Details

analyze2.4s

Algorithm

sampling

Space saved by range analysis: 0.292611%

Space saved by search: 67.502597%

Guaranteed chance to sample good point: 12.659176%

sample89.0ms

Algorithm

intervals

Results

18.0ms	224×	body	80	valid
16.0ms	160×	body	80	invalid
13.0ms	169×	body	80	nan
6.0ms	14×	body	640	valid
2.0ms	9×	body	320	valid
2.0ms	2×	body	1280	invalid
1.0ms	8×	body	160	valid
1.0ms	5×	body	320	invalid
1.0ms	2×	body	640	invalid
1.0ms	5×	body	160	invalid
1.0ms	1×	body	1280	valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	10
1	58	10
2	129	10
3	318	10
4	1073	10
5	5001	10

prune6.0ms

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: 3.5b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.1b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.6b	(log (- 1.0 z))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

27×	`log-prod`
24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`associate--l+`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`add-cube-cbrt` `associate-+r+`
10×	`associate-+l+` `associate-*r/`
9×	`add-log-exp`
8×	`pow1`
7×	`add-exp-log`
6×	`sub-neg` `flip3--` `associate-r` `add-cbrt-cube` `flip--`
5×	`distribute-lft-out--`
4×	`frac-add` `difference-of-squares`
3×	`exp-prod` `associate-l`
2×	`log-div` `sum-log` `log-pow` `rem-exp-log`
1×	`+-commutative` `flip3-+` `rem-log-exp` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

17.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
13.0ms	(* y (- (log z) t))
12.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series105.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
13.0ms	(* y (- (log z) t))
38.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

simplify65.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	657	992
1	2473	924
2	5001	894

prune200.0ms

Filtered

83 candidates to 113 candidates (-36.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	4	114

Merged error: 0.5b

Counts

114 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.0b	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.1b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate--l+`
27×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
24×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
17×	`add-cube-cbrt`
14×	`associate-+r+`
13×	`associate-r`
12×	`sub-neg` `associate-*r/`
10×	`pow1` `associate-+l+`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`flip3--` `associate-l` `flip--`
4×	`frac-add`
3×	`exp-prod`
2×	`pow-prod-down` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `rem-exp-log` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `flip3-+` `exp-sum` `flip-+`

Counts

4 → 123

Calls

4 calls:

18.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
22.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
7.0ms	(* y (- (log z) t))
21.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series182.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
20.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
16.0ms	(* y (- (log z) t))
54.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify97.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	662	1755
1	2763	1645
2	5002	1626

prune308.0ms

Filtered

87 candidates to 135 candidates (-55.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	135	4	139

Merged error: 0.0b

Counts

139 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.0b	(pow E (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.1b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate--l+`
28×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
24×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
18×	`add-cube-cbrt`
14×	`associate-+r+`
13×	`associate-r`
12×	`sub-neg` `associate-*r/`
11×	`pow1`
10×	`associate-+l+`
9×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`flip3--` `associate-l` `flip--` `add-log-exp`
4×	`frac-add`
3×	`unpow-prod-down` `pow-unpow`
2×	`pow-prod-down` `pow-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`unpow-prod-up` `+-commutative` `pow-to-exp` `e-exp-1` `pow-pow` `flip3-+` `sum-log` `flip-+` `sqr-pow`

Counts

4 → 129

Calls

4 calls:

20.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
17.0ms	(pow E (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
10.0ms	(* y (- (log z) t))
22.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
65.0ms	(pow E (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
14.0ms	(* y (- (log z) t))
251.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify85.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	717	1910
1	3066	1814
2	5002	1795

prune353.0ms

Filtered

92 candidates to 141 candidates (-53.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	142	3	145

Merged error: 0.0b

Counts

145 → 3

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* y (- (log z) t))
0.1b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.5b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

56×	`associate--l+`
36×	`log-prod`
34×	`distribute-rgt-in` `distribute-lft-in`
28×	`add-sqr-sqrt` `associate-+r+`
26×	`*-un-lft-identity`
20×	`add-cube-cbrt` `associate-+l+` `associate-*r/`
16×	`sub-neg`
12×	`associate-r`
10×	`pow1` `flip3--` `flip--`
8×	`add-exp-log` `frac-add` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
4×	`distribute-lft-out--`
2×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `flip-+` `difference-of-squares` `unswap-sqr`

Counts

4 → 144

Calls

4 calls:

7.0ms	(* y (- (log z) t))
7.0ms	(* y (- (log z) t))
21.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
21.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series135.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* y (- (log z) t))
13.0ms	(* y (- (log z) t))
55.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
53.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify65.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	507	2032
1	1982	1926
2	5001	1898

prune556.0ms

Filtered

108 candidates to 156 candidates (-44.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	156	3	159

Merged error: 0.0b

Counts

159 → 3

regimes591.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	34
1	39	34
2	39	34

end0.0ms

analyze2.3s

Algorithm

sampling

Space saved by range analysis: 0.292611%

Space saved by search: 67.502597%

Guaranteed chance to sample good point: 12.659176%

sample2.6s

Algorithm

intervals

Results

654.0ms	7240×	body	80	valid
444.0ms	4921×	body	80	invalid
415.0ms	4639×	body	80	nan
119.0ms	258×	body	640	valid
78.0ms	264×	body	320	valid
57.0ms	123×	body	640	invalid
46.0ms	51×	body	1280	valid
37.0ms	133×	body	320	invalid
37.0ms	187×	body	160	valid
18.0ms	20×	body	1280	invalid
18.0ms	98×	body	160	invalid

Details

analyze2.4s

sample89.0ms

simplify38.0ms

prune6.0ms

localize15.0ms

rewrite50.0ms

series105.0ms

simplify65.0ms

prune200.0ms

localize21.0ms

rewrite73.0ms

series182.0ms

simplify97.0ms

prune308.0ms

localize23.0ms

rewrite74.0ms

series350.0ms

simplify85.0ms

prune353.0ms

localize29.0ms

rewrite65.0ms

series135.0ms

simplify65.0ms

prune556.0ms

regimes591.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

analyze2.3s

sample2.6s

Profiling