Details

sample2.5s

Algorithm

intervals

Results

2.1s	127×	body	10240	exit
89.0ms	257×	body	80	valid
87.0ms	47×	body	1280	nan
60.0ms	41×	body	640	nan
25.0ms	25×	body	320	nan
5.0ms	7×	body	160	nan
2.0ms	8×	body	80	nan

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	4112
2	625
1	155
0	60

prune73.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize209.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (pow (+ (- 7 z) 0.5) (+ 0.5 (- 0 z))) (exp (+ (- 7 z) 0.5)))
1.0b	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
1.0b	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))))
1.0b	(sqrt (* 2 PI))

rewrite21.1s

Algorithm

rewrite-expression-head

Rules

281×	`*-un-lft-identity`
141×	`distribute-lft-out`
110×	`add-log-exp`
103×	`frac-add`
87×	`times-frac`
85×	`sum-log`
45×	`flip3-+` `flip-+`
35×	`add-sqr-sqrt` `add-cube-cbrt`
29×	`fma-def`
25×	`unpow-prod-down`
19×	`distribute-lft-out--`
11×	`exp-sum`
10×	`associate-/l*`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
5×	`unpow-prod-up` `sqr-pow`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u`
3×	`div-exp` `associate-/r/` `pow-sub` `associate-/l/`
2×	`+-commutative` `sqrt-pow1` `div-inv` `sub0-neg`
1×	`pow-to-exp` `cbrt-undiv` `associate-+l+` `associate-+r+` `clear-num` `associate-+r-` `frac-2neg` `pow1/2` `exp-diff` `unsub-neg` `pow-prod-down` `pow-exp` `associate-+l-` `sqrt-prod`

Counts

4 → 237

Calls

4 calls:

244.0ms	(/ (pow (+ (- 7 z) 0.5) (+ 0.5 (- 0 z))) (exp (+ (- 7 z) 0.5)))
507.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
20.3s	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))))
5.0ms	(sqrt (* 2 PI))

series510.0ms

Counts

4 → 10

Calls

4 calls:

202.0ms	(/ (pow (+ (- 7 z) 0.5) (+ 0.5 (- 0 z))) (exp (+ (- 7 z) 0.5)))
84.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
224.0ms	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))))
0.0ms	(sqrt (* 2 PI))

simplify4.7s

Counts

247 → 247

Iterations

Iter	Nodes
done	5002
1	1993
0	602

prune3.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize205.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
1.0b	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
1.0b	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (cbrt (* (* (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2)))) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))))
1.0b	(sqrt (* 2 PI))

rewrite4.2s

Algorithm

rewrite-expression-head

Rules

1586×	`frac-add`
629×	`flip3-+` `flip-+`
486×	`frac-times`
378×	`cbrt-div`
300×	`*-un-lft-identity`
162×	`associate-*l/`
140×	`distribute-lft-out`
90×	`associate-*r/`
86×	`times-frac`
73×	`add-log-exp`
53×	`sum-log`
50×	`fma-def`
24×	`distribute-lft-out--`
23×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`+-commutative`
2×	`sqrt-pow1` `div-inv`
1×	`associate-+l+` `associate-+r+` `pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 559

Calls

4 calls:

425.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
418.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
3.3s	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (cbrt (* (* (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2)))) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))))
9.0ms	(sqrt (* 2 PI))

series368.0ms

Counts

4 → 10

Calls

4 calls:

81.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
72.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
214.0ms	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (cbrt (* (* (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2)))) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))))
0.0ms	(sqrt (* 2 PI))

simplify13.3s

Counts

569 → 569

Iterations

Iter	Nodes
done	5002
0	2357

prune18.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize373.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt (* (+ (- 1 z) 2) (+ 1 (+ (- 1 z) 2))))
1.0b	(cbrt (* (+ (- 1 z) 2) (+ 1 (+ (- 1 z) 2))))
1.0b	(cbrt (* (+ (- 1 z) 2) (+ 1 (+ (- 1 z) 2))))
1.0b	(sqrt (* 2 PI))

rewrite326.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-div`
18×	`flip3-+` `flip-+`
12×	`frac-times`
7×	`pow1`
6×	`associate-l/` `associate-r/`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
2×	`sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 74

