Details

sample436.0ms

Algorithm

intervals

Results

125.0ms	128×	body	10240	exit
102.0ms	118×	body	1280	valid
48.0ms	73×	body	640	valid
47.0ms	58×	body	1280	nan
30.0ms	55×	body	640	nan
18.0ms	41×	body	320	valid
6.0ms	15×	body	320	nan
5.0ms	17×	body	160	valid
3.0ms	10×	body	160	nan
2.0ms	18×	body	80	nan
1.0ms	10×	body	80	valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	133	48
1	455	48
2	2797	47
3	5001	47

prune30.0ms

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: 62.0b

Counts

2 → 2

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1.0) 1.0))) (/ -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)))) (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))
5.3b	(+ (- z 1.0) 1.0)

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

112×	`frac-add`
34×	`associate-*r/`
33×	`associate-/l/`
32×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
21×	`associate-+l-`
20×	`add-exp-log`
18×	`pow-sub`
17×	`flip3-+` `flip-+`
16×	`frac-times` `add-cube-cbrt`
15×	`add-cbrt-cube`
11×	`associate-+l+` `associate-r`
10×	`prod-exp`
9×	`prod-diff` `add-log-exp`
7×	`pow1` `unpow-prod-down` `distribute-lft-out`
5×	`fma-def` `div-exp`
4×	`expm1-log1p-u` `times-frac` `associate-l` `associate-/r*` `cbrt-unprod` `log1p-expm1-u`
3×	`cbrt-undiv` `distribute-lft-out--` `unswap-sqr`
2×	`pow-to-exp` `sqrt-pow1` `exp-sum` `pow-exp` `sum-log` `sqrt-prod` `sqr-pow`
1×	`unpow-prod-up` `+-commutative` `sub-neg` `frac-2neg` `pow1/2` `exp-diff` `diff-log` `pow-prod-down` `associate-l/` `clear-num` `associate-/r/` `-commutative` `div-inv` `associate-/l*` `difference-of-squares`

Counts

4 → 142

Calls

4 calls:

150.0ms	(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1.0) 1.0))) (/ -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)))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
21.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms	(sqrt (* PI 2.0))
8.0ms	(+ (- z 1.0) 1.0)

series887.0ms

Counts

4 → 10

Calls

4 calls:

617.0ms	(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1.0) 1.0))) (/ -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)))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
260.0ms	(* (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)

simplify89.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	1851	4342
1	5001	3934

prune1.5s

Filtered

152 candidates to 126 candidates (82.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	146	6	152
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	148	6	154

Merged error: 0.3b

Counts

154 → 6

localize67.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (sqrt 2.0) (exp 6.5))
1.0b	(* (log 6.5) (sqrt 2.0))
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))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

132×	`add-sqr-sqrt`
104×	`unpow-prod-down`
84×	`times-frac`
68×	`*-un-lft-identity`
62×	`associate-l`
56×	`add-cube-cbrt`
53×	`add-exp-log`
40×	`sqrt-prod`
38×	`unswap-sqr`
26×	`pow-exp`
25×	`prod-exp`
20×	`sqr-pow`
18×	`associate-r`
13×	`div-exp`
12×	`add-cbrt-cube`
8×	`pow-to-exp`
7×	`pow1`
6×	`rec-exp` `1-exp` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `frac-2neg` `pow-prod-down` `clear-num` `log-pow`

Counts

4 → 218

Calls

4 calls:

5.0ms	(/ (sqrt 2.0) (exp 6.5))
6.0ms	(* (log 6.5) (sqrt 2.0))
14.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
18.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/ (sqrt 2.0) (exp 6.5))
0.0ms	(* (log 6.5) (sqrt 2.0))
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))

simplify72.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	572	1976
1	1989	1932
2	5002	1865

prune2.1s

Filtered

222 candidates to 138 candidates (62.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	219	3	222
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	219	9	228

Merged error: 0.1b

Counts

228 → 9

localize79.0ms

Local error

Found 4 expressions with local error:

1.0b	(expm1 (log1p (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))))
1.0b	(* (log 6.5) (sqrt 2.0))
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))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-sqr-sqrt`
104×	`unpow-prod-down`
66×	`times-frac`
62×	`associate-l`
53×	`*-un-lft-identity`
52×	`add-exp-log`
41×	`add-cube-cbrt`
38×	`unswap-sqr`
28×	`sqrt-prod`
26×	`pow-exp`
25×	`prod-exp`
20×	`sqr-pow`
18×	`associate-r`
12×	`div-exp`
10×	`add-cbrt-cube`
8×	`pow-to-exp`
7×	`pow1`
6×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `cbrt-unprod`
2×	`div-inv`
1×	`expm1-log1p` `pow-prod-down` `log-pow` `expm1-udef`

Counts

4 → 188

Calls

4 calls:

1.0ms	(expm1 (log1p (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))))
11.0ms	(* (log 6.5) (sqrt 2.0))
15.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
15.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(expm1 (log1p (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))))
0.0ms	(* (log 6.5) (sqrt 2.0))
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))

simplify93.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	372	1475
1	1052	1433
2	3355	1389
3	5001	1375

prune1.9s

Filtered

192 candidates to 117 candidates (60.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	192	9	201

Merged error: 0.1b

Counts

201 → 9

localize71.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (sqrt 2.0) (exp 6.5))
1.0b	(* (log 6.5) (sqrt 2.0))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b	(* 1656.8104518737205 (sqrt PI))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
52×	`unpow-prod-down`
51×	`times-frac`
48×	`*-un-lft-identity`
42×	`add-cube-cbrt`
36×	`associate-l`
32×	`add-exp-log` `sqrt-prod`
22×	`unswap-sqr`
18×	`associate-r`
14×	`prod-exp`
13×	`pow-exp`
12×	`add-cbrt-cube`
10×	`sqr-pow`
9×	`pow1`
7×	`div-exp`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow-to-exp` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-/r` `-commutative` `cbrt-unprod`
2×	`pow-prod-down` `div-inv`
1×	`cbrt-undiv` `frac-2neg` `clear-num` `log-pow`

Counts

4 → 166

Calls

4 calls:

5.0ms	(/ (sqrt 2.0) (exp 6.5))
5.0ms	(* (log 6.5) (sqrt 2.0))
14.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
5.0ms	(* 1656.8104518737205 (sqrt PI))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/ (sqrt 2.0) (exp 6.5))
0.0ms	(* (log 6.5) (sqrt 2.0))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms	(* 1656.8104518737205 (sqrt PI))

simplify71.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	649	1398
1	2382	1363
2	5001	1299

prune1.6s

Filtered

170 candidates to 108 candidates (63.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	168	2	170
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	169	10	179

Merged error: 0.0b

Counts

179 → 10

regimes301.0ms

Accuracy

0% (1.1b remaining)

Error of 1.2b against oracle of 0.1b and baseline of 1.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	85
1	81	85

end0.0ms

sample11.8s

Algorithm

intervals

Results

4.0s	3788×	body	10240	exit
2.9s	3307×	body	1280	valid
1.6s	2488×	body	640	valid
1.1s	1477×	body	1280	nan
699.0ms	1235×	body	640	nan
579.0ms	1297×	body	320	valid
254.0ms	625×	body	320	nan
191.0ms	644×	body	160	valid
84.0ms	308×	body	160	nan
50.0ms	349×	body	80	valid
41.0ms	320×	body	80	nan