Details

sample2.5s

Algorithm

intervals

Results

2.0s	129×	body	10240	exit
137.0ms	258×	body	80	valid
90.0ms	50×	body	1280	nan
75.0ms	31×	body	640	nan
17.0ms	18×	body	320	nan
5.0ms	8×	body	160	nan
4.0ms	11×	body	80	nan

simplify2.7s

Counts

1 → 1

Iterations

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

prune56.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.8b

localize232.0ms

Local error

Found 4 expressions with local error:

5.3b	(- (- 1.0 z) 1.0)
5.3b	(- (- 1.0 z) 1.0)
5.3b	(- (- 1.0 z) 1.0)
5.3b	(- (- 1.0 z) 1.0)

rewrite252.0ms

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:

70.0ms	(- (- 1.0 z) 1.0)
69.0ms	(- (- 1.0 z) 1.0)
47.0ms	(- (- 1.0 z) 1.0)
51.0ms	(- (- 1.0 z) 1.0)

series82.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(- (- 1.0 z) 1.0)
20.0ms	(- (- 1.0 z) 1.0)
20.0ms	(- (- 1.0 z) 1.0)
21.0ms	(- (- 1.0 z) 1.0)

simplify1.8s

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

localize165.0ms

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:

1.0m	(/ (+ (/ 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))))
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)))))
149.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
4.0ms	(sqrt (* 2.0 PI))

series747.0ms

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))))
253.0ms	(+ (+ (+ (/ 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)))))
99.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
0.0ms	(sqrt (* 2.0 PI))

simplify1.3s

Counts

418 → 418

Iterations

Iter	Nodes
done	5001
1	3318
0	836

prune8.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize639.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (/ 771.3234287776531 (- 3.0 z)) 3)
1.0b	(pow (+ (/ 12.507343278686905 (- 5.0 z)) (/ -0.13857109526572012 (- 6.0 z))) 3)
1.0b	(sqrt (* 2.0 PI))
1.0b	(fma (+ (pow (/ -1259.1392167224028 (+ 2.0 (- z))) 3) (pow (/ -176.6150291621406 (+ (- z) 4.0)) 3)) (fma (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (- (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ 771.3234287776531 (- 3.0 z))) (* (/ 771.3234287776531 (- 3.0 z)) (/ 771.3234287776531 (- 3.0 z)))) (* (+ (pow (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) 3) (pow (/ 771.3234287776531 (- 3.0 z)) 3)) (fma (/ -1259.1392167224028 (+ 2.0 (- z))) (/ -1259.1392167224028 (+ 2.0 (- z))) (* (/ -176.6150291621406 (+ (- z) 4.0)) (- (/ -176.6150291621406 (+ (- z) 4.0)) (/ -1259.1392167224028 (+ 2.0 (- z))))))))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

82×	`*-un-lft-identity`
46×	`times-frac`
38×	`add-sqr-sqrt`
29×	`unpow-prod-down` `cube-prod`
26×	`add-cube-cbrt`
14×	`distribute-lft-out--`
10×	`distribute-lft-out`
9×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow-unpow` `difference-of-squares`
4×	`cube-div` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `pow-pow` `sqrt-pow1` `flip3--` `unpow3` `div-inv` `flip--` `sqr-pow`
1×	`cbrt-undiv` `flip3-+` `pow1/2` `div-exp` `pow-prod-down` `frac-add` `sqrt-prod` `flip-+` `fma-udef`

Counts

4 → 125

Calls

4 calls:

12.0ms	(pow (/ 771.3234287776531 (- 3.0 z)) 3)
128.0ms	(pow (+ (/ 12.507343278686905 (- 5.0 z)) (/ -0.13857109526572012 (- 6.0 z))) 3)
3.0ms	(sqrt (* 2.0 PI))
0.0ms	(fma (+ (pow (/ -1259.1392167224028 (+ 2.0 (- z))) 3) (pow (/ -176.6150291621406 (+ (- z) 4.0)) 3)) (fma (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (- (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ 771.3234287776531 (- 3.0 z))) (* (/ 771.3234287776531 (- 3.0 z)) (/ 771.3234287776531 (- 3.0 z)))) (* (+ (pow (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) 3) (pow (/ 771.3234287776531 (- 3.0 z)) 3)) (fma (/ -1259.1392167224028 (+ 2.0 (- z))) (/ -1259.1392167224028 (+ 2.0 (- z))) (* (/ -176.6150291621406 (+ (- z) 4.0)) (- (/ -176.6150291621406 (+ (- z) 4.0)) (/ -1259.1392167224028 (+ 2.0 (- z))))))))

series952.0ms

Counts

4 → 10

Calls

4 calls:

