Details

sample391.0ms

Algorithm

intervals

Results

131.0ms	124×	body	1280	valid
57.0ms	74×	body	640	valid
55.0ms	46×	body	1280	nan
29.0ms	38×	body	320	valid
26.0ms	31×	body	640	nan
18.0ms	102×	body	80	overflowed
11.0ms	19×	body	320	nan
5.0ms	13×	body	160	valid
3.0ms	13×	body	80	valid
3.0ms	7×	body	160	nan
2.0ms	11×	body	80	nan

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

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

localize54.0ms

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))
4.4b	(+ (- z 1.0) 1.0)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
20×	`add-log-exp`
17×	`add-cube-cbrt` `distribute-lft-out`
16×	`exp-prod`
11×	`associate-+l+` `associate-r`
9×	`add-exp-log` `prod-diff`
7×	`pow1` `unpow-prod-down` `sum-log`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `add-cbrt-cube`
5×	`fma-def` `rem-exp-log` `distribute-lft-out--`
4×	`expm1-log1p-u` `associate-l` `neg-log` `log1p-expm1-u`
3×	`prod-exp` `unswap-sqr`
2×	`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` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

11.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
19.0ms	(* (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)

series319.0ms

Counts

4 → 10

Calls

4 calls:

17.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
292.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))
10.0ms	(+ (- z 1.0) 1.0)

simplify72.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	595	821
1	2411	692
2	5001	670

prune977.0ms

Filtered

122 candidates to 89 candidates (73.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	121	3	124

Merged error: 1.3b

Counts

124 → 3

localize46.0ms

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))
1.2b	(* (* (* (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))))

rewrite392.0ms

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×	`expm1-log1p-u` `pow-prod-down` `neg-log` `log1p-expm1-u`
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 → 231

Calls

4 calls:

11.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
23.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms	(sqrt (* PI 2.0))
335.0ms	(* (* (* (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))))

series919.0ms

Counts

4 → 10

Calls

4 calls:

17.0ms	(exp (- (+ (+ (- 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))
618.0ms	(* (* (* (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))))

simplify304.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 1 (66.0ms)

Iter	Nodes	Cost
0	3852	23664
1	5002	23540

prune1.9s

Filtered

241 candidates to 148 candidates (61.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	236	5	241
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	238	6	244

Merged error: 0.0b

Counts

244 → 6

localize60.0ms

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))

rewrite87.0ms

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` `expm1-log1p-u` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

4 → 304

Calls

4 calls:

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))
15.0ms	(* (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))

simplify70.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	412	2880
1	1325	2828
2	5001	2796

prune2.6s

Filtered

308 candidates to 201 candidates (65.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	307	1	308
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	307	7	314

Merged error: 0b

Counts

314 → 7

localize63.0ms

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))

rewrite77.0ms

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` `expm1-log1p-u` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

4 → 304

Calls

4 calls:

18.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
14.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
14.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
14.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

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))

simplify72.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	434	2840
1	1476	2764
2	5001	2644

prune2.2s

Filtered

308 candidates to 185 candidates (60.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	308	0	308
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	308	7	315

Merged error: 0b

Counts

315 → 7

regimes128.0ms

Accuracy

0% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 1.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	90
1	71	90

end0.0ms

sample10.9s

Algorithm

intervals

Results

3.6s	3401×	body	1280	valid
1.9s	2513×	body	640	valid
1.6s	1476×	body	1280	nan
1.1s	1270×	body	640	nan
875.0ms	3832×	body	80	overflowed
685.0ms	1239×	body	320	valid
379.0ms	642×	body	320	nan
205.0ms	577×	body	160	valid
130.0ms	355×	body	160	nan
65.0ms	358×	body	80	valid
44.0ms	290×	body	80	nan