Details

sample1.3s

Algorithm

intervals

Results

786.0ms	124×	body	10240	exit
232.0ms	112×	body	1280	valid
93.0ms	71×	body	640	valid
52.0ms	33×	body	1280	nan
44.0ms	48×	body	320	valid
31.0ms	26×	body	640	nan
11.0ms	11×	body	320	nan
9.0ms	16×	body	160	valid
3.0ms	10×	body	80	valid
3.0ms	6×	body	160	nan
2.0ms	7×	body	80	nan

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5019
3	2301
2	420
1	140
0	55

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize141.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.6s

Algorithm

rewrite-expression-head

Rules

552×	`frac-add`
168×	`flip3-+` `flip-+`
155×	`*-un-lft-identity`
116×	`distribute-lft-out`
72×	`frac-times` `associate-*r/`
31×	`associate-r`
27×	`add-exp-log`
21×	`associate-l`
20×	`add-cbrt-cube`
19×	`add-sqr-sqrt`
14×	`prod-exp`
12×	`add-cube-cbrt`
9×	`pow1`
8×	`times-frac` `div-exp`
6×	`unpow-prod-down` `cbrt-unprod`
4×	`cbrt-undiv` `associate-/r*` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `unpow-prod-up` `exp-sum` `associate-*l/` `pow-exp`
2×	`associate-+r-` `sqrt-pow1` `exp-diff` `pow-prod-down` `associate-/r/` `*-commutative` `sqrt-prod` `div-inv` `pow-sub` `sqr-pow`
1×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `pow1/2` `associate-/l*` `distribute-lft-out--` `associate--r-` `associate-/l/`

Counts

4 → 275

Calls

4 calls:

129.0ms	(/ (* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2))) (exp (+ 0.5 (- z -6))))
194.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
43.2s	(* (/ (* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2))) (exp (+ 0.5 (- z -6)))) (+ (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5))) (+ (+ (+ (/ 12.507343278686905 (+ z 4)) 0.9999999999998099) (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2)))) (/ -176.6150291621406 (+ 3 z)))))
3.0ms	(sqrt (* PI 2))

series1.8s

Counts

4 → 10

Calls

4 calls:

581.0ms	(/ (* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2))) (exp (+ 0.5 (- z -6))))
409.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
850.0ms	(* (/ (* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2))) (exp (+ 0.5 (- z -6)))) (+ (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5))) (+ (+ (+ (/ 12.507343278686905 (+ z 4)) 0.9999999999998099) (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2)))) (/ -176.6150291621406 (+ 3 z)))))
0.0ms	(sqrt (* PI 2))

simplify9.5s

Counts

285 → 285

Iterations

Iter	Nodes
done	5000
0	1026

prune6.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize323.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* (/ 12.507343278686905 (+ z 4)) (/ 12.507343278686905 (+ z 4))) (- (* 0.9999999999998099 0.9999999999998099) (* (/ 12.507343278686905 (+ z 4)) 0.9999999999998099)))
1.0b	(+ (* (/ 12.507343278686905 (+ z 4)) (/ 12.507343278686905 (+ z 4))) (- (* 0.9999999999998099 0.9999999999998099) (* (/ 12.507343278686905 (+ z 4)) 0.9999999999998099)))
1.0b	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
1.0b	(sqrt (* PI 2))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
12×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `frac-add`
9×	`add-exp-log`
7×	`pow1` `add-cube-cbrt`
6×	`unpow-prod-down` `flip3--` `add-cbrt-cube` `flip--`
5×	`associate-*l/`
4×	`frac-times` `associate-+r+` `sum-log` `associate-r` `associate-*r/` `insert-posit16`
3×	`unpow-prod-up` `sub-neg` `prod-exp` `unswap-sqr`
2×	`+-commutative` `associate-+r-` `sqrt-pow1` `flip3-+` `diff-log` `sqrt-prod` `flip-+` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `pow1/2` `pow-prod-down` `pow-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `associate--r-` `pow-sub`

Counts

4 → 89

Calls

4 calls:

64.0ms	(+ (* (/ 12.507343278686905 (+ z 4)) (/ 12.507343278686905 (+ z 4))) (- (* 0.9999999999998099 0.9999999999998099) (* (/ 12.507343278686905 (+ z 4)) 0.9999999999998099)))
37.0ms	(+ (* (/ 12.507343278686905 (+ z 4)) (/ 12.507343278686905 (+ z 4))) (- (* 0.9999999999998099 0.9999999999998099) (* (/ 12.507343278686905 (+ z 4)) 0.9999999999998099)))
151.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
4.0ms	(sqrt (* PI 2))

series508.0ms

Counts

4 → 10

Calls

4 calls:

53.0ms	(+ (* (/ 12.507343278686905 (+ z 4)) (/ 12.507343278686905 (+ z 4))) (- (* 0.9999999999998099 0.9999999999998099) (* (/ 12.507343278686905 (+ z 4)) 0.9999999999998099)))
63.0ms	(+ (* (/ 12.507343278686905 (+ z 4)) (/ 12.507343278686905 (+ z 4))) (- (* 0.9999999999998099 0.9999999999998099) (* (/ 12.507343278686905 (+ z 4)) 0.9999999999998099)))
392.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))

