Details

sample1.8s

Algorithm

intervals

Results

501.0ms	114×	body	10240	exit
486.0ms	34×	body	1280	nan
296.0ms	103×	body	1280	valid
150.0ms	83×	body	640	valid
125.0ms	49×	body	640	nan
52.0ms	37×	body	320	valid
25.0ms	18×	body	320	nan
21.0ms	21×	body	160	valid
16.0ms	18×	body	160	nan
7.0ms	15×	body	80	valid
6.0ms	14×	body	80	nan

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
3	2093
2	410
1	139
0	55

prune67.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize195.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
22×	`associate-l`
20×	`add-sqr-sqrt`
14×	`unpow-prod-down` `add-exp-log`
10×	`pow1` `add-cube-cbrt` `distribute-lft-out`
8×	`add-cbrt-cube` `associate-r`
6×	`prod-exp` `unswap-sqr`
4×	`sqrt-pow1` `sqrt-prod` `insert-posit16` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-up` `pow1/2` `pow-prod-down` `associate-l/` `pow-exp` `-commutative` `associate-+l-` `cbrt-unprod` `distribute-lft-out--` `pow-sub`

Counts

4 → 88

Calls

4 calls:

518.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
516.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
5.0ms	(sqrt (* PI 2))
5.0ms	(sqrt (* PI 2))

series828.0ms

Counts

4 → 8

Calls

4 calls:

417.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
410.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))
0.0ms	(sqrt (* PI 2))

simplify3.6s

Counts

96 → 96

Iterations

Iter	Nodes
3	6266
2	1324
1	399
0	159

prune3.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize177.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (* PI 2)) (+ (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (/ 12.507343278686905 (+ 4 z)) (+ (+ (+ (+ (/ -176.6150291621406 (+ z 3)) 0.9999999999998099) (/ -1259.1392167224028 (+ 1 z))) (/ 771.3234287776531 (+ 2 z))) (/ 676.5203681218851 z)))) (/ -0.13857109526572012 (- z -5))))
0.9b	(+ (/ -176.6150291621406 (+ z 3)) 0.9999999999998099)
1.0b	(/ (pow (+ 0.5 (+ z 6)) (- z (- 1 0.5))) (exp (+ 0.5 (+ z 6))))
1.0b	(sqrt (* PI 2))

rewrite3.7m

Algorithm

rewrite-expression-head

Rules

132×	`frac-add`
130×	`*-un-lft-identity`
77×	`distribute-lft-out`
48×	`times-frac`
34×	`associate-*r/`
31×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
28×	`flip3-+` `flip-+`
25×	`unpow-prod-down`
16×	`associate-r`
15×	`unpow-prod-up`
13×	`exp-sum`
12×	`associate-/l*`
9×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`sub-neg` `associate--r-` `sqr-pow`
4×	`associate-/r` `associate-l*` `insert-posit16`
3×	`div-exp`
2×	`sqrt-pow1` `pow-prod-down` `sqrt-prod`
1×	`distribute-rgt-in` `pow-to-exp` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `distribute-lft-in` `pow1/2` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `pow-sub` `unswap-sqr` `associate-/l/`

Counts

4 → 174

Calls

4 calls:

3.7m	(* (sqrt (* PI 2)) (+ (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (/ 12.507343278686905 (+ 4 z)) (+ (+ (+ (+ (/ -176.6150291621406 (+ z 3)) 0.9999999999998099) (/ -1259.1392167224028 (+ 1 z))) (/ 771.3234287776531 (+ 2 z))) (/ 676.5203681218851 z)))) (/ -0.13857109526572012 (- z -5))))
41.0ms	(+ (/ -176.6150291621406 (+ z 3)) 0.9999999999998099)
127.0ms	(/ (pow (+ 0.5 (+ z 6)) (- z (- 1 0.5))) (exp (+ 0.5 (+ z 6))))
6.0ms	(sqrt (* PI 2))

series415.0ms

Counts

4 → 10

Calls

4 calls:

