Details

sample3.1s

Algorithm

intervals

Results

2.7s	146×	body	10240	exit
153.0ms	261×	body	80	valid
110.0ms	38×	body	1280	nan
70.0ms	47×	body	640	nan
28.0ms	28×	body	320	nan
6.0ms	10×	body	160	nan
2.0ms	6×	body	80	nan

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	3604
2	604
1	148
0	60

prune68.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize175.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0)))
1.0b	(/ (pow (+ (+ 7.0 (- 0 z)) 0.5) (+ 0.5 (- 0 z))) (exp (+ (+ 7.0 (- 0 z)) 0.5)))
1.0b	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0))))
1.0b	(sqrt (* 2.0 PI))

rewrite3.8s

Algorithm

rewrite-expression-head

Rules

175×	`*-un-lft-identity`
77×	`times-frac`
69×	`distribute-lft-out`
36×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`unpow-prod-down`
27×	`add-log-exp`
25×	`fma-def`
19×	`frac-add`
16×	`sum-log`
14×	`distribute-lft-out--`
12×	`flip3-+` `exp-sum` `flip-+`
11×	`associate-/l*`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
5×	`unpow-prod-up` `associate-/r/` `sqr-pow`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `sub0-neg`
3×	`exp-diff` `div-exp` `associate-+l-` `pow-sub` `associate-/l/`
2×	`+-commutative` `associate-+r-` `sqrt-pow1` `unsub-neg` `div-inv`
1×	`pow-to-exp` `cbrt-undiv` `associate-+l+` `associate-+r+` `clear-num` `frac-2neg` `pow1/2` `pow-prod-down` `pow-exp` `sqrt-prod`

Counts

4 → 179

Calls

4 calls:

210.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0)))
710.0ms	(/ (pow (+ (+ 7.0 (- 0 z)) 0.5) (+ 0.5 (- 0 z))) (exp (+ (+ 7.0 (- 0 z)) 0.5)))
2.9s	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0))))
7.0ms	(sqrt (* 2.0 PI))

series507.0ms

Counts

4 → 10

Calls

4 calls:

101.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0)))
254.0ms	(/ (pow (+ (+ 7.0 (- 0 z)) 0.5) (+ 0.5 (- 0 z))) (exp (+ (+ 7.0 (- 0 z)) 0.5)))
151.0ms	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0))))
0.0ms	(sqrt (* 2.0 PI))

simplify3.3s

Counts

189 → 189

Iterations

Iter	Nodes
done	5000
2	4970
1	1132
0	403

prune3.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize156.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0)))
1.0b	(/ (pow (+ (+ 7.0 (- 0 z)) 0.5) (+ 0.5 (- 0 z))) (exp 7.0))
1.0b	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0))))
1.0b	(sqrt (* 2.0 PI))

rewrite3.4s

Algorithm

rewrite-expression-head

Rules

164×	`*-un-lft-identity`
66×	`times-frac`
64×	`distribute-lft-out`
34×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`add-log-exp`
25×	`fma-def`
24×	`unpow-prod-down`
19×	`frac-add`
16×	`sum-log`
13×	`distribute-lft-out--`
12×	`flip3-+` `flip-+`
11×	`associate-/l*`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `unpow-prod-up` `log1p-expm1-u` `sqr-pow`
3×	`associate-/r*` `div-exp` `pow-sub` `associate-/l/`
2×	`+-commutative` `sqrt-pow1` `associate-/r/` `div-inv` `sub0-neg`
1×	`pow-to-exp` `cbrt-undiv` `associate-+l+` `associate-+r+` `clear-num` `associate-+r-` `frac-2neg` `pow1/2` `unsub-neg` `pow-prod-down` `pow-exp` `sqrt-prod`

Counts

4 → 164

Calls

4 calls:

207.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0)))
398.0ms	(/ (pow (+ (+ 7.0 (- 0 z)) 0.5) (+ 0.5 (- 0 z))) (exp 7.0))
2.7s	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0))))
7.0ms	(sqrt (* 2.0 PI))

series436.0ms

Counts

4 → 10

Calls

4 calls:

106.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0)))
211.0ms	(/ (pow (+ (+ 7.0 (- 0 z)) 0.5) (+ 0.5 (- 0 z))) (exp 7.0))
120.0ms	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0))))
0.0ms	(sqrt (* 2.0 PI))

simplify2.6s

Counts

174 → 174

Iterations

Iter	Nodes
done	5000
2	4445
1	1028
0	353

prune3.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize218.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (pow (+ (+ 7.0 (- 0 z)) 0.5) (+ 0.5 (- 0 z))) (exp 7.0))
1.0b	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (fma (/ 1 (* (cbrt (+ 3.0 (- 0 z))) (cbrt (+ 3.0 (- 0 z))))) (/ 771.3234287776531 (cbrt (+ 3.0 (- 0 z)))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0))))
1.0b	(fma (/ 1 (* (cbrt (+ 3.0 (- 0 z))) (cbrt (+ 3.0 (- 0 z))))) (/ 771.3234287776531 (cbrt (+ 3.0 (- 0 z)))) (/ -176.6150291621406 (+ (- 0 z) 4.0)))
1.0b	(sqrt (* 2.0 PI))

rewrite780.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
33×	`times-frac`
29×	`distribute-lft-out`
25×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down`
16×	`add-log-exp`
11×	`associate-/l*`
8×	`sum-log`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `unpow-prod-up` `fma-def` `frac-add` `log1p-expm1-u` `distribute-lft-out--` `sqr-pow`
3×	`associate-/r*` `div-exp` `pow-sub` `associate-/l/`
2×	`sqrt-pow1` `sub0-neg`
1×	`pow-to-exp` `cbrt-undiv` `+-commutative` `associate-+l+` `associate-+r+` `clear-num` `associate-+r-` `frac-2neg` `pow1/2` `unsub-neg` `pow-prod-down` `pow-exp` `sqrt-prod` `fma-udef` `div-inv`

