Details

sample1.2s

Algorithm

intervals

Results

418.0ms	33×	body	320	valid
221.0ms	97×	body	1280	valid
204.0ms	112×	body	10240	exit
143.0ms	93×	body	640	valid
48.0ms	43×	body	1280	nan
31.0ms	32×	body	640	nan
13.0ms	26×	body	160	valid
11.0ms	17×	body	320	nan
7.0ms	15×	body	160	nan
2.0ms	10×	body	80	valid
2.0ms	7×	body	80	nan

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 3 (508.0ms)

Iter	Nodes	Cost
0	55	94
1	133	94
2	449	92
3	2515	89
done	5001	89

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize78.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099))))))
1.0b	(/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
1.0b	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
1.0b	(sqrt (* PI 2.0))

rewrite1.6m

Algorithm

rewrite-expression-head

Rules

648×	`frac-add`
186×	`flip3-+` `flip-+`
159×	`*-un-lft-identity`
119×	`distribute-lft-out`
82×	`frac-times` `associate-*r/`
31×	`associate-r`
27×	`add-exp-log`
20×	`associate-l` `add-cbrt-cube`
19×	`add-sqr-sqrt`
14×	`prod-exp`
12×	`add-cube-cbrt`
9×	`pow1`
8×	`times-frac` `div-exp`
7×	`unpow-prod-down`
6×	`associate-+l-` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `exp-sum` `associate-*l/` `pow-exp`
2×	`sqrt-pow1` `exp-diff` `pow-prod-down` `sqrt-prod` `associate-/r/` `*-commutative` `div-inv` `pow-sub` `sqr-pow`
1×	`unpow-prod-up` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow1/2` `clear-num` `associate-/l/` `associate-/l*` `distribute-lft-out--`

Counts

4 → 298

Calls

4 calls:

1.5m	(* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099))))))
805.0ms	(/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
913.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
5.0ms	(sqrt (* PI 2.0))

series2.0s

Counts

4 → 10

Calls

4 calls:

894.0ms	(* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099))))))
629.0ms	(/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
461.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms	(sqrt (* PI 2.0))

simplify759.0ms

Counts

308 → 308

Iterations

Useful iterations: done (655.0ms)

Iter	Nodes	Cost
0	1114	66543
done	5000	60831

prune6.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize247.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma 676.5203681218851 (fma (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (* 0.9999999999998099 (- 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0))))) (* z (+ (pow (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 3) (pow 0.9999999999998099 3))))
1.0b	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
1.0b	(pow (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) 3)
1.0b	(sqrt (* PI 2.0))

rewrite920.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
30×	`times-frac`
28×	`unpow-prod-down`
26×	`add-cube-cbrt`
21×	`cube-prod`
17×	`distribute-lft-out`
12×	`add-exp-log`
11×	`associate-l`
9×	`add-cbrt-cube`
8×	`pow1`
7×	`distribute-lft-out--`
4×	`expm1-log1p-u` `associate-r` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-exp` `prod-exp` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `sqrt-pow1` `flip3-+` `sqrt-prod` `flip-+` `div-inv` `rem-cube-cbrt`
1×	`cbrt-undiv` `unpow-prod-up` `cube-div` `cube-mult` `associate-+l-` `pow-pow` `pow1/2` `unpow3` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `cbrt-unprod` `fma-udef` `pow-sub`

Counts

4 → 120

Calls

4 calls:

0.0ms	(fma 676.5203681218851 (fma (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (* 0.9999999999998099 (- 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0))))) (* z (+ (pow (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 3) (pow 0.9999999999998099 3))))
822.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
83.0ms	(pow (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) 3)
10.0ms	(sqrt (* PI 2.0))

series528.0ms

Counts

4 → 10

Calls

4 calls:

106.0ms	(fma 676.5203681218851 (fma (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (* 0.9999999999998099 (- 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0))))) (* z (+ (pow (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 3) (pow 0.9999999999998099 3))))
369.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
53.0ms	(pow (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) 3)
0.0ms	(sqrt (* PI 2.0))

simplify1.9s

Counts

130 → 130

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	331	3207
1	962	3029
2	3448	2717
done	5000	2712

prune3.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize746.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma (fma 9.984369578019572e-06 (+ (- z 1.0) 8.0) (* (+ (- z 1.0) 7.0) 1.5056327351493116e-07)) (+ (- z 1.0) 5.0) (* (* (+ (- z 1.0) 7.0) (+ (- z 1.0) 8.0)) 12.507343278686905))
1.0b	(fma 676.5203681218851 (fma (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (* 0.9999999999998099 (- 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0))))) (* z (+ (pow (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 3) (pow 0.9999999999998099 3))))
1.0b	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
1.0b	(sqrt (* PI 2.0))

rewrite812.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`associate-l`
9×	`add-exp-log`
7×	`pow1` `add-cube-cbrt` `unpow-prod-down`
6×	`add-cbrt-cube`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `unswap-sqr`
2×	`sqrt-pow1` `sqrt-prod` `fma-udef` `sqr-pow`
1×	`unpow-prod-up` `pow-to-exp` `associate-+l-` `pow1/2` `pow-prod-down` `associate-l/` `pow-exp` `-commutative` `cbrt-unprod` `distribute-lft-out--` `pow-sub`

