Details

sample187.0ms

Algorithm

intervals

Results

75.0ms	1179×	body	80	nan
27.0ms	411×	body	80	valid
4.0ms	4×	body	1280	valid
3.0ms	8×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	8×	body	160	valid

simplify37.0ms

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

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: 2.2b

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))))
0.2b	(* y (- (log z) t))
0.8b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.6b	(log (- 1.0 z))

rewrite34.0ms

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:

8.0ms	(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))

series618.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
70.0ms	(* y (- (log z) t))
354.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
46.0ms	(log (- 1.0 z))

simplify69.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	630	971
1	2443	914
2	5001	902

prune354.0ms

Filtered

113 candidates to 84 candidates (74.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	3	114

Merged error: 0.7b

Counts

114 → 3

localize27.0ms

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

rewrite69.0ms

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:

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

series740.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
196.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
71.0ms	(* y (- (log z) t))
239.0ms	(+ (* 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 (60.0ms)

Iter	Nodes	Cost
0	646	1698
1	2787	1557
2	5003	1544

prune447.0ms

Filtered

116 candidates to 82 candidates (70.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	114	5	119

Merged error: 0b

Counts

119 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate--l+`
28×	`associate-+r+`
24×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
20×	`associate-+l+`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `-un-lft-identity` `associate-r/`
12×	`sub-neg`
8×	`flip3--` `sqrt-pow1` `frac-add` `sqrt-prod` `flip--` `add-log-exp`
6×	`pow1` `exp-prod`
4×	`add-exp-log` `add-cbrt-cube`
2×	`+-commutative` `rem-sqrt-square` `flip3-+` `pow1/2` `exp-sum` `sum-log` `flip-+`

Counts

4 → 112

Calls

4 calls:

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

series1.0s

Counts

4 → 12

Calls

4 calls:

270.0ms	(sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
283.0ms	(sqrt (exp (+ (* 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)))
239.0ms	(+ (* 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

124 → 124

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	487	2362
1	1774	2262
2	5003	2252

prune698.0ms

Filtered

124 candidates to 102 candidates (82.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	124	5	129

Merged error: 0b

Counts

129 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt z)
0.7b	(cbrt z)
0.8b	(+ (+ (* y (* 2 (log (cbrt z)))) (* y (- (log (cbrt z)) t))) (* a (- (log (- 1.0 z)) b)))
5.6b	(log (- 1.0 z))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

1.0ms	(cbrt z)
1.0ms	(cbrt z)
16.0ms	(+ (+ (* y (* 2 (log (cbrt z)))) (* y (- (log (cbrt z)) t))) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series699.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt z)
185.0ms	(cbrt z)
292.0ms	(+ (+ (* y (* 2 (log (cbrt z)))) (* y (- (log (cbrt z)) t))) (* a (- (log (- 1.0 z)) b)))
42.0ms	(log (- 1.0 z))

simplify62.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	552	963
1	1996	921
2	5003	917

prune338.0ms

Filtered

81 candidates to 67 candidates (82.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	81	5	86

Merged error: 0b

Counts

86 → 5

regimes221.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	34
1	35	34

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.3s	40715×	body	80	nan
792.0ms	12598×	body	80	valid
133.0ms	382×	body	640	valid
82.0ms	385×	body	320	valid
48.0ms	66×	body	1280	valid
36.0ms	271×	body	160	valid