Details

sample373.0ms

Algorithm

intervals

Results

104.0ms	99×	body	1280	valid
61.0ms	81×	body	640	valid
56.0ms	47×	body	1280	nan
32.0ms	40×	body	640	nan
24.0ms	45×	body	320	valid
18.0ms	108×	body	80	overflowed
12.0ms	21×	body	320	nan
6.0ms	17×	body	160	valid
5.0ms	14×	body	160	nan
3.0ms	17×	body	80	valid
2.0ms	11×	body	80	nan

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	133	48
1	453	48
2	2766	47
3	5002	47

prune27.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 60.1b

Counts

2 → 2

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
1.0b	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b	(sqrt (* PI 2.0))
5.9b	(+ (- z 1.0) 1.0)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
20×	`add-log-exp`
17×	`distribute-lft-out`
16×	`exp-prod`
15×	`add-sqr-sqrt`
11×	`associate-r`
10×	`add-cube-cbrt`
9×	`add-exp-log`
7×	`pow1` `unpow-prod-down` `sum-log`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `add-cbrt-cube`
5×	`rem-exp-log`
4×	`associate-l` `neg-log` `distribute-lft-out--`
3×	`prod-exp` `unswap-sqr`
2×	`associate-+l-` `associate-+l+` `sqrt-pow1` `diff-log` `sqrt-prod` `sqr-pow`
1×	`unpow-prod-up` `+-commutative` `neg-sub0` `exp-neg` `pow-to-exp` `neg-mul-1` `sub-neg` `distribute-neg-in` `flip3-+` `pow1/2` `exp-diff` `associate-r/` `exp-sum` `pow-prod-down` `pow-exp` `-commutative` `cbrt-unprod` `flip-+` `pow-sub`

Counts

4 → 90

Calls

4 calls:

11.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
18.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms	(sqrt (* PI 2.0))
7.0ms	(+ (- z 1.0) 1.0)

series295.0ms

Counts

4 → 10

Calls

4 calls:

17.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
264.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))
14.0ms	(+ (- z 1.0) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	552	708
1	2026	642
2	5001	637

prune725.0ms

Filtered

100 candidates to 68 candidates (68.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	98	4	102

Merged error: 1.2b

Counts

102 → 4

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
1.0b	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b	(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
1.0b	(sqrt (* PI 2.0))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

392×	`frac-add`
130×	`frac-times`
102×	`associate-*r/`
82×	`*-un-lft-identity`
56×	`flip3-+` `flip-+`
52×	`exp-neg` `associate-+l-` `pow-sub`
51×	`distribute-lft-out`
35×	`neg-sub0` `exp-diff`
23×	`associate-*l/`
22×	`associate-r`
21×	`add-exp-log`
17×	`un-div-inv`
16×	`add-sqr-sqrt` `exp-prod`
15×	`prod-exp` `add-cbrt-cube` `add-log-exp`
12×	`pow1`
11×	`add-cube-cbrt`
7×	`unpow-prod-down` `cbrt-unprod`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`associate-l` `sum-log` `rem-exp-log`
4×	`pow-prod-down` `neg-log`
3×	`distribute-lft-out--` `unswap-sqr`
2×	`pow-to-exp` `sqrt-pow1` `pow-exp` `sqrt-prod` `*-commutative` `sqr-pow`
1×	`unpow-prod-up` `distribute-rgt-in` `neg-mul-1` `distribute-neg-in` `distribute-lft-in` `pow1/2` `diff-log` `exp-sum`

Counts

4 → 223

Calls

4 calls:

10.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
18.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
144.0ms	(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
2.0ms	(sqrt (* PI 2.0))

series886.0ms

Counts

4 → 10

Calls

4 calls:

16.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
270.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
600.0ms	(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
0.0ms	(sqrt (* PI 2.0))

simplify296.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 1 (63.0ms)

Iter	Nodes	Cost
0	3749	23934
1	5001	23816

prune1.9s

Filtered

233 candidates to 140 candidates (60.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	221	12	233
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	225	12	237

