Details

sample1.5s

Algorithm

intervals

Results

1.3s	126×	body	10240	exit
48.0ms	259×	body	80	valid
35.0ms	35×	body	1280	nan
31.0ms	42×	body	640	nan
7.0ms	13×	body	320	nan
3.0ms	8×	body	160	nan
1.0ms	7×	body	80	nan

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	60	123
1	148	123
2	592	121
3	3593	88
done	5001	78

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.4b

localize53.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
1.0b	(sqrt (* PI 2.0))
1.0b	(* PI (sqrt (* PI 2.0)))
2.6b	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
11×	`add-log-exp`
9×	`pow1`
8×	`add-sqr-sqrt` `times-frac` `distribute-lft-out`
6×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`associate-r` `sum-log` `distribute-lft-out--`
3×	`flip3-+` `associate-l` `frac-add` `flip-+`
2×	`+-commutative` `sqrt-pow1` `pow-prod-down` `sqrt-prod`
1×	`associate-+l+` `pow1/2` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

42.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
1.0ms	(sqrt (* PI 2.0))
8.0ms	(* PI (sqrt (* PI 2.0)))
99.0ms	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))

series131.0ms

Counts

4 → 8

Calls

4 calls:

76.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
0.0ms	(sqrt (* PI 2.0))
0.0ms	(* PI (sqrt (* PI 2.0)))
55.0ms	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))

simplify425.0ms

Counts

72 → 72

Iterations

Useful iterations: done (422.0ms)

Iter	Nodes	Cost
0	191	1182
1	480	1129
2	1433	1047
done	5002	1033

prune662.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

1.0b	(* PI (sqrt (* PI 2.0)))
1.0b	(* PI (sqrt (* PI 2.0)))
1.0b	(* PI (sqrt (* PI 2.0)))
2.6b	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`associate-r`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
9×	`associate-l` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `sum-log` `sqrt-prod` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
2×	`flip3-+` `frac-add` `flip-+`
1×	`+-commutative` `associate-+l+`

Counts

4 → 74

Calls

4 calls:

7.0ms	(* PI (sqrt (* PI 2.0)))
7.0ms	(* PI (sqrt (* PI 2.0)))
7.0ms	(* PI (sqrt (* PI 2.0)))
97.0ms	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))

series54.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(* PI (sqrt (* PI 2.0)))
0.0ms	(* PI (sqrt (* PI 2.0)))
0.0ms	(* PI (sqrt (* PI 2.0)))
54.0ms	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))

simplify1.1s

Counts

80 → 80

Iterations

Useful iterations: 3 (477.0ms)

Iter	Nodes	Cost
0	105	1022
1	261	956
2	770	886
3	2608	874
done	5001	874

prune766.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 771.3234287776531 (- 3.0 z)) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z)))))
1.0b	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
1.0b	(sqrt (* PI 2.0))
1.0b	(* PI (sqrt (* PI 2.0)))

rewrite414.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
15×	`add-log-exp`
11×	`distribute-lft-out`
9×	`pow1`
8×	`add-sqr-sqrt` `times-frac`
7×	`sum-log`
6×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`associate-r` `distribute-lft-out--`
3×	`flip3-+` `associate-l` `frac-add` `flip-+`
2×	`+-commutative` `sqrt-pow1` `pow-prod-down` `sqrt-prod`
1×	`associate-+r+` `pow1/2` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

359.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z)))))
45.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
1.0ms	(sqrt (* PI 2.0))
7.0ms	(* PI (sqrt (* PI 2.0)))

series154.0ms

Counts

4 → 8

Calls

4 calls:

79.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (+ 0.9999999999998099 (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z)))))
74.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
0.0ms	(sqrt (* PI 2.0))
0.0ms	(* PI (sqrt (* PI 2.0)))

simplify452.0ms

Counts

74 → 74

Iterations

Useful iterations: done (449.0ms)

Iter	Nodes	Cost
0	169	1278
1	453	1202
2	1386	1108
done	5000	1090

prune620.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (sqrt PI) (sqrt (* PI 2.0)))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(* (sqrt PI) (* (sqrt PI) (sqrt (* PI 2.0))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
17×	`add-sqr-sqrt`
15×	`pow-prod-down`
14×	`sqrt-prod`
12×	`sqrt-pow1` `associate-l`
11×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
7×	`pow1/2`
5×	`associate-r`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`sqrt-unprod`
2×	`rem-sqrt-square` `*-commutative` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

9.0ms	(* (sqrt PI) (sqrt (* PI 2.0)))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
22.0ms	(* (sqrt PI) (* (sqrt PI) (sqrt (* PI 2.0))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(* (sqrt PI) (sqrt (* PI 2.0)))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(* (sqrt PI) (* (sqrt PI) (sqrt (* PI 2.0))))

simplify3.7s

Counts

82 → 82

Iterations

Useful iterations: 4 (637.0ms)

Iter	Nodes	Cost
0	60	700
1	130	548
2	402	514
3	1074	510
4	1659	506
5	4227	506
done	5000	506

prune685.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes118.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	95
1	75	95
done	75	95

end0.0ms

sample45.8s

Algorithm

intervals

Results

41.0s	3916×	body	10240	exit
1.5s	1486×	body	1280	nan
1.4s	8078×	body	80	valid
877.0ms	1234×	body	640	nan
321.0ms	640×	body	320	nan
93.0ms	281×	body	160	nan
49.0ms	293×	body	80	nan