Details

sample8.6s

Algorithm

intervals

Results

5.8s	161×	body	10240	exit
2.0s	54×	body	640	nan
166.0ms	42×	body	1280	nan
152.0ms	256×	body	80	valid
150.0ms	33×	body	320	nan
10.0ms	12×	body	160	nan
9.0ms	13×	body	80	nan

simplify12.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
3	3597
2	604
1	148
0	60

prune86.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.6b

localize296.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
1.0b	(/ (pow (+ (+ 7.0 0.5) (- 0 z)) (+ (- 0 z) 0.5)) (exp (+ (+ 7.0 0.5) (- 0 z))))
1.0b	(sqrt (* 2.0 PI))
1.0b	(+ (/ -1259.1392167224028 (+ 2.0 (- 0 z))) (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

149×	`*-un-lft-identity`
78×	`times-frac`
51×	`distribute-lft-out`
45×	`add-sqr-sqrt` `add-cube-cbrt`
42×	`fma-def`
35×	`unpow-prod-down`
18×	`add-log-exp`
16×	`distribute-lft-out--`
13×	`exp-sum`
12×	`associate-/l*`
9×	`sum-log`
8×	`frac-add`
7×	`pow1` `flip3-+` `associate-/r/` `flip-+`
6×	`add-exp-log` `add-cbrt-cube`
5×	`unpow-prod-up` `sqr-pow`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`exp-diff` `div-exp` `div-inv`
2×	`+-commutative` `associate-+r+` `sqrt-pow1` `sub0-neg`
1×	`cbrt-undiv` `pow-to-exp` `associate-+l-` `associate-+r-` `frac-2neg` `pow1/2` `unsub-neg` `pow-prod-down` `pow-exp` `clear-num` `sqrt-prod` `associate-/l/` `pow-sub`

Counts

4 → 181

Calls

4 calls:

370.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
655.0ms	(/ (pow (+ (+ 7.0 0.5) (- 0 z)) (+ (- 0 z) 0.5)) (exp (+ (+ 7.0 0.5) (- 0 z))))
10.0ms	(sqrt (* 2.0 PI))
1.1s	(+ (/ -1259.1392167224028 (+ 2.0 (- 0 z))) (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))

series681.0ms

Counts

4 → 10

Calls

4 calls:

103.0ms	(+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
388.0ms	(/ (pow (+ (+ 7.0 0.5) (- 0 z)) (+ (- 0 z) 0.5)) (exp (+ (+ 7.0 0.5) (- 0 z))))
0.0ms	(sqrt (* 2.0 PI))
190.0ms	(+ (/ -1259.1392167224028 (+ 2.0 (- 0 z))) (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))

simplify6.3s

Counts

191 → 191

Iterations

Iter	Nodes
done	5001
2	3269
1	886
0	346

prune7.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize344.0ms

Local error

Found 4 expressions with local error:

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

rewrite948.0ms

Algorithm

rewrite-expression-head

Rules

113×	`*-un-lft-identity`
63×	`times-frac`
37×	`distribute-lft-out`
36×	`add-sqr-sqrt` `add-cube-cbrt`
35×	`unpow-prod-down`
21×	`fma-def`
13×	`exp-sum` `distribute-lft-out--`
12×	`associate-/l*`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`unpow-prod-up` `associate-/r/` `sqr-pow`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`exp-diff` `div-exp`
2×	`sqrt-pow1` `flip3-+` `sub0-neg` `flip-+` `fma-udef` `div-inv`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `associate-+l-` `associate-+r-` `associate-+r+` `frac-2neg` `pow1/2` `unsub-neg` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `sqrt-prod` `associate-/l/` `pow-sub`

Counts

4 → 143

Calls

4 calls:

1.0ms	(fma (/ 1 (sqrt (+ 3.0 (- 0 z)))) (/ 771.3234287776531 (sqrt (+ 3.0 (- 0 z)))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
666.0ms	(/ (pow (+ (+ 7.0 0.5) (- 0 z)) (+ (- 0 z) 0.5)) (exp (+ (+ 7.0 0.5) (- 0 z))))
10.0ms	(sqrt (* 2.0 PI))
258.0ms	(+ (/ -1259.1392167224028 (+ 2.0 (- 0 z))) (fma (/ 1 (sqrt (+ 3.0 (- 0 z)))) (/ 771.3234287776531 (sqrt (+ 3.0 (- 0 z)))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))

series1.2s

Counts

4 → 10

Calls

4 calls:

