Details

sample174.0ms

Algorithm

intervals

Results

70.0ms	1227×	body	80	nan
25.0ms	404×	body	80	valid
5.0ms	14×	body	640	valid
4.0ms	5×	body	1280	valid
2.0ms	16×	body	160	valid
1.0ms	5×	body	320	valid

simplify39.0ms

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: 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))))
0.2b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.6b	(log (- 1.0 z))

rewrite39.0ms

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:

12.0ms	(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)))
4.0ms	(log (- 1.0 z))

series448.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
69.0ms	(* y (- (log z) t))
192.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
42.0ms	(log (- 1.0 z))

simplify67.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (56.0ms)

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

prune360.0ms

Filtered

113 candidates to 84 candidates (74.3%)

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: 0.0b

Counts

114 → 4

localize22.0ms

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))
0.3b	(+ (* 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:

25.0ms	(* 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))
21.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series679.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
162.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
68.0ms	(* y (- (log z) t))
231.0ms	(+ (* 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

116 → 116

Iterations

Useful iterations: 2 (64.0ms)

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

prune487.0ms

Filtered

116 candidates to 83 candidates (71.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	115	5	120

Merged error: 0.0b

Counts

120 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (pow E (+ (* y (- (log z) t)) (* 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))))
0.2b	(* 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)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

16.0ms	(* x (pow E (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
16.0ms	(pow E (+ (* 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))
26.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series715.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(* x (pow E (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
165.0ms	(pow E (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
74.0ms	(* 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)))

simplify88.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	714	1997
1	3146	1883
2	5001	1874

prune525.0ms

Filtered

130 candidates to 92 candidates (70.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	130	5	135

Merged error: 0.0b

Counts

135 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y (- (log z) t))
0.2b	(log (exp (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.6b	(log (- 1.0 z))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

7.0ms	(* y (- (log z) t))
6.0ms	(log (exp (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))
12.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms	(log (- 1.0 z))

series436.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* y (- (log z) t))
133.0ms	(log (exp (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))
185.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
47.0ms	(log (- 1.0 z))

simplify70.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	645	1055
1	2448	977
2	5002	965

prune409.0ms

Filtered

116 candidates to 88 candidates (75.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	117	4	121

Merged error: 0.0b

Counts

121 → 4

regimes209.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	16
1	37	16
2	37	16

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.3s	41085×	body	80	nan
777.0ms	12535×	body	80	valid
122.0ms	354×	body	640	valid
82.0ms	380×	body	320	valid
48.0ms	66×	body	1280	valid
39.0ms	286×	body	160	valid