Details

sample2.9s

Algorithm

intervals

Results

2.3s	146×	body	10240	exit
133.0ms	261×	body	80	valid
127.0ms	38×	body	1280	nan
65.0ms	47×	body	640	nan
46.0ms	10×	body	160	nan
27.0ms	28×	body	320	nan
2.0ms	6×	body	80	nan

simplify4.0s

Counts

1 → 1

Iterations

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

prune79.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.8b

localize259.0ms

Local error

Found 4 expressions with local error:

6.1b	(- (- 1.0 z) 1.0)
6.1b	(- (- 1.0 z) 1.0)
6.1b	(- (- 1.0 z) 1.0)
6.1b	(- (- 1.0 z) 1.0)

rewrite182.0ms

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:

42.0ms	(- (- 1.0 z) 1.0)
43.0ms	(- (- 1.0 z) 1.0)
53.0ms	(- (- 1.0 z) 1.0)
37.0ms	(- (- 1.0 z) 1.0)

series67.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (- 1.0 z) 1.0)
16.0ms	(- (- 1.0 z) 1.0)
16.0ms	(- (- 1.0 z) 1.0)
16.0ms	(- (- 1.0 z) 1.0)

simplify2.1s

Counts

212 → 212

Iterations

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

prune3.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.8b

localize238.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.1m

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:

7.8s	(+ (+ (+ (/ 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)))))
1.0m	(/ (+ (/ 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))))
109.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
4.0ms	(sqrt (* 2.0 PI))

series647.0ms

Counts

4 → 10

Calls

4 calls:

273.0ms	(+ (+ (+ (/ 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)))))
314.0ms	(/ (+ (/ 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))))
60.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
0.0ms	(sqrt (* 2.0 PI))

simplify4.3s

Counts

418 → 418

Iterations

Iter	Nodes
done	5000
1	3319
0	836

prune7.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize220.0ms

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))))
1.0b	(sqrt (* 2.0 PI))
1.0b	(log (exp (/ (+ (/ 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))))))

rewrite1.7m

Algorithm

rewrite-expression-head

Rules

1271×	`*-un-lft-identity`
990×	`distribute-lft-out`
310×	`frac-add`
215×	`times-frac`
108×	`log-pow`
107×	`exp-prod`
88×	`flip3-+` `flip-+`
75×	`add-sqr-sqrt` `add-cube-cbrt`
74×	`associate-/l/`
51×	`exp-sum`
25×	`associate-/l*`
21×	`fma-def`
9×	`add-log-exp`
8×	`pow1` `associate-/r/`
6×	`add-cbrt-cube` `exp-diff`
5×	`add-exp-log`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`log-prod` `sum-log` `distribute-rgt-neg-in` `div-inv`
2×	`neg-sub0` `associate-+r-` `sqrt-pow1` `unsub-neg`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `clear-num` `frac-2neg` `pow1/2` `div-exp` `rem-log-exp` `pow-prod-down` `sqrt-prod`

Counts

4 → 394

Calls

4 calls:

42.0s	(/ (+ (/ 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))))
144.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
7.0ms	(sqrt (* 2.0 PI))
57.2s	(log (exp (/ (+ (/ 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))))))

series556.0ms

Counts

4 → 10

Calls

4 calls:

247.0ms	(/ (+ (/ 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))))
54.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
0.0ms	(sqrt (* 2.0 PI))
255.0ms	(log (exp (/ (+ (/ 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))))))

simplify2.5s

Counts

404 → 404

Iterations

Iter	Nodes
done	5001
1	1744
0	534

prune3.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize139.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (+ (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (+ (/ -1259.1392167224028 (+ (- 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))
1.0b	(log (exp (* (/ (+ (/ 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))) (exp z))))

rewrite5.2s

Algorithm

rewrite-expression-head

Rules

238×	`frac-add`
161×	`*-un-lft-identity`
118×	`add-log-exp`
111×	`distribute-lft-out`
90×	`sum-log`
87×	`flip3-+` `flip-+`
30×	`fma-def`
15×	`add-sqr-sqrt` `times-frac` `add-cube-cbrt`
8×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`log-prod` `distribute-rgt-neg-in` `log-pow`
2×	`+-commutative` `associate-+r+` `sqrt-pow1` `associate-/r/`
1×	`associate-+l+` `exp-prod` `exp-to-pow` `pow1/2` `rem-log-exp` `pow-prod-down` `sqrt-prod` `div-inv`

Counts

4 → 204

Calls

4 calls:

5.1s	(+ (+ (+ (/ 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)))))
100.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
3.0ms	(sqrt (* 2.0 PI))
27.0ms	(log (exp (* (/ (+ (/ 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))) (exp z))))

series492.0ms

Counts

4 → 10

Calls

4 calls:

183.0ms	(+ (+ (+ (/ 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)))))
53.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
0.0ms	(sqrt (* 2.0 PI))
255.0ms	(log (exp (* (/ (+ (/ 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))) (exp z))))

simplify2.4s

Counts

214 → 214

Iterations

Iter	Nodes
done	5000
1	2700
0	637

prune3.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes222.0ms

Accuracy

0% (0.4b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify22.0ms

Iterations

Iter	Nodes
done	87
1	87
0	63

end0.0ms

sample55.3s

Algorithm

intervals

Results

46.0s	3907×	body	10240	exit
2.9s	8089×	body	80	valid
2.9s	1457×	body	1280	nan
2.4s	1247×	body	640	nan
502.0ms	645×	body	320	nan
129.0ms	305×	body	160	nan
59.0ms	271×	body	80	nan