Details

sample2.8s

Algorithm

intervals

Results

2.4s	143×	body	10240	exit
151.0ms	44×	body	1280	nan
92.0ms	256×	body	80	valid
55.0ms	39×	body	640	nan
45.0ms	6×	body	160	nan
24.0ms	22×	body	320	nan
3.0ms	8×	body	80	nan

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	4612
2	614
1	148
0	60

prune48.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.8b

localize641.0ms

Local error

Found 4 expressions with local error:

6.4b	(- (- 1.0 z) 1.0)
6.4b	(- (- 1.0 z) 1.0)
6.4b	(- (- 1.0 z) 1.0)
6.4b	(- (- 1.0 z) 1.0)

rewrite198.0ms

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×	`associate--l-` `expm1-log1p-u` `pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `flip--`

Counts

4 → 200

Calls

4 calls:

44.0ms	(- (- 1.0 z) 1.0)
40.0ms	(- (- 1.0 z) 1.0)
57.0ms	(- (- 1.0 z) 1.0)
49.0ms	(- (- 1.0 z) 1.0)

series75.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(- (- 1.0 z) 1.0)
22.0ms	(- (- 1.0 z) 1.0)
13.0ms	(- (- 1.0 z) 1.0)
18.0ms	(- (- 1.0 z) 1.0)

simplify1.7s

Counts

212 → 212

Iterations

Iter	Nodes
done	5000
3	3073
2	511
1	184
0	84

prune3.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.8b

localize215.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.2m

Algorithm

rewrite-expression-head

Rules

846×	`*-un-lft-identity`
656×	`distribute-lft-out`
546×	`frac-add`
172×	`flip3-+` `flip-+`
117×	`add-log-exp`
115×	`times-frac`
90×	`sum-log`
74×	`associate-/l/`
45×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`fma-def`
26×	`exp-sum`
25×	`associate-/l*`
7×	`pow1`
6×	`add-cbrt-cube`
5×	`add-exp-log` `associate-/r/`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`distribute-rgt-neg-in` `exp-diff`
2×	`+-commutative` `associate-+r+` `sqrt-pow1` `div-inv`
1×	`neg-sub0` `cbrt-undiv` `associate-+l+` `clear-num` `associate-+r-` `frac-2neg` `pow1/2` `div-exp` `unsub-neg` `pow-prod-down` `sqrt-prod`

Counts

4 → 408

Calls

4 calls:

1.1m	(/ (+ (/ 9.984369578019572e-06 (+ 7.0 (- z))) (+ (+ (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (+ (/ -1259.1392167224028 (+ (- z) 2.0)) (/ -176.6150291621406 (+ (- z) 4.0)))) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 12.507343278686905 (+ 5.0 (- z)))) (/ 1.5056327351493116e-07 (+ 8.0 (- z)))))) (exp (+ (+ 0.5 7.0) (- z))))
7.9s	(+ (+ (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (+ (/ -1259.1392167224028 (+ (- z) 2.0)) (/ -176.6150291621406 (+ (- z) 4.0)))) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 12.507343278686905 (+ 5.0 (- z)))) (/ 1.5056327351493116e-07 (+ 8.0 (- z)))))
195.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
7.0ms	(sqrt (* 2.0 PI))

series717.0ms

Counts

4 → 10

Calls

4 calls:

394.0ms	(/ (+ (/ 9.984369578019572e-06 (+ 7.0 (- z))) (+ (+ (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (+ (/ -1259.1392167224028 (+ (- z) 2.0)) (/ -176.6150291621406 (+ (- z) 4.0)))) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 12.507343278686905 (+ 5.0 (- z)))) (/ 1.5056327351493116e-07 (+ 8.0 (- z)))))) (exp (+ (+ 0.5 7.0) (- z))))
252.0ms	(+ (+ (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (+ (/ -1259.1392167224028 (+ (- z) 2.0)) (/ -176.6150291621406 (+ (- z) 4.0)))) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 12.507343278686905 (+ 5.0 (- z)))) (/ 1.5056327351493116e-07 (+ 8.0 (- z)))))
71.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
0.0ms	(sqrt (* 2.0 PI))