Merged error: 0.1b

Counts

237 → 12

localize56.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)))
0.9b	(/ (* (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z))) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5))))
0.9b	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
1.0b	(sqrt (* PI 2.0))

rewrite306.0ms

Algorithm

rewrite-expression-head

Rules

112×	`frac-add`
75×	`add-exp-log`
61×	`*-un-lft-identity`
53×	`prod-exp`
41×	`distribute-lft-out`
34×	`associate-*l/`
32×	`add-cbrt-cube`
23×	`associate-l`
20×	`div-exp`
16×	`flip3-+` `flip-+` `associate-/l/`
13×	`add-sqr-sqrt` `cbrt-unprod`
11×	`pow-to-exp` `pow-exp`
9×	`pow1`
8×	`add-cube-cbrt` `associate-+l-`
7×	`unpow-prod-down`
6×	`cbrt-undiv`
5×	`associate-r`
4×	`exp-diff` `pow-sub` `add-log-exp`
3×	`associate-/r/` `unswap-sqr`
2×	`unpow-prod-up` `frac-times` `sqrt-pow1` `associate-r/` `pow-prod-down` `-commutative` `sqr-pow`
1×	`sub-neg` `frac-2neg` `times-frac` `pow1/2` `exp-sum` `clear-num` `associate-/r` `sqrt-prod` `div-inv` `associate-/l` `distribute-lft-out--`

Counts

4 → 146

Calls

4 calls:

125.0ms	(* (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)))
146.0ms	(/ (* (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z))) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5))))
23.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
2.0ms	(sqrt (* PI 2.0))

series1.4s

Counts

4 → 10

Calls

4 calls:

319.0ms	(* (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z)))
874.0ms	(/ (* (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z))) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5))))
206.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))

simplify128.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	2893	8062
1	5002	7466

prune1.4s

Filtered

156 candidates to 107 candidates (68.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	152	4	156
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	158	10	168

Merged error: 0.1b

Counts

168 → 10

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (+ (+ (- z 1.0) 7.0) 0.5))
0.9b	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
1.0b	(/ (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z))))
1.0b	(sqrt (* PI 2.0))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

308×	`*-un-lft-identity`
226×	`distribute-lft-out`
67×	`times-frac`
60×	`add-exp-log`
56×	`frac-add`
33×	`div-exp`
31×	`add-sqr-sqrt`
27×	`prod-exp`
26×	`add-cube-cbrt`
24×	`add-cbrt-cube`
16×	`associate-/l/`
14×	`add-log-exp`
13×	`div-inv`
12×	`associate-l`
11×	`associate-/l*`
9×	`cbrt-undiv` `pow-to-exp` `pow-exp`
8×	`flip3-+` `flip-+`
7×	`pow1` `unpow-prod-down`
6×	`associate-+l-` `exp-prod`
5×	`associate-/r*` `sum-log` `cbrt-unprod`
4×	`associate-r` `rem-exp-log`
3×	`exp-diff` `unswap-sqr`
2×	`unpow-prod-up` `sqrt-pow1` `exp-sum` `distribute-lft-out--` `pow-sub` `sqr-pow`
1×	`frac-times` `sub-neg` `frac-2neg` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `sqrt-prod` `associate-/r/` `*-commutative`

Counts

4 → 184

Calls

4 calls:

14.0ms	(exp (+ (+ (- z 1.0) 7.0) 0.5))
24.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
148.0ms	(/ (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z))))
2.0ms	(sqrt (* PI 2.0))

series1.3s

Counts

4 → 10

Calls

4 calls:

11.0ms	(exp (+ (+ (- z 1.0) 7.0) 0.5))
202.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
1.1s	(/ (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) z))))
0.0ms	(sqrt (* PI 2.0))

simplify119.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1904	8701
1	5003	8379

prune1.1s

Filtered

194 candidates to 105 candidates (54.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	195	9	204

Merged error: 0.1b

Counts

204 → 9

regimes168.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	51
1	80	51

end0.0ms

sample10.5s

Algorithm

intervals

Results

3.5s	3320×	body	1280	valid
1.9s	2490×	body	640	valid
1.6s	1448×	body	1280	nan
1.0s	1248×	body	640	nan
684.0ms	1264×	body	320	valid
668.0ms	3814×	body	80	overflowed
356.0ms	602×	body	320	nan
227.0ms	642×	body	160	valid
143.0ms	349×	body	160	nan
67.0ms	371×	body	80	valid
42.0ms	263×	body	80	nan