simplify3.4s

Counts

99 → 99

Iterations

Iter	Nodes
done	5002
2	3368
1	810
0	261

prune3.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize350.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* (/ 12.507343278686905 (+ z 4)) (/ 12.507343278686905 (+ z 4))) (- (* 0.9999999999998099 0.9999999999998099) (* (/ 12.507343278686905 (+ z 4)) 0.9999999999998099)))
1.0b	(+ (* (/ 12.507343278686905 (+ z 4)) (/ 12.507343278686905 (+ z 4))) (- (* 0.9999999999998099 0.9999999999998099) (* (/ 12.507343278686905 (+ z 4)) 0.9999999999998099)))
1.0b	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
1.0b	(sqrt (* PI 2))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
12×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `frac-add`
9×	`add-exp-log`
7×	`pow1` `add-cube-cbrt`
6×	`unpow-prod-down` `flip3--` `add-cbrt-cube` `flip--`
5×	`associate-*l/`
4×	`frac-times` `associate-+r+` `sum-log` `associate-r` `associate-*r/` `insert-posit16`
3×	`unpow-prod-up` `sub-neg` `prod-exp` `unswap-sqr`
2×	`+-commutative` `associate-+r-` `sqrt-pow1` `flip3-+` `diff-log` `sqrt-prod` `flip-+` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `pow1/2` `pow-prod-down` `pow-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `associate--r-` `pow-sub`

Counts

4 → 89

Calls

4 calls:

38.0ms	(+ (* (/ 12.507343278686905 (+ z 4)) (/ 12.507343278686905 (+ z 4))) (- (* 0.9999999999998099 0.9999999999998099) (* (/ 12.507343278686905 (+ z 4)) 0.9999999999998099)))
37.0ms	(+ (* (/ 12.507343278686905 (+ z 4)) (/ 12.507343278686905 (+ z 4))) (- (* 0.9999999999998099 0.9999999999998099) (* (/ 12.507343278686905 (+ z 4)) 0.9999999999998099)))
138.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
3.0ms	(sqrt (* PI 2))

series561.0ms

Counts

4 → 10

Calls

4 calls:

71.0ms	(+ (* (/ 12.507343278686905 (+ z 4)) (/ 12.507343278686905 (+ z 4))) (- (* 0.9999999999998099 0.9999999999998099) (* (/ 12.507343278686905 (+ z 4)) 0.9999999999998099)))
58.0ms	(+ (* (/ 12.507343278686905 (+ z 4)) (/ 12.507343278686905 (+ z 4))) (- (* 0.9999999999998099 0.9999999999998099) (* (/ 12.507343278686905 (+ z 4)) 0.9999999999998099)))
432.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))

simplify2.2s

Counts

99 → 99

Iterations

Iter	Nodes
done	5003
2	2339
1	629
0	212

prune3.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize345.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7)))) (- (* (/ -0.13857109526572012 (+ z 5)) (/ -0.13857109526572012 (+ z 5))) (* (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5)))))
1.0b	(+ (* (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7)))) (- (* (/ -0.13857109526572012 (+ z 5)) (/ -0.13857109526572012 (+ z 5))) (* (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5)))))
1.0b	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
1.0b	(sqrt (* PI 2))

rewrite727.0ms

Algorithm

rewrite-expression-head

Rules

1330×	`frac-add`
930×	`frac-times`
661×	`associate-*l/`
630×	`frac-sub`
582×	`flip3-+` `flip-+`
540×	`associate-*r/`
60×	`sub-div`
30×	`flip3--` `flip--`
14×	`add-log-exp`
12×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*`
9×	`add-exp-log`
7×	`pow1` `add-cube-cbrt`
6×	`unpow-prod-down` `add-cbrt-cube`
4×	`associate-+l+` `associate-+r+` `sum-log` `associate-r` `insert-posit16`
3×	`unpow-prod-up` `sub-neg` `prod-exp` `unswap-sqr`
2×	`distribute-rgt-in` `+-commutative` `associate-+r-` `distribute-lft-in` `sqrt-pow1` `diff-log` `sqrt-prod` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `pow1/2` `pow-prod-down` `pow-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `associate--r-` `pow-sub`

Counts

4 → 831

Calls

4 calls:

223.0ms	(+ (* (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7)))) (- (* (/ -0.13857109526572012 (+ z 5)) (/ -0.13857109526572012 (+ z 5))) (* (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5)))))
227.0ms	(+ (* (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7)))) (- (* (/ -0.13857109526572012 (+ z 5)) (/ -0.13857109526572012 (+ z 5))) (* (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5)))))
151.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
6.0ms	(sqrt (* PI 2))

series1.1s

Counts

4 → 10

Calls

4 calls:

309.0ms	(+ (* (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7)))) (- (* (/ -0.13857109526572012 (+ z 5)) (/ -0.13857109526572012 (+ z 5))) (* (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5)))))
317.0ms	(+ (* (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7)))) (- (* (/ -0.13857109526572012 (+ z 5)) (/ -0.13857109526572012 (+ z 5))) (* (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5)))))
425.0ms	(* (pow (+ 0.5 (- z -6)) (- z (- 1 0.5))) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))

simplify8.5s

Counts

841 → 841

Iterations

Iter	Nodes
done	5000
1	4787
0	1508

prune36.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes282.0ms

Accuracy

0% (0.6b remaining)

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

bsearch0.0ms

simplify39.0ms

Iterations

Iter	Nodes
done	120
1	120
0	76

end0.0ms

sample33.9s

Algorithm

intervals

Results

11.5s	3915×	body	10240	exit
8.1s	3391×	body	1280	valid
3.9s	2477×	body	640	valid
3.3s	1489×	body	1280	nan
2.3s	1280×	body	640	nan
1.9s	1250×	body	320	valid
1.3s	624×	body	320	nan
584.0ms	306×	body	160	nan
399.0ms	617×	body	160	valid
99.0ms	345×	body	80	valid
73.0ms	293×	body	80	nan