Details

sample214.0ms

Algorithm

intervals

Results

100.0ms	1371×	body	80	nan
32.0ms	411×	body	80	valid
3.0ms	7×	body	640	valid
3.0ms	3×	body	1280	valid
2.0ms	14×	body	160	valid
2.0ms	8×	body	320	valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 1.3b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
7.2b	(log (- 1.0 z))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

4.0ms	(- (log z) t)
7.0ms	(* y (- (log z) t))
12.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series366.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (log z) t)
74.0ms	(* y (- (log z) t))
187.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
47.0ms	(log (- 1.0 z))

simplify70.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	593	882
1	2248	832
2	5001	830

prune362.0ms

Filtered

118 candidates to 85 candidates (72.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	117	2	119

Merged error: 0.3b

Counts

119 → 2

localize28.0ms

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)))))
0.0b	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

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)))))
18.0ms	(* 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)))

series649.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
106.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
75.0ms	(* y (- (log z) t))
245.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify96.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	677	1907
1	3019	1768
2	5001	1757

prune541.0ms

Filtered

141 candidates to 94 candidates (66.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	137	4	141
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	138	5	143

Merged error: 0.0b

Counts

143 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* y (- (log z) t))
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.3b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite66.0ms

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)))
25.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series626.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* y (- (log z) t))
72.0ms	(* y (- (log z) t))
238.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
242.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify69.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	494	2014
1	2047	1920
2	5003	1910

prune816.0ms

Filtered

156 candidates to 110 candidates (70.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	156	5	161

Merged error: 0.0b

Counts

161 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* y (- (log z) t))
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.3b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite64.0ms

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))
24.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
20.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series820.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* y (- (log z) t))
72.0ms	(* y (- (log z) t))
237.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
436.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify74.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	494	2014
1	2047	1920
2	5003	1910

prune810.0ms

Filtered

156 candidates to 110 candidates (70.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	156	5	161

Merged error: 0.0b

Counts

161 → 5

regimes358.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	34
1	35	34

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.9s	41072×	body	80	nan
995.0ms	12544×	body	80	valid
150.0ms	360×	body	640	valid
107.0ms	407×	body	320	valid
59.0ms	76×	body	1280	valid
42.0ms	257×	body	160	valid