Details

sample1.5s

Algorithm

intervals

Results

1.3s	119×	body	10240	exit
51.0ms	257×	body	80	valid
45.0ms	39×	body	1280	nan
21.0ms	30×	body	640	nan
9.0ms	18×	body	320	nan
4.0ms	11×	body	160	nan
1.0ms	7×	body	80	nan

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 3 (554.0ms)

Iter	Nodes	Cost
0	60	123
1	148	123
2	611	121
3	3878	88
done	5001	88

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.8b

localize55.0ms

Local error

Found 4 expressions with local error:

5.0b	(- (- 1.0 z) 1.0)
5.0b	(- (- 1.0 z) 1.0)
5.0b	(- (- 1.0 z) 1.0)
5.0b	(- (- 1.0 z) 1.0)

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

116×	`*-un-lft-identity`
104×	`add-sqr-sqrt`
96×	`prod-diff`
64×	`add-cube-cbrt`
44×	`associate--l+`
28×	`distribute-lft-out--`
24×	`add-log-exp`
20×	`fma-neg` `difference-of-squares`
12×	`diff-log`
8×	`sub-neg`
4×	`pow1` `add-exp-log` `associate--l-` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

4 → 200

Calls

4 calls:

42.0ms	(- (- 1.0 z) 1.0)
43.0ms	(- (- 1.0 z) 1.0)
43.0ms	(- (- 1.0 z) 1.0)
44.0ms	(- (- 1.0 z) 1.0)

series51.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (- 1.0 z) 1.0)
12.0ms	(- (- 1.0 z) 1.0)
12.0ms	(- (- 1.0 z) 1.0)
16.0ms	(- (- 1.0 z) 1.0)

simplify1.9s

Counts

212 → 212

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	84	2848
1	169	2152
2	321	1656
3	1240	1132
done	5000	904

prune1.7s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.8b

localize56.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (+ (/ -1259.1392167224028 (+ (- z) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))))) (exp (+ 0.5 (+ (- z) 7.0))))
1.0b	(+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z))))
1.0b	(+ (/ -1259.1392167224028 (+ (- z) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z))))))))
1.0b	(sqrt (* PI 2.0))

rewrite1.1m

Algorithm

rewrite-expression-head

Rules

654×	`*-un-lft-identity`
501×	`distribute-lft-out`
370×	`frac-add`
111×	`add-log-exp`
95×	`times-frac`
87×	`sum-log`
86×	`flip3-+` `flip-+`
46×	`associate-/l/`
40×	`add-sqr-sqrt` `add-cube-cbrt`
26×	`fma-def`
21×	`exp-sum`
20×	`associate-/l*`
7×	`pow1`
6×	`add-cbrt-cube`
5×	`add-exp-log`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`distribute-rgt-neg-in` `associate-/r/`
2×	`+-commutative` `sqrt-pow1` `div-inv`
1×	`cbrt-undiv` `neg-sub0` `associate-+l-` `associate-+r-` `associate-+l+` `associate-+r+` `frac-2neg` `pow1/2` `exp-diff` `div-exp` `pow-prod-down` `clear-num` `sqrt-prod`

Counts

4 → 318

Calls

4 calls:

51.8s	(/ (+ (/ -1259.1392167224028 (+ (- z) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))))) (exp (+ 0.5 (+ (- z) 7.0))))
897.0ms	(+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z))))
14.9s	(+ (/ -1259.1392167224028 (+ (- z) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z))))))))
5.0ms	(sqrt (* PI 2.0))

series510.0ms

Counts

4 → 10

Calls

4 calls:

234.0ms	(/ (+ (/ -1259.1392167224028 (+ (- z) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))))) (exp (+ 0.5 (+ (- z) 7.0))))
77.0ms	(+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z))))
199.0ms	(+ (/ -1259.1392167224028 (+ (- z) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z))))))))
0.0ms	(sqrt (* PI 2.0))

simplify1.1s

Counts

328 → 328

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	793	34040
1	2950	28685
done	5001	28328

prune3.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize132.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))
1.0b	(* (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))
1.0b	(pow (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))) 3)
1.0b	(sqrt (* PI 2.0))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