Calls

4 calls:

94.0ms	(cbrt (* (+ (- 1 z) 2) (+ 1 (+ (- 1 z) 2))))
130.0ms	(cbrt (* (+ (- 1 z) 2) (+ 1 (+ (- 1 z) 2))))
95.0ms	(cbrt (* (+ (- 1 z) 2) (+ 1 (+ (- 1 z) 2))))
4.0ms	(sqrt (* 2 PI))

series227.0ms

Counts

4 → 10

Calls

4 calls:

71.0ms	(cbrt (* (+ (- 1 z) 2) (+ 1 (+ (- 1 z) 2))))
78.0ms	(cbrt (* (+ (- 1 z) 2) (+ 1 (+ (- 1 z) 2))))
78.0ms	(cbrt (* (+ (- 1 z) 2) (+ 1 (+ (- 1 z) 2))))
0.0ms	(sqrt (* 2 PI))

simplify3.8s

Counts

84 → 84

Iterations

Iter	Nodes
done	5002
2	1761
1	491
0	184

prune3.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize202.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
1.0b	(/ (/ 1 (cbrt (exp (+ 0.5 (- 7 z))))) (cbrt (exp (+ 0.5 (- 7 z)))))
1.0b	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))))
1.0b	(sqrt (* 2 PI))

rewrite21.2s

Algorithm

rewrite-expression-head

Rules

401×	`*-un-lft-identity`
397×	`times-frac`
204×	`cbrt-prod`
180×	`add-sqr-sqrt` `add-cube-cbrt`
131×	`distribute-lft-out`
110×	`add-log-exp`
103×	`frac-add`
85×	`sum-log`
51×	`exp-sum`
45×	`flip3-+` `flip-+`
29×	`fma-def`
26×	`associate-/l*`
14×	`distribute-lft-out--`
13×	`add-exp-log`
11×	`associate-/r/`
10×	`pow1` `div-inv`
9×	`cbrt-div` `associate-+r-` `exp-diff`
7×	`associate-/r*`
6×	`add-cbrt-cube` `div-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-div`
2×	`+-commutative` `sqrt-pow1` `pow1/3` `pow-flip`
1×	`rec-exp` `associate-+l+` `associate-+r+` `clear-num` `frac-2neg` `pow1/2` `1-exp` `pow-prod-down` `sqrt-prod` `inv-pow` `associate-/l/`

Counts

4 → 401

Calls

4 calls:

466.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
164.0ms	(/ (/ 1 (cbrt (exp (+ 0.5 (- 7 z))))) (cbrt (exp (+ 0.5 (- 7 z)))))
20.6s	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))))
5.0ms	(sqrt (* 2 PI))

series546.0ms

Counts

4 → 10

Calls

4 calls:

71.0ms	(+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))
293.0ms	(/ (/ 1 (cbrt (exp (+ 0.5 (- 7 z))))) (cbrt (exp (+ 0.5 (- 7 z)))))
183.0ms	(+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) (+ (/ 771.3234287776531 (+ (- 1 z) 2)) (/ -176.6150291621406 (+ 1 (+ (- 1 z) 2))))) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1 z)) (/ -1259.1392167224028 (- 2 z))))))
0.0ms	(sqrt (* 2 PI))

simplify3.6s

Counts

411 → 411

Iterations

Iter	Nodes
done	5000
1	2495
0	821

prune6.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

regimes214.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify25.0ms

Iterations

Iter	Nodes
done	80
1	80
0	60

end0.0ms

sample1.1m

Algorithm

intervals

Results

57.2s	3824×	body	10240	exit
3.1s	1443×	body	1280	nan
2.8s	8082×	body	80	valid
1.9s	1179×	body	640	nan
544.0ms	591×	body	320	nan
198.0ms	309×	body	160	nan
107.0ms	280×	body	80	nan