Counts

4 → 66

Calls

4 calls:

0.0ms	(fma (fma 9.984369578019572e-06 (+ (- z 1.0) 8.0) (* (+ (- z 1.0) 7.0) 1.5056327351493116e-07)) (+ (- z 1.0) 5.0) (* (* (+ (- z 1.0) 7.0) (+ (- z 1.0) 8.0)) 12.507343278686905))
0.0ms	(fma 676.5203681218851 (fma (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (* 0.9999999999998099 (- 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0))))) (* z (+ (pow (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 3) (pow 0.9999999999998099 3))))
800.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
9.0ms	(sqrt (* PI 2.0))

series590.0ms

Counts

4 → 10

Calls

4 calls:

101.0ms	(fma (fma 9.984369578019572e-06 (+ (- z 1.0) 8.0) (* (+ (- z 1.0) 7.0) 1.5056327351493116e-07)) (+ (- z 1.0) 5.0) (* (* (+ (- z 1.0) 7.0) (+ (- z 1.0) 8.0)) 12.507343278686905))
124.0ms	(fma 676.5203681218851 (fma (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (* 0.9999999999998099 (- 0.9999999999998099 (/ -1259.1392167224028 (+ (- z 1.0) 2.0))))) (* z (+ (pow (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 3) (pow 0.9999999999998099 3))))
364.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms	(sqrt (* PI 2.0))

simplify1.2s

Counts

76 → 76

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	224	2413
1	595	2344
2	2294	2122
done	5000	2117

prune1.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize166.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
1.0b	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
1.0b	(* (fma (- (* (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (* (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0)))) (* z (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099)) (* (- (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (fma 676.5203681218851 (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099) (* z (- (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (* 0.9999999999998099 0.9999999999998099)))))) (+ (- z 1.0) 4.0))
1.0b	(sqrt (* PI 2.0))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
17×	`add-exp-log`
14×	`associate-l`
13×	`add-cbrt-cube`
11×	`add-cube-cbrt`
9×	`pow1` `associate-r`
7×	`unpow-prod-down` `prod-exp` `distribute-lft-out`
4×	`expm1-log1p-u` `associate-+l-` `times-frac` `div-exp` `associate-/r*` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`cbrt-unprod`
2×	`cbrt-undiv` `pow-to-exp` `sqrt-pow1` `associate-r/` `exp-sum` `pow-prod-down` `associate-l/` `pow-exp` `sqrt-prod` `*-commutative` `distribute-lft-out--` `pow-sub` `sqr-pow`
1×	`unpow-prod-up` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `flip3-+` `pow1/2` `exp-diff` `clear-num` `associate-/r/` `flip-+` `div-inv` `associate-/l/` `associate-/l*`

Counts

4 → 101

Calls

4 calls:

788.0ms	(/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
775.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
80.0ms	(* (fma (- (* (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (* (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0)))) (* z (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099)) (* (- (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (fma 676.5203681218851 (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099) (* z (- (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (* 0.9999999999998099 0.9999999999998099)))))) (+ (- z 1.0) 4.0))
5.0ms	(sqrt (* PI 2.0))

series1.3s

Counts

4 → 10

Calls

4 calls:

538.0ms	(/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
400.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
337.0ms	(* (fma (- (* (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (* (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0)))) (* z (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099)) (* (- (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (fma 676.5203681218851 (- (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099) (* z (- (* (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (* 0.9999999999998099 0.9999999999998099)))))) (+ (- z 1.0) 4.0))
0.0ms	(sqrt (* PI 2.0))

simplify1.8s

Counts

111 → 111

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	316	5716
1	882	5593
2	3699	4982
done	5001	4972

prune2.2s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes324.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify18.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	85	462
1	120	462
done	120	462

end0.0ms

sample25.8s

Algorithm

intervals

Results

9.9s	3839×	body	10240	exit
5.1s	3384×	body	1280	valid
4.1s	2431×	body	640	valid
1.9s	1481×	body	1280	nan
1.5s	1244×	body	320	valid
1.2s	1258×	body	640	nan
689.0ms	672×	body	160	valid
504.0ms	613×	body	320	nan
184.0ms	314×	body	160	nan
110.0ms	358×	body	80	valid
50.0ms	283×	body	80	nan