Details

sample381.0ms

Algorithm

intervals

Results

122.0ms	117×	body	1280	valid
61.0ms	54×	body	1280	nan
54.0ms	69×	body	640	valid
30.0ms	48×	body	320	valid
26.0ms	31×	body	640	nan
19.0ms	114×	body	80	overflowed
6.0ms	11×	body	320	nan
6.0ms	16×	body	160	valid
2.0ms	6×	body	160	nan
2.0ms	13×	body	80	nan
2.0ms	9×	body	80	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	133	48
1	453	48
2	2769	47
3	5002	47

prune28.0ms

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: 62.5b

Counts

2 → 2

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (neg (+ (+ (- 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))
4.9b	(+ (- z 1.0) 1.0)

rewrite41.0ms

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 (neg (+ (+ (- 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)

series311.0ms

Counts

4 → 10

Calls

4 calls:

17.0ms	(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
284.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))
9.0ms	(+ (- z 1.0) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	552	704
1	2036	643
2	5001	638

prune797.0ms

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: 0.8b

Counts

102 → 4

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
0.7b	(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (neg (+ (+ (- 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)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b	(sqrt (* PI 2.0))

rewrite209.0ms

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 (neg (+ (+ (- z 1.0) 7.0) 0.5)))
154.0ms	(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (neg (+ (+ (- 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))))
22.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms	(sqrt (* PI 2.0))

series918.0ms

Counts

4 → 10

Calls

4 calls:

20.0ms	(exp (neg (+ (+ (- z 1.0) 7.0) 0.5)))
610.0ms	(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (neg (+ (+ (- 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))))
287.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))

simplify296.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 1 (64.0ms)

Iter	Nodes	Cost
0	3745	23932
1	5002	23816

prune2.0s

Filtered

233 candidates to 140 candidates (60.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	228	5	233
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	231	6	237

Merged error: 0b

Counts

237 → 6

localize55.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (sqrt (* PI 2.0)) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (* 2 (+ (- z 1.0) 0.5)))))
1.0b	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (* 2 (+ (- z 1.0) 0.5))))
1.0b	(* (* PI 2.0) (* (sqrt (* PI 2.0)) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (* 2 (+ (- z 1.0) 0.5))))))
1.0b	(sqrt (* PI 2.0))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-exp-log`
99×	`prod-exp`
32×	`add-cbrt-cube`
27×	`*-un-lft-identity`
24×	`pow-to-exp` `pow-exp`
21×	`pow1` `add-sqr-sqrt`
19×	`cbrt-unprod`
18×	`unpow-prod-down`
16×	`associate-l`
14×	`associate-r`
10×	`pow-prod-down` `distribute-lft-out`
9×	`add-cube-cbrt` `unswap-sqr`
8×	`sqr-pow`
4×	`add-log-exp`
3×	`unpow-prod-up` `associate-+l-` `associate-r/` `associate-l/` `*-commutative` `pow-sub`
2×	`sqrt-pow1` `sqrt-prod` `distribute-lft-out--`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/2` `pow-prod-up`

Counts

4 → 133

Calls

4 calls:

33.0ms	(* (sqrt (* PI 2.0)) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (* 2 (+ (- z 1.0) 0.5)))))
31.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (* 2 (+ (- z 1.0) 0.5))))
35.0ms	(* (* PI 2.0) (* (sqrt (* PI 2.0)) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (* 2 (+ (- z 1.0) 0.5))))))
2.0ms	(sqrt (* PI 2.0))

series1.2s

Counts

4 → 10

Calls

4 calls:

416.0ms	(* (sqrt (* PI 2.0)) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (* 2 (+ (- z 1.0) 0.5)))))
205.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (* 2 (+ (- z 1.0) 0.5))))
576.0ms	(* (* PI 2.0) (* (sqrt (* PI 2.0)) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (* 2 (+ (- z 1.0) 0.5))))))
0.0ms	(sqrt (* PI 2.0))

simplify125.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	911	2744
1	3986	2145
2	5001	2011

prune963.0ms

Filtered

143 candidates to 78 candidates (54.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	143	6	149

Merged error: 0b

Counts

149 → 6

localize67.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

216×	`add-sqr-sqrt`
208×	`unpow-prod-down`
132×	`times-frac`
116×	`associate-l`
96×	`add-exp-log` `*-un-lft-identity`
72×	`add-cube-cbrt` `unswap-sqr`
52×	`pow-exp`
48×	`prod-exp` `sqrt-prod`
40×	`sqr-pow`
24×	`div-exp` `associate-r`
16×	`pow-to-exp`
12×	`rec-exp` `1-exp` `add-cbrt-cube`
4×	`pow1` `*-commutative` `cbrt-unprod` `div-inv` `add-log-exp`

Counts

4 → 296

Calls

4 calls:

14.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
15.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
14.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
19.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

simplify78.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	435	2848
1	1533	2748
2	5001	2604

prune2.4s

Filtered

300 candidates to 177 candidates (59.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	300	0	300
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	300	6	306

Merged error: 0b

Counts

306 → 6

regimes158.0ms

Accuracy

0% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	57
1	92	57
2	92	57

end0.0ms

sample10.7s

Algorithm

intervals

Results

3.5s	3378×	body	1280	valid
1.9s	2500×	body	640	valid
1.7s	1535×	body	1280	nan
1.0s	1260×	body	640	nan
678.0ms	3866×	body	80	overflowed
669.0ms	1232×	body	320	valid
357.0ms	609×	body	320	nan
227.0ms	637×	body	160	valid
118.0ms	308×	body	160	nan
64.0ms	342×	body	80	valid
49.0ms	306×	body	80	nan

Details

sample381.0ms

simplify74.0ms

prune28.0ms

localize53.0ms

rewrite41.0ms

series311.0ms

simplify58.0ms

prune797.0ms

localize48.0ms

rewrite209.0ms

series918.0ms

simplify296.0ms

prune2.0s

localize55.0ms

rewrite108.0ms

series1.2s

simplify125.0ms

prune963.0ms

localize67.0ms

rewrite79.0ms

series0.0ms

simplify78.0ms

prune2.4s

regimes158.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample10.7s

Profiling