Details

sample405.0ms

Algorithm

intervals

Results

120.0ms	108×	body	10240	exit
104.0ms	113×	body	1280	valid
47.0ms	74×	body	640	valid
31.0ms	43×	body	1280	nan
15.0ms	28×	body	640	nan
13.0ms	29×	body	320	valid
8.0ms	27×	body	160	valid
7.0ms	19×	body	320	nan
4.0ms	16×	body	160	nan
3.0ms	17×	body	80	valid
1.0ms	9×	body	80	nan

simplify678.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (137.0ms)

Iter	Nodes	Cost
0	55	94
1	133	94
2	442	92
3	2477	89
done	5001	89

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (+ (+ (- z 1.0) 7.0) 0.5))
0.9b	(/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
1.0b	(* (* (sqrt (* PI 2.0)) (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (/ 676.5203681218851 z)) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))))
1.0b	(sqrt (* PI 2.0))

rewrite26.5s

Algorithm

rewrite-expression-head

Rules

624×	`frac-add`
218×	`*-un-lft-identity`
176×	`flip3-+` `flip-+`
161×	`associate-*r/`
142×	`distribute-lft-out`
80×	`frac-times`
44×	`times-frac`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`associate-r`
19×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`add-log-exp`
13×	`exp-sum`
12×	`pow1`
11×	`associate-/l*`
9×	`prod-exp`
6×	`exp-prod` `div-exp` `distribute-lft-out--`
5×	`unpow-prod-up` `associate-+l-` `sum-log` `cbrt-unprod` `sqr-pow`
4×	`pow-prod-down` `associate-/r*` `rem-exp-log`
2×	`cbrt-undiv` `pow-to-exp` `sqrt-pow1` `exp-diff` `pow-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow1/2` `diff-log` `associate-l` `associate-l/` `clear-num` `sqrt-prod` `associate-/r/` `-commutative` `div-inv` `associate-/l/` `pow-sub`

Counts

4 → 314

Calls

4 calls:

148.0ms	(exp (+ (+ (- z 1.0) 7.0) 0.5))
423.0ms	(/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
25.9s	(* (* (sqrt (* PI 2.0)) (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (/ 676.5203681218851 z)) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))))
2.0ms	(sqrt (* PI 2.0))

series1.1s

Counts

4 → 10

Calls

4 calls:

11.0ms	(exp (+ (+ (- z 1.0) 7.0) 0.5))
182.0ms	(/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
879.0ms	(* (* (sqrt (* PI 2.0)) (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (/ 676.5203681218851 z)) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))))
0.0ms	(sqrt (* PI 2.0))

simplify464.0ms

Counts

324 → 324

Iterations

Useful iterations: done (392.0ms)

Iter	Nodes	Cost
0	1095	65614
done	5000	60718

prune4.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize104.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (* (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
1.0b	(* (+ (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) 676.5203681218851)
1.0b	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
1.0b	(sqrt (* PI 2.0))

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

186×	`*-un-lft-identity`
100×	`times-frac`
68×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
48×	`distribute-lft-out`
39×	`swap-sqr`
24×	`associate-r` `associate-l` `distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube`
16×	`pow1`
9×	`associate-*l/` `frac-sub`
8×	`associate-/r/`
7×	`frac-times` `associate-*r/`
6×	`add-log-exp`
5×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
4×	`cbrt-undiv` `div-exp` `div-inv`
3×	`pow-prod-down`
2×	`sqrt-pow1` `*-commutative`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `pow1/2` `diff-log` `sqrt-prod` `pow-sqr` `pow-prod-up` `flip--` `difference-of-squares`

Counts

4 → 162

Calls

4 calls:

23.0ms	(- (* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (* (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
247.0ms	(* (+ (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) 676.5203681218851)
85.0ms	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
1.0ms	(sqrt (* PI 2.0))

series196.0ms

Counts

4 → 10

Calls

4 calls:

