) (cbrt (exp (+ (- 7 z) 0.5)))))
0.0ms	(sqrt (* 2 PI))
0.0ms	(* (sqrt (* 2 PI)) PI)
23.0ms	(- (- 1 z) 1)

simplify3.3s

Counts

262 → 262

Iterations

Iter	Nodes
2	5344
1	1349
0	486

prune12.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize174.0ms

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)
5.7b	(- (- 1 z) 1)

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

77×	`*-un-lft-identity`
55×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
27×	`prod-diff`
23×	`times-frac`
21×	`fma-def`
14×	`distribute-lft-out--`
13×	`difference-of-squares`
11×	`associate--l+` `add-log-exp`
9×	`pow1`
7×	`add-exp-log`
6×	`add-cbrt-cube` `fma-neg`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u`
3×	`diff-log` `associate-r`
2×	`sub-neg` `sqrt-pow1` `flip3--` `pow-prod-down` `associate-/r/` `sqrt-prod` `flip--`
1×	`associate--l-` `+-commutative` `expm1-def` `sum-log` `flip3-+` `pow1/2` `difference-of-sqr-1` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 135

Calls

4 calls:

36.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
5.0ms	(sqrt (* 2 PI))
15.0ms	(* (sqrt (* 2 PI)) PI)
45.0ms	(- (- 1 z) 1)

series79.0ms

Counts

4 → 8

Calls

4 calls:

62.0ms	(+ (/ 9.984369578019572e-06 (- 7 z)) (/ -0.13857109526572012 (- 6 z)))
0.0ms	(sqrt (* 2 PI))
0.0ms	(* (sqrt (* 2 PI)) PI)
16.0ms	(- (- 1 z) 1)

simplify3.7s

Counts

143 → 143

Iterations

Iter	Nodes
3	3134
2	1086
1	439
0	201

prune6.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes221.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify21.0ms

Iterations

Iter	Nodes
2	77
1	77
0	61

end0.0ms

sample40.7s

Algorithm

intervals

Results

23.2s	3793×	body	10240	exit
6.0s	1527×	body	1280	nan
5.9s	8076×	body	80	valid
3.3s	1258×	body	640	nan
1.2s	584×	body	320	nan
382.0ms	280×	body	160	nan
191.0ms	271×	body	80	nan