Details

sample10.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 67.407227%

Guaranteed chance to sample good point: 12.659176%

Results

19.0ms	227×	body	80	valid
16.0ms	168×	body	80	nan
14.0ms	168×	body	80	invalid
4.0ms	9×	body	640	invalid
4.0ms	8×	body	640	valid
3.0ms	12×	body	320	valid
2.0ms	2×	body	1280	valid
1.0ms	7×	body	160	valid
1.0ms	4×	body	320	invalid
0.0ms	1×	body	160	invalid

simplify36.0ms

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

prune5.0ms

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: 1.5b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.1b	(* y (- (log z) t))
0.8b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.8b	(log (- 1.0 z))

rewrite37.0ms

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:

11.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
7.0ms	(* y (- (log z) t))
12.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series107.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
14.0ms	(* y (- (log z) t))
38.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

simplify66.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (56.0ms)

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

prune209.0ms

Filtered

83 candidates to 113 candidates (-36.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	6	114

Merged error: 0.3b

Counts

114 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
0.1b	(exp (+ (* 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))
0.8b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

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

series216.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
58.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
16.0ms	(* y (- (log z) t))
53.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify76.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	663	1710
1	2729	1561
2	5003	1542

prune300.0ms

Filtered

81 candidates to 116 candidates (-43.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	111	5	116
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	117	5	122

Merged error: 0.0b

Counts

122 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* y (- (log z) t))
0.8b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.8b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.8b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

72×	`associate--l+`
42×	`associate-+r+` `log-prod`
41×	`distribute-rgt-in` `distribute-lft-in`
30×	`associate-+l+`
26×	`associate-*r/`
24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
20×	`add-cube-cbrt` `sub-neg`
13×	`flip3--` `flip--`
12×	`frac-add`
10×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `associate-r` `add-cbrt-cube`
3×	`+-commutative` `flip3-+` `associate-l` `sum-log` `flip-+`
2×	`distribute-lft-out--`
1×	`pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`

Counts

4 → 150

Calls

4 calls:

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)))
24.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* 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)))
52.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
56.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify72.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	507	2686
1	1982	2563
2	5001	2533

prune1.2s

Filtered

120 candidates to 162 candidates (-35.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	163	4	167

Merged error: 0.0b

Counts

167 → 4

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))
0.8b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.8b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.8b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

66×	`associate--l+`
42×	`associate-+r+`
36×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
30×	`associate-+l+`
24×	`associate-*r/`
18×	`sub-neg`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`flip3--` `frac-add` `flip--`
10×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`+-commutative` `flip3-+` `sum-log` `flip-+`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 126

Calls

4 calls:

17.0ms	(cbrt (* x (exp (+ (* 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)))
23.0ms	(+ (* 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)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))
54.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
52.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
55.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify72.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	525	2764
1	1900	2622
2	5001	2613

prune1.2s

Filtered

113 candidates to 138 candidates (-22.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	136	6	142

Merged error: 0.0b

Counts

142 → 6

regimes700.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	53
1	36	53

end0.0ms

sample13.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 67.407227%

Guaranteed chance to sample good point: 12.659176%

Results

634.0ms	7159×	body	80	valid
425.0ms	4862×	body	80	invalid
384.0ms	4504×	body	80	nan
135.0ms	296×	body	640	valid
84.0ms	288×	body	320	valid
54.0ms	119×	body	640	invalid
54.0ms	62×	body	1280	valid
38.0ms	127×	body	320	invalid
37.0ms	195×	body	160	valid
17.0ms	96×	body	160	invalid
11.0ms	14×	body	1280	invalid

Details

sample10.3s

simplify36.0ms

prune5.0ms

localize16.0ms

rewrite37.0ms

series107.0ms

simplify66.0ms

prune209.0ms

localize24.0ms

rewrite75.0ms

series216.0ms

simplify76.0ms

prune300.0ms

localize29.0ms

rewrite81.0ms

series174.0ms

simplify72.0ms

prune1.2s

localize29.0ms

rewrite89.0ms

series305.0ms

simplify72.0ms

prune1.2s

regimes700.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample13.3s

Profiling