simplify1.4s

Counts

418 → 418

Iterations

Iter	Nodes
done	5001
1	3318
0	836

prune8.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize416.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z)))
1.0b	(+ (+ (+ (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))) (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ -176.6150291621406 (+ (- z) 4.0)))
1.0b	(+ (+ (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))) (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (+ 2.0 (- z))))
1.0b	(sqrt (* 2.0 PI))

rewrite5.5s

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
29×	`add-log-exp`
26×	`distribute-lft-out`
18×	`frac-add`
17×	`sum-log`
14×	`fma-def`
8×	`flip3-+` `flip-+`
7×	`add-sqr-sqrt` `pow1` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`+-commutative`
2×	`associate-+l+` `sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 91

Calls

4 calls:

27.0ms	(+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z)))
4.5s	(+ (+ (+ (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))) (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ -176.6150291621406 (+ (- z) 4.0)))
1.0s	(+ (+ (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))) (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (+ 2.0 (- z))))
4.0ms	(sqrt (* 2.0 PI))

series259.0ms

Counts

4 → 10

Calls

4 calls:

28.0ms	(+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z)))
119.0ms	(+ (+ (+ (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))) (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ -176.6150291621406 (+ (- z) 4.0)))
112.0ms	(+ (+ (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z))) (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (+ 2.0 (- z))))
0.0ms	(sqrt (* 2.0 PI))

simplify1.1s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	3261
1	789
0	255

prune2.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize632.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (/ 771.3234287776531 (+ 3.0 (- z))) 3)
1.0b	(* (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 12.507343278686905 (+ 5.0 (- z)))))
1.0b	(pow (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) 3)
1.0b	(sqrt (* 2.0 PI))

rewrite828.0ms

Algorithm

rewrite-expression-head

Rules

1032×	`*-un-lft-identity`
440×	`distribute-lft-out`
390×	`times-frac`
126×	`distribute-rgt-neg-in`
87×	`swap-sqr`
32×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
25×	`unpow-prod-down` `cube-prod`
16×	`pow1`
13×	`associate-r` `associate-l`
11×	`flip3-+` `flip-+`
10×	`add-cbrt-cube` `add-exp-log`
9×	`frac-times`
8×	`frac-add`
6×	`pow-unpow`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `associate-l/` `pow-exp` `associate-r/` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `pow-pow` `sqrt-pow1` `unpow3` `pow-prod-down` `div-inv` `sqr-pow`
1×	`pow2` `distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `pow-plus` `pow1/2` `div-exp` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-prod` `cbrt-unprod` `unswap-sqr`

Counts

4 → 254

Calls

4 calls:

28.0ms	(pow (/ 771.3234287776531 (+ 3.0 (- z))) 3)
719.0ms	(* (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 12.507343278686905 (+ 5.0 (- z)))))
35.0ms	(pow (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) 3)
3.0ms	(sqrt (* 2.0 PI))

series278.0ms

Counts

4 → 10

Calls

4 calls:

70.0ms	(pow (/ 771.3234287776531 (+ 3.0 (- z))) 3)
135.0ms	(* (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 12.507343278686905 (+ 5.0 (- z)))))
73.0ms	(pow (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) 3)
0.0ms	(sqrt (* 2.0 PI))

simplify668.0ms

Counts

264 → 264

Iterations

Iter	Nodes
done	5001
1	1362
0	362

prune4.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes628.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify41.0ms

Iterations

Iter	Nodes
done	146
3	146
2	144
1	139
0	99

end0.0ms

sample60.0s

Algorithm

intervals

Results

49.0s	4012×	body	10240	exit
3.9s	1571×	body	1280	nan
3.5s	8086×	body	80	valid
1.9s	1243×	body	640	nan
863.0ms	619×	body	320	nan
179.0ms	315×	body	160	nan
100.0ms	301×	body	80	nan