215.0ms	(* (sqrt (* PI 2)) (+ (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (/ 12.507343278686905 (+ 4 z)) (+ (+ (+ (+ (/ -176.6150291621406 (+ z 3)) 0.9999999999998099) (/ -1259.1392167224028 (+ 1 z))) (/ 771.3234287776531 (+ 2 z))) (/ 676.5203681218851 z)))) (/ -0.13857109526572012 (- z -5))))
26.0ms	(+ (/ -176.6150291621406 (+ z 3)) 0.9999999999998099)
173.0ms	(/ (pow (+ 0.5 (+ z 6)) (- z (- 1 0.5))) (exp (+ 0.5 (+ z 6))))
0.0ms	(sqrt (* PI 2))

simplify2.6s

Counts

184 → 184

Iterations

Iter	Nodes
1	2460
0	727

prune4.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize182.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (/ -176.6150291621406 (+ z 3)) 0.9999999999998099)
1.0b	(/ (pow (+ 0.5 (+ z 6)) (- z (- 1 0.5))) (exp (+ 0.5 (+ z 6))))
1.0b	(* (+ (/ -176.6150291621406 (+ z 3)) 0.9999999999998099) (+ (/ -176.6150291621406 (+ z 3)) 0.9999999999998099))
1.0b	(sqrt (* PI 2))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
48×	`times-frac`
33×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
25×	`unpow-prod-down`
22×	`distribute-lft-out`
15×	`unpow-prod-up`
14×	`pow1`
13×	`exp-sum`
12×	`associate-/l*`
8×	`add-cbrt-cube` `add-exp-log`
7×	`flip3-+` `flip-+`
6×	`swap-sqr` `add-log-exp`
5×	`sub-neg` `associate--r-` `sqr-pow`
4×	`frac-times` `associate-/r` `associate-r` `associate-l*` `insert-posit16`
3×	`div-exp`
2×	`sqrt-pow1` `pow-prod-down` `associate-l/` `associate-r/`
1×	`pow2` `distribute-rgt-in` `pow-to-exp` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `distribute-lft-in` `pow-plus` `pow1/2` `pow-exp` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-prod` `cbrt-unprod` `div-inv` `pow-sub` `unswap-sqr` `associate-/l/`

Counts

4 → 146

Calls

4 calls:

21.0ms	(+ (/ -176.6150291621406 (+ z 3)) 0.9999999999998099)
85.0ms	(/ (pow (+ 0.5 (+ z 6)) (- z (- 1 0.5))) (exp (+ 0.5 (+ z 6))))
116.0ms	(* (+ (/ -176.6150291621406 (+ z 3)) 0.9999999999998099) (+ (/ -176.6150291621406 (+ z 3)) 0.9999999999998099))
5.0ms	(sqrt (* PI 2))

series235.0ms

Counts

4 → 10

Calls

4 calls:

23.0ms	(+ (/ -176.6150291621406 (+ z 3)) 0.9999999999998099)
175.0ms	(/ (pow (+ 0.5 (+ z 6)) (- z (- 1 0.5))) (exp (+ 0.5 (+ z 6))))
37.0ms	(* (+ (/ -176.6150291621406 (+ z 3)) 0.9999999999998099) (+ (/ -176.6150291621406 (+ z 3)) 0.9999999999998099))
0.0ms	(sqrt (* PI 2))

simplify1.3s

Counts

156 → 156

Iterations

Iter	Nodes
2	2943
1	839
0	338

prune5.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize138.0ms

Local error

Found 4 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
8×	`sqrt-pow1`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube` `pow1/2` `pow-prod-down` `add-exp-log` `add-cube-cbrt` `sqrt-prod` `insert-posit16` `add-log-exp`

Counts

4 → 48

Calls

4 calls:

3.0ms	(sqrt (* PI 2))
3.0ms	(sqrt (* PI 2))
3.0ms	(sqrt (* PI 2))
3.0ms	(sqrt (* PI 2))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify3.8s

Counts

52 → 52

Iterations

Iter	Nodes
7	5149
6	1896
5	770
4	368
3	179
2	91
1	45
0	27

prune1.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes119.0ms

Accuracy

0% (0.4b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 0.9b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
2	70
1	70
0	52

end0.0ms

sample31.9s

Algorithm

intervals

Results

11.6s	3841×	body	10240	exit
7.2s	3437×	body	1280	valid
4.3s	2408×	body	640	valid
3.1s	1473×	body	1280	nan
2.1s	1253×	body	320	valid
1.8s	1206×	body	640	nan
641.0ms	650×	body	320	nan
394.0ms	621×	body	160	valid
179.0ms	313×	body	160	nan
151.0ms	373×	body	80	valid
106.0ms	303×	body	80	nan