92.0ms	(- (* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (* (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
61.0ms	(* (+ (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) 676.5203681218851)
41.0ms	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
0.0ms	(sqrt (* PI 2.0))

simplify1.2s

Counts

172 → 172

Iterations

Useful iterations: 2 (341.0ms)

Iter	Nodes	Cost
0	353	4790
1	1084	4424
2	4559	3908
done	5000	3908

prune2.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize122.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0)))
1.0b	(pow (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) 3)
1.0b	(sqrt (* PI 2.0))
1.0b	(pow (+ 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) 3)

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

240×	`*-un-lft-identity`
130×	`times-frac`
86×	`add-sqr-sqrt`
74×	`add-cube-cbrt`
62×	`distribute-lft-out`
39×	`swap-sqr`
30×	`distribute-lft-out--`
25×	`unpow-prod-down` `cube-prod`
21×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
16×	`pow1`
12×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`pow-unpow` `div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`cube-div` `pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `pow-pow` `sqrt-pow1` `unpow3` `pow-prod-down` `sqr-pow`
1×	`pow2` `frac-times` `pow-plus` `pow1/2` `associate-r/` `associate-l/` `sqrt-prod` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 209

Calls

4 calls:

83.0ms	(* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0)))
21.0ms	(pow (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) 3)
1.0ms	(sqrt (* PI 2.0))
65.0ms	(pow (+ 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) 3)

series153.0ms

Counts

4 → 10

Calls

4 calls:

35.0ms	(* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0)))
61.0ms	(pow (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) 3)
0.0ms	(sqrt (* PI 2.0))
57.0ms	(pow (+ 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) 3)

simplify375.0ms

Counts

219 → 219

Iterations

Useful iterations: done (359.0ms)

Iter	Nodes	Cost
0	394	4786
1	1281	4251
done	5000	4069

prune3.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (- (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) 676.5203681218851)
1.0b	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
1.0b	(* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0)))
1.0b	(sqrt (* PI 2.0))

rewrite833.0ms

Algorithm

rewrite-expression-head

Rules

371×	`*-un-lft-identity`
201×	`times-frac`
133×	`add-sqr-sqrt`
102×	`add-cube-cbrt`
97×	`distribute-lft-out`
78×	`swap-sqr`
50×	`distribute-lft-out--`
49×	`associate-l`
45×	`associate-r`
30×	`add-exp-log` `add-cbrt-cube`
23×	`pow1`
16×	`associate-/r/`
9×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
8×	`cbrt-undiv` `div-exp` `div-inv`
6×	`associate-*l/`
4×	`pow-prod-down` `add-log-exp`
3×	`*-commutative`
2×	`pow2` `frac-times` `sqrt-pow1` `pow-plus` `associate-*r/` `pow-sqr` `pow-prod-up` `frac-sub` `difference-of-squares`
1×	`flip3--` `pow1/2` `sqrt-prod` `flip--`

Counts

4 → 255

Calls

4 calls:

639.0ms	(* (- (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) 676.5203681218851)
83.0ms	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
88.0ms	(* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0)))
2.0ms	(sqrt (* PI 2.0))

series142.0ms

Counts

4 → 10

Calls

4 calls:

65.0ms	(* (- (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) 676.5203681218851)
40.0ms	(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
36.0ms	(* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0)))
0.0ms	(sqrt (* PI 2.0))

simplify392.0ms

Counts

265 → 265

Iterations

Useful iterations: done (378.0ms)

Iter	Nodes	Cost
0	423	6215
1	1286	5578
done	5000	5438

prune2.4s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes280.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	86	383
1	126	383
done	126	383

end0.0ms

sample12.3s

Algorithm

intervals

Results

4.2s	3890×	body	10240	exit
3.2s	3431×	body	1280	valid
1.6s	2478×	body	640	valid
1.0s	1461×	body	1280	nan
683.0ms	1251×	body	640	nan
571.0ms	1229×	body	320	valid
271.0ms	672×	body	320	nan
174.0ms	585×	body	160	valid
93.0ms	343×	body	160	nan
54.0ms	365×	body	80	valid
41.0ms	329×	body	80	nan