327.0ms	(fma (/ 1 (sqrt (+ 3.0 (- 0 z)))) (/ 771.3234287776531 (sqrt (+ 3.0 (- 0 z)))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))
509.0ms	(/ (pow (+ (+ 7.0 0.5) (- 0 z)) (+ (- 0 z) 0.5)) (exp (+ (+ 7.0 0.5) (- 0 z))))
0.0ms	(sqrt (* 2.0 PI))
401.0ms	(+ (/ -1259.1392167224028 (+ 2.0 (- 0 z))) (fma (/ 1 (sqrt (+ 3.0 (- 0 z)))) (/ 771.3234287776531 (sqrt (+ 3.0 (- 0 z)))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))

simplify4.5s

Counts

153 → 153

Iterations

Iter	Nodes
done	5001
2	1759
1	588
0	269

prune6.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize551.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
24×	`cbrt-prod` `distribute-lft-out`
21×	`fma-def`
17×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`times-frac`
14×	`unpow-prod-down`
13×	`add-log-exp`
7×	`pow1` `distribute-lft-out--`
6×	`frac-add` `sum-log`
4×	`add-exp-log` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`unpow-prod-up` `associate-+l-` `cbrt-div` `sqrt-pow1` `pow1/3` `associate-/r/` `pow-sub` `sqr-pow`
1×	`+-commutative` `associate-+r+` `pow1/2` `pow-prod-down` `sqrt-prod` `div-inv`

Counts

4 → 103

Calls

4 calls:

180.0ms	(cbrt (pow (+ (+ 7.0 0.5) (- 0 z)) (+ (- 0 z) 0.5)))
405.0ms	(cbrt (pow (+ (+ 7.0 0.5) (- 0 z)) (+ (- 0 z) 0.5)))
16.0ms	(sqrt (* 2.0 PI))
1.6s	(+ (/ -1259.1392167224028 (+ 2.0 (- 0 z))) (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))

series1.8s

Counts

4 → 10

Calls

4 calls:

828.0ms	(cbrt (pow (+ (+ 7.0 0.5) (- 0 z)) (+ (- 0 z) 0.5)))
769.0ms	(cbrt (pow (+ (+ 7.0 0.5) (- 0 z)) (+ (- 0 z) 0.5)))
0.0ms	(sqrt (* 2.0 PI))
218.0ms	(+ (/ -1259.1392167224028 (+ 2.0 (- 0 z))) (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))

simplify6.5s

Counts

113 → 113

Iterations

Iter	Nodes
done	5005
2	2354
1	622
0	224

prune6.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize491.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
24×	`cbrt-prod` `distribute-lft-out`
21×	`fma-def`
17×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`times-frac`
14×	`unpow-prod-down`
13×	`add-log-exp`
7×	`pow1` `distribute-lft-out--`
6×	`frac-add` `sum-log`
4×	`add-exp-log` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`unpow-prod-up` `associate-+l-` `cbrt-div` `sqrt-pow1` `pow1/3` `associate-/r/` `pow-sub` `sqr-pow`
1×	`+-commutative` `associate-+r+` `pow1/2` `pow-prod-down` `sqrt-prod` `div-inv`

Counts

4 → 103

Calls

4 calls:

240.0ms	(cbrt (pow (+ (+ 7.0 0.5) (- 0 z)) (+ (- 0 z) 0.5)))
327.0ms	(cbrt (pow (+ (+ 7.0 0.5) (- 0 z)) (+ (- 0 z) 0.5)))
10.0ms	(sqrt (* 2.0 PI))
1.3s	(+ (/ -1259.1392167224028 (+ 2.0 (- 0 z))) (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))

series3.0s

Counts

4 → 10

Calls

4 calls:

1.3s	(cbrt (pow (+ (+ 7.0 0.5) (- 0 z)) (+ (- 0 z) 0.5)))
1.1s	(cbrt (pow (+ (+ 7.0 0.5) (- 0 z)) (+ (- 0 z) 0.5)))
0.0ms	(sqrt (* 2.0 PI))
550.0ms	(+ (/ -1259.1392167224028 (+ 2.0 (- 0 z))) (+ (/ 771.3234287776531 (+ 3.0 (- 0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))

simplify6.6s

Counts

113 → 113

Iterations

Iter	Nodes
done	5002
2	2336
1	614
0	221

prune4.0s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

regimes661.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify37.0ms

Iterations

Iter	Nodes
done	87
1	87
0	63

end0.0ms

sample3.3m

Algorithm

intervals

Results

2.5m	3833×	body	10240	exit
15.9s	1268×	body	640	nan
15.9s	1446×	body	1280	nan
9.6s	8084×	body	80	valid
2.0s	618×	body	320	nan
1.3s	292×	body	160	nan
165.0ms	304×	body	80	nan