Details

sample388.0ms

Algorithm

intervals

Results

107.0ms	102×	body	10240	exit
106.0ms	124×	body	1280	valid
45.0ms	74×	body	640	valid
32.0ms	46×	body	1280	nan
21.0ms	31×	body	640	nan
16.0ms	38×	body	320	valid
7.0ms	19×	body	320	nan
4.0ms	13×	body	160	valid
3.0ms	13×	body	80	valid
2.0ms	7×	body	160	nan
1.0ms	11×	body	80	nan

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	133	48
1	453	48
2	2766	47
3	5002	47

prune36.0ms

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

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

rewrite46.0ms

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:

14.0ms	(exp (- (+ (+ (- 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)

series310.0ms

Counts

4 → 10

Calls

4 calls:

18.0ms	(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))
10.0ms	(+ (- z 1.0) 1.0)

simplify254.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	552	708
1	2026	642
2	5001	637

prune752.0ms

Filtered

100 candidates to 68 candidates (68.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	99	3	102

Merged error: 1.3b

Counts

102 → 3

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))
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))))

rewrite206.0ms

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:

11.0ms	(exp (- (+ (+ (- 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))
151.0ms	(* (* (* (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))))

series937.0ms

Counts

4 → 10

Calls

4 calls:

17.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
288.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))
631.0ms	(* (* (* (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))))

simplify305.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 1 (65.0ms)

Iter	Nodes	Cost
0	3749	23934
1	5001	23816

prune1.9s

Filtered

233 candidates to 140 candidates (60.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	227	6	233
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	229	7	236

Merged error: 0.0b

Counts

236 → 7

localize68.0ms

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))

rewrite84.0ms

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:

19.0ms	(* (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))

simplify75.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	429	2848
1	1483	2748
2	5001	2600

prune2.4s

Filtered

300 candidates to 177 candidates (59.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	299	1	300
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	300	7	307

Merged error: 0b

Counts

307 → 7

localize57.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(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))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

114×	`add-sqr-sqrt`
104×	`unpow-prod-down`
66×	`times-frac`
58×	`associate-l`
52×	`*-un-lft-identity`
50×	`add-exp-log`
40×	`add-cube-cbrt`
36×	`unswap-sqr`
30×	`sqrt-prod`
26×	`pow-exp`
24×	`prod-exp`
20×	`sqr-pow`
12×	`div-exp` `associate-r`
8×	`pow-to-exp` `add-cbrt-cube`
6×	`pow1` `rec-exp` `1-exp`
4×	`add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 174

Calls

4 calls:

2.0ms	(sqrt PI)
1.0ms	(sqrt PI)
19.0ms	(* (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	(sqrt PI)
0.0ms	(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))

simplify57.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	406	1554
1	1274	1528
2	5002	1480

prune1.3s

Filtered

178 candidates to 109 candidates (61.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	179	6	185

Merged error: 0b

Counts

185 → 6

regimes105.0ms

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	84	94
1	84	94

end0.0ms

sample11.8s

Algorithm

intervals

Results

3.9s	3832×	body	10240	exit
3.0s	3401×	body	1280	valid
1.8s	2513×	body	640	valid
1.1s	1476×	body	1280	nan
691.0ms	1270×	body	640	nan
538.0ms	1239×	body	320	valid
253.0ms	642×	body	320	nan
160.0ms	577×	body	160	valid
95.0ms	355×	body	160	nan
51.0ms	358×	body	80	valid
37.0ms	290×	body	80	nan

Details

sample388.0ms

simplify70.0ms

prune36.0ms

localize46.0ms

rewrite46.0ms

series310.0ms

simplify254.0ms

prune752.0ms

localize49.0ms

rewrite206.0ms

series937.0ms

simplify305.0ms

prune1.9s

localize68.0ms

rewrite84.0ms

series0.0ms

simplify75.0ms

prune2.4s

localize57.0ms

rewrite48.0ms

series0.0ms

simplify57.0ms

prune1.3s

regimes105.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample11.8s

Profiling