Details

sample444.0ms

Algorithm

intervals

Results

139.0ms	137×	body	10240	exit
105.0ms	115×	body	1280	valid
50.0ms	78×	body	640	valid
37.0ms	52×	body	1280	nan
34.0ms	41×	body	640	nan
17.0ms	38×	body	320	valid
6.0ms	15×	body	320	nan
6.0ms	20×	body	160	valid
3.0ms	10×	body	160	nan
2.0ms	13×	body	80	valid
1.0ms	12×	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

prune27.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 62.5b

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))
5.8b	(+ (- z 1.0) 1.0)

rewrite45.0ms

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)))
3.0ms	(sqrt (* PI 2.0))
8.0ms	(+ (- z 1.0) 1.0)

series329.0ms

Counts

4 → 10

Calls

4 calls:

18.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
301.0ms	(* (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)

simplify69.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (59.0ms)

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

prune1.0s

Filtered

122 candidates to 89 candidates (73.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
0.9b	(* (* (* (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 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))))
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))

rewrite211.0ms

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:

12.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
155.0ms	(* (* (* (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 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))))
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))

series971.0ms

Counts

4 → 10

Calls

4 calls:

17.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
658.0ms	(* (* (* (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 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))))
296.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))

simplify305.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 1 (66.0ms)

Iter	Nodes	Cost
0	3855	24889
1	5001	24763

prune2.0s

Filtered

241 candidates to 148 candidates (61.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

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))

rewrite80.0ms

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))
18.0ms	(* (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))

simplify69.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	412	2880
1	1325	2828
2	5001	2712

prune2.7s

Filtered

308 candidates to 185 candidates (60.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize61.0ms

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` `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))
15.0ms	(* (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))

simplify68.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 2 (42.0ms)

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

prune2.3s

Filtered

308 candidates to 185 candidates (60.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes77.0ms

Accuracy

0% (1.0b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 1.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	82
1	79	82

end0.0ms

sample12.2s

Algorithm

intervals

Results

4.1s	3896×	body	10240	exit
3.1s	3446×	body	1280	valid
1.6s	2481×	body	640	valid
1.1s	1466×	body	1280	nan
725.0ms	1235×	body	640	nan
541.0ms	1203×	body	320	valid
275.0ms	649×	body	320	nan
176.0ms	596×	body	160	valid
85.0ms	316×	body	160	nan
57.0ms	375×	body	80	valid
37.0ms	272×	body	80	nan