Counts

4 → 119

Calls

4 calls:

392.0ms	(/ (pow (+ (+ 7.0 (- 0 z)) 0.5) (+ 0.5 (- 0 z))) (exp 7.0))
380.0ms	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (fma (/ 1 (* (cbrt (+ 3.0 (- 0 z))) (cbrt (+ 3.0 (- 0 z))))) (/ 771.3234287776531 (cbrt (+ 3.0 (- 0 z)))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0))))
0.0ms	(fma (/ 1 (* (cbrt (+ 3.0 (- 0 z))) (cbrt (+ 3.0 (- 0 z))))) (/ 771.3234287776531 (cbrt (+ 3.0 (- 0 z)))) (/ -176.6150291621406 (+ (- 0 z) 4.0)))
4.0ms	(sqrt (* 2.0 PI))

series1.3s

Counts

4 → 10

Calls

4 calls:

252.0ms	(/ (pow (+ (+ 7.0 (- 0 z)) 0.5) (+ 0.5 (- 0 z))) (exp 7.0))
662.0ms	(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ (fma (/ 1 (* (cbrt (+ 3.0 (- 0 z))) (cbrt (+ 3.0 (- 0 z))))) (/ 771.3234287776531 (cbrt (+ 3.0 (- 0 z)))) (/ -176.6150291621406 (+ (- 0 z) 4.0))) (/ -1259.1392167224028 (+ (- 0 z) 2.0))))
421.0ms	(fma (/ 1 (* (cbrt (+ 3.0 (- 0 z))) (cbrt (+ 3.0 (- 0 z))))) (/ 771.3234287776531 (cbrt (+ 3.0 (- 0 z)))) (/ -176.6150291621406 (+ (- 0 z) 4.0)))
0.0ms	(sqrt (* 2.0 PI))

simplify3.4s

Counts

129 → 129

Iterations

Iter	Nodes
done	5015
2	3442
1	989
0	374

prune3.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize249.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (cbrt (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))
1.0b	(+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0)))
1.0b	(/ (pow (+ (+ 7.0 (- 0 z)) 0.5) (+ 0.5 (- 0 z))) (exp (+ (+ 7.0 (- 0 z)) 0.5)))
1.0b	(sqrt (* 2.0 PI))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

173×	`*-un-lft-identity`
77×	`times-frac`
59×	`distribute-lft-out`
51×	`add-sqr-sqrt`
43×	`add-cube-cbrt`
30×	`unpow-prod-down`
24×	`cbrt-prod`
21×	`fma-def`
14×	`pow1` `distribute-lft-out--`
12×	`cbrt-div` `exp-sum`
11×	`associate-/l*`
9×	`swap-sqr`
8×	`flip3-+` `add-exp-log` `flip-+`
7×	`associate-r` `associate-l`
6×	`add-cbrt-cube` `pow1/3` `add-log-exp`
5×	`unpow-prod-up` `associate-/r/` `sqr-pow`
4×	`expm1-log1p-u` `frac-times` `associate-/r*` `log1p-expm1-u` `unswap-sqr` `sub0-neg`
3×	`exp-diff` `div-exp` `pow-prod-down` `associate-+l-` `pow-sub` `associate-/l/`
2×	`associate-+r-` `sqrt-pow1` `unsub-neg` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up` `div-inv`
1×	`pow2` `pow-to-exp` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-plus` `pow1/2` `frac-add` `pow-exp` `prod-exp` `*-commutative` `sqrt-prod` `cbrt-unprod`

Counts

4 → 194

Calls

4 calls:

213.0ms	(* (cbrt (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (cbrt (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))
209.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0)))
754.0ms	(/ (pow (+ (+ 7.0 (- 0 z)) 0.5) (+ 0.5 (- 0 z))) (exp (+ (+ 7.0 (- 0 z)) 0.5)))
4.0ms	(sqrt (* 2.0 PI))

series611.0ms

Counts

4 → 10

Calls

4 calls:

258.0ms	(* (cbrt (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (cbrt (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))
110.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (/ -176.6150291621406 (+ (- 0 z) 4.0)))
242.0ms	(/ (pow (+ (+ 7.0 (- 0 z)) 0.5) (+ 0.5 (- 0 z))) (exp (+ (+ 7.0 (- 0 z)) 0.5)))
0.0ms	(sqrt (* 2.0 PI))

simplify2.2s

Counts

204 → 204

Iterations

Iter	Nodes
done	5000
2	2431
1	832
0	357

prune3.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes270.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify27.0ms

Iterations

Iter	Nodes
done	90
1	90
0	66

end0.0ms

sample1.3m

Algorithm

intervals

Results

1.1m	3907×	body	10240	exit
5.7s	8089×	body	80	valid
3.6s	1457×	body	1280	nan
2.6s	1247×	body	640	nan
1.2s	645×	body	320	nan
646.0ms	305×	body	160	nan
87.0ms	271×	body	80	nan