Details

sample458.0ms

Algorithm

intervals

Results

149.0ms	133×	body	10240	exit
113.0ms	113×	body	1280	valid
52.0ms	78×	body	640	valid
41.0ms	53×	body	1280	nan
19.0ms	42×	body	320	valid
18.0ms	25×	body	640	nan
11.0ms	19×	body	320	nan
5.0ms	16×	body	160	valid
2.0ms	6×	body	160	nan
2.0ms	10×	body	80	valid
1.0ms	8×	body	80	nan

simplify75.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

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

prune19.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 62.0b

Counts

2 → 1

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))
4.7b	(+ (- z 1.0) 1.0)

rewrite46.0ms

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))
9.0ms	(+ (- z 1.0) 1.0)

series317.0ms

Counts

4 → 10

Calls

4 calls:

17.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
283.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))
16.0ms	(+ (- z 1.0) 1.0)

simplify73.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	595	823
1	2400	692
2	5001	670

prune1.0s

Filtered

122 candidates to 89 candidates (73.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	6	123

Merged error: 1.2b

Counts

123 → 6

localize52.0ms

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 (* 1 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))

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:

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)))
156.0ms	(* (* (* (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 (* 1 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))))
3.0ms	(sqrt (* PI 2.0))

series957.0ms

Counts

4 → 10

Calls

4 calls:

25.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
295.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
636.0ms	(* (* (* (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 (* 1 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))

simplify328.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 1 (68.0ms)

Iter	Nodes	Cost
0	3856	24889
1	5001	24763

prune2.1s

Filtered

241 candidates to 148 candidates (61.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	230	11	241
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	236	11	247

Merged error: 0.1b

Counts

247 → 11

localize54.0ms

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)))
1.0b	(* (* (exp (log (* (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 (* 1 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))
1.6b	(log (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

392×	`frac-add`
130×	`frac-times`
103×	`associate-*r/`
85×	`exp-diff`
61×	`*-un-lft-identity`
56×	`flip3-+` `flip-+`
53×	`associate-+l-` `pow-sub`
52×	`log-div`
51×	`exp-neg`
41×	`distribute-lft-out`
34×	`neg-sub0`
23×	`associate-*l/`
22×	`associate-r`
18×	`add-exp-log`
17×	`un-div-inv`
13×	`pow1` `add-sqr-sqrt`
11×	`add-cbrt-cube`
9×	`prod-exp`
8×	`add-cube-cbrt`
7×	`unpow-prod-down`
5×	`associate-l`
4×	`expm1-log1p-u` `rem-log-exp` `pow-prod-down` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`pow-to-exp` `sqrt-pow1` `pow-exp` `sqrt-prod` `*-commutative` `sqr-pow`
1×	`unpow-prod-up` `distribute-rgt-in` `log-prod` `distribute-lft-in` `pow1/2` `log-pow` `distribute-lft-out--`

Counts

4 → 210

Calls

4 calls:

19.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
159.0ms	(* (* (exp (log (* (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 (* 1 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))))
3.0ms	(sqrt (* PI 2.0))
17.0ms	(log (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))))

series1.5s

Counts

4 → 10

Calls

4 calls:

328.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
652.0ms	(* (* (exp (log (* (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 (* 1 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))
513.0ms	(log (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))))

simplify335.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 1 (71.0ms)

Iter	Nodes	Cost
0	3872	24734
1	5002	24579

prune2.1s

Filtered

220 candidates to 135 candidates (61.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	216	4	220
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	220	11	231

Merged error: 0.1b

Counts

231 → 11

localize62.0ms

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))

rewrite83.0ms

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))
20.0ms	(* (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))

simplify71.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 2 (40.0ms)

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

prune2.5s

Filtered

308 candidates to 185 candidates (60.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	307	1	308
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	308	11	319

Merged error: 0.1b

Counts

319 → 11

regimes245.0ms

Accuracy

0% (0.9b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 1.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	82
1	79	82

end0.0ms

sample12.7s

Algorithm

intervals

Results

4.4s	3997×	body	10240	exit
3.2s	3438×	body	1280	valid
1.6s	2435×	body	640	valid
1.2s	1529×	body	1280	nan
740.0ms	1234×	body	640	nan
592.0ms	1229×	body	320	valid
260.0ms	595×	body	320	nan
189.0ms	635×	body	160	valid
91.0ms	314×	body	160	nan
55.0ms	359×	body	80	valid
40.0ms	309×	body	80	nan