2063×	`*-un-lft-identity`
896×	`distribute-lft-out`
756×	`times-frac`
252×	`distribute-rgt-neg-in`
174×	`swap-sqr`
26×	`associate-r` `associate-l`
22×	`pow1`
19×	`add-sqr-sqrt`
18×	`frac-times`
17×	`flip3-+` `frac-add` `flip-+`
15×	`add-cube-cbrt`
13×	`unpow-prod-down` `cube-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r/` `associate-l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `pow-unpow` `pow-prod-down`
2×	`pow2` `distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `pow-plus` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `pow-pow` `pow1/2` `unpow3` `pow-exp` `sqrt-prod` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 357

Calls

4 calls:

623.0ms	(* (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))
623.0ms	(* (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))
162.0ms	(pow (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))) 3)
4.0ms	(sqrt (* PI 2.0))

series289.0ms

Counts

4 → 10

Calls

4 calls:

90.0ms	(* (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))
90.0ms	(* (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))
109.0ms	(pow (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))) 3)
0.0ms	(sqrt (* PI 2.0))

simplify1.8s

Counts

367 → 367

Iterations

Useful iterations: 2 (593.0ms)

Iter	Nodes	Cost
0	259	12192
1	814	9441
2	4128	6418
done	5000	6418

prune3.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z)))
1.0b	(+ (+ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 9.984369578019572e-06 (+ (- z) 7.0))))) (/ -1259.1392167224028 (+ (- z) 2.0)))
1.0b	(+ (+ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 9.984369578019572e-06 (+ (- z) 7.0))))) (/ -1259.1392167224028 (+ (- z) 2.0)))
1.0b	(sqrt (* PI 2.0))

rewrite1.5m

Algorithm

rewrite-expression-head

Rules

364×	`*-un-lft-identity`
360×	`frac-add`
288×	`distribute-lft-out`
202×	`add-log-exp`
162×	`sum-log`
80×	`flip3-+` `flip-+`
42×	`fma-def`
7×	`pow1` `add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`+-commutative` `associate-+l+`
2×	`sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 256

Calls

4 calls:

2.4s	(+ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z)))
42.7s	(+ (+ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 9.984369578019572e-06 (+ (- z) 7.0))))) (/ -1259.1392167224028 (+ (- z) 2.0)))
41.9s	(+ (+ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 9.984369578019572e-06 (+ (- z) 7.0))))) (/ -1259.1392167224028 (+ (- z) 2.0)))
4.0ms	(sqrt (* PI 2.0))

series530.0ms

Counts

4 → 10

Calls

4 calls:

108.0ms	(+ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z)))
211.0ms	(+ (+ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 9.984369578019572e-06 (+ (- z) 7.0))))) (/ -1259.1392167224028 (+ (- z) 2.0)))
211.0ms	(+ (+ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 9.984369578019572e-06 (+ (- z) 7.0))))) (/ -1259.1392167224028 (+ (- z) 2.0)))
0.0ms	(sqrt (* PI 2.0))

simplify1.1s

Counts

266 → 266

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	661	35121
1	2795	31475
done	5002	31251

prune3.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

regimes346.0ms

Accuracy

0% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 0.6b

bsearch0.0ms

simplify15.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	103	493
1	152	493
done	152	493

end0.0ms

sample45.8s

Algorithm

intervals

Results

41.0s	3879×	body	10240	exit
1.5s	1444×	body	1280	nan
1.5s	8094×	body	80	valid
801.0ms	1168×	body	640	nan
306.0ms	616×	body	320	nan
107.0ms	314×	body	160	nan
48.0ms	286×	body	80	nan