98.0ms	(pow (/ 771.3234287776531 (- 3.0 z)) 3)
164.0ms	(pow (+ (/ 12.507343278686905 (- 5.0 z)) (/ -0.13857109526572012 (- 6.0 z))) 3)
0.0ms	(sqrt (* 2.0 PI))
690.0ms	(fma (+ (pow (/ -1259.1392167224028 (+ 2.0 (- z))) 3) (pow (/ -176.6150291621406 (+ (- z) 4.0)) 3)) (fma (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (- (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ 771.3234287776531 (- 3.0 z))) (* (/ 771.3234287776531 (- 3.0 z)) (/ 771.3234287776531 (- 3.0 z)))) (* (+ (pow (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) 3) (pow (/ 771.3234287776531 (- 3.0 z)) 3)) (fma (/ -1259.1392167224028 (+ 2.0 (- z))) (/ -1259.1392167224028 (+ 2.0 (- z))) (* (/ -176.6150291621406 (+ (- z) 4.0)) (- (/ -176.6150291621406 (+ (- z) 4.0)) (/ -1259.1392167224028 (+ 2.0 (- z))))))))

simplify1.8s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	4433
1	1076
0	305

prune3.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize798.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (/ 771.3234287776531 (- 3.0 z)) 3)
1.0b	(pow (+ (/ 12.507343278686905 (- 5.0 z)) (/ -0.13857109526572012 (- 6.0 z))) 3)
1.0b	(sqrt PI)
1.0b	(fma (+ (pow (/ -1259.1392167224028 (+ 2.0 (- z))) 3) (pow (/ -176.6150291621406 (+ (- z) 4.0)) 3)) (fma (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (- (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ 771.3234287776531 (- 3.0 z))) (* (/ 771.3234287776531 (- 3.0 z)) (/ 771.3234287776531 (- 3.0 z)))) (* (+ (pow (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) 3) (pow (/ 771.3234287776531 (- 3.0 z)) 3)) (fma (/ -1259.1392167224028 (+ 2.0 (- z))) (/ -1259.1392167224028 (+ 2.0 (- z))) (* (/ -176.6150291621406 (+ (- z) 4.0)) (- (/ -176.6150291621406 (+ (- z) 4.0)) (/ -1259.1392167224028 (+ 2.0 (- z))))))))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
46×	`times-frac`
40×	`add-sqr-sqrt`
29×	`unpow-prod-down` `cube-prod`
27×	`add-cube-cbrt`
14×	`distribute-lft-out--`
10×	`distribute-lft-out`
8×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`pow-unpow` `difference-of-squares`
4×	`cube-div` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`pow-exp` `sqrt-prod` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `pow-pow` `flip3--` `unpow3` `div-inv` `flip--` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `frac-add` `flip-+` `fma-udef`

Counts

4 → 127

Calls

4 calls:

23.0ms	(pow (/ 771.3234287776531 (- 3.0 z)) 3)
190.0ms	(pow (+ (/ 12.507343278686905 (- 5.0 z)) (/ -0.13857109526572012 (- 6.0 z))) 3)
2.0ms	(sqrt PI)
1.0ms	(fma (+ (pow (/ -1259.1392167224028 (+ 2.0 (- z))) 3) (pow (/ -176.6150291621406 (+ (- z) 4.0)) 3)) (fma (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (- (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ 771.3234287776531 (- 3.0 z))) (* (/ 771.3234287776531 (- 3.0 z)) (/ 771.3234287776531 (- 3.0 z)))) (* (+ (pow (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) 3) (pow (/ 771.3234287776531 (- 3.0 z)) 3)) (fma (/ -1259.1392167224028 (+ 2.0 (- z))) (/ -1259.1392167224028 (+ 2.0 (- z))) (* (/ -176.6150291621406 (+ (- z) 4.0)) (- (/ -176.6150291621406 (+ (- z) 4.0)) (/ -1259.1392167224028 (+ 2.0 (- z))))))))

series847.0ms

Counts

4 → 10

Calls

4 calls:

78.0ms	(pow (/ 771.3234287776531 (- 3.0 z)) 3)
145.0ms	(pow (+ (/ 12.507343278686905 (- 5.0 z)) (/ -0.13857109526572012 (- 6.0 z))) 3)
0.0ms	(sqrt PI)
623.0ms	(fma (+ (pow (/ -1259.1392167224028 (+ 2.0 (- z))) 3) (pow (/ -176.6150291621406 (+ (- z) 4.0)) 3)) (fma (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (- (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ 771.3234287776531 (- 3.0 z))) (* (/ 771.3234287776531 (- 3.0 z)) (/ 771.3234287776531 (- 3.0 z)))) (* (+ (pow (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) 3) (pow (/ 771.3234287776531 (- 3.0 z)) 3)) (fma (/ -1259.1392167224028 (+ 2.0 (- z))) (/ -1259.1392167224028 (+ 2.0 (- z))) (* (/ -176.6150291621406 (+ (- z) 4.0)) (- (/ -176.6150291621406 (+ (- z) 4.0)) (/ -1259.1392167224028 (+ 2.0 (- z))))))))

simplify1.7s

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
2	4048
1	985
0	277

prune3.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes609.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify409.0ms

Iterations

Iter	Nodes
done	102
1	102
0	80

end0.0ms

sample1.3m

Algorithm

intervals

Results

1.1m	3939×	body	10240	exit
4.5s	1549×	body	1280	nan
3.9s	8087×	body	80	valid
2.3s	1324×	body	640	nan
1.0s	567×	body	320	nan
817.0ms	316×	body	160	nan
99.0ms	304×	body	80	nan