Details

sample233.0ms

Algorithm

intervals

Results

116.0ms	1166×	body	80	nan
41.0ms	385×	body	80	valid
5.0ms	13×	body	640	valid
3.0ms	4×	body	1280	valid
2.0ms	7×	body	320	valid
1.0ms	7×	body	160	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	31	10
1	62	10
2	137	10
3	344	10
4	1155	10
5	5001	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize17.0ms

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))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.3b	(log (- 1.0 z))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

72×	`prod-diff`
66×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
56×	`add-cube-cbrt`
53×	`distribute-rgt-in` `distribute-lft-in`
38×	`associate-+r+`
34×	`associate-+l+`
27×	`log-prod`
26×	`pow1`
22×	`associate--l+`
20×	`log-pow`
10×	`associate-*r/`
9×	`add-log-exp`
7×	`add-exp-log`
6×	`sub-neg` `flip3--` `associate-r` `add-cbrt-cube` `flip--`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u` `difference-of-squares`
3×	`exp-prod` `associate-l`
2×	`log-div` `sum-log` `rem-exp-log`
1×	`+-commutative` `fma-def` `flip3-+` `rem-log-exp` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 182

Calls

4 calls:

17.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
15.0ms	(* y (- (log z) t))
22.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series448.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
74.0ms	(* y (- (log z) t))
187.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
49.0ms	(log (- 1.0 z))

simplify95.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	904	1913
1	3501	1501
2	5001	1500

prune664.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
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)))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

120×	`prod-diff`
106×	`*-un-lft-identity`
100×	`add-sqr-sqrt`
82×	`add-cube-cbrt`
74×	`associate-+r+`
71×	`distribute-rgt-in` `distribute-lft-in`
55×	`associate--l+`
36×	`pow1`
34×	`associate-+l+`
30×	`log-pow`
21×	`log-prod`
16×	`distribute-lft-out--`
10×	`associate-*r/` `add-log-exp`
9×	`sub-neg`
8×	`difference-of-squares`
6×	`add-exp-log` `flip3--` `associate-r` `add-cbrt-cube` `flip--`
4×	`expm1-log1p-u` `fma-neg` `frac-add` `log1p-expm1-u`
3×	`exp-prod` `associate-l`
2×	`sum-log` `rem-exp-log`
1×	`+-commutative` `fma-def` `flip3-+` `diff-log` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 236

Calls

4 calls:

4.0ms	(- (log z) t)
104.0ms	(exp (+ (* 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))
166.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series543.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (log z) t)
162.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
73.0ms	(* 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)))

simplify115.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	996	3661
1	3785	2813
2	5001	2807

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
13×	`pow1`
12×	`prod-diff`
8×	`associate-l` `add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
4×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
3×	`log-prod` `exp-prod` `associate-r` `associate--l+`
2×	`flip3--` `associate-*l/` `flip--` `rem-exp-log` `distribute-lft-out` `difference-of-squares`
1×	`sub-neg` `diff-log` `exp-sum` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

30.0ms	(* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)
4.0ms	(- (log z) t)
9.0ms	(exp (+ (* y (log 1)) (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))))
0.0ms	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

series553.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)
62.0ms	(- (log z) t)
174.0ms	(exp (+ (* y (log 1)) (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))))
232.0ms	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

simplify44.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	371	1079
1	1172	879
2	5001	871

prune489.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`pow1`
12×	`add-exp-log` `prod-diff`
11×	`associate-r` `associate-l`
8×	`add-cbrt-cube`
7×	`log-pow`
6×	`distribute-lft-out--`
5×	`prod-exp` `add-log-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `fma-neg` `log1p-expm1-u` `unswap-sqr`
3×	`log-prod` `associate--l+`
2×	`flip3--` `associate-l/` `pow-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out` `difference-of-squares` `sqr-pow`
1×	`unpow-prod-up` `pow-to-exp` `sub-neg` `e-exp-1` `diff-log` `pow-prod-down` `fma-udef`

Counts

4 → 102

Calls

4 calls:

34.0ms	(* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)
6.0ms	(* x (pow E (+ (* y (log 1)) (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))))
4.0ms	(- (log z) t)
0.0ms	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

series611.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)
243.0ms	(* x (pow E (+ (* y (log 1)) (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))))
63.0ms	(- (log z) t)
227.0ms	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

simplify63.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	493	1409
1	1810	1190
2	5003	1173

prune514.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

regimes196.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	38
1	42	38

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.0s	41070×	body	80	nan
1.4s	12621×	body	80	valid
151.0ms	363×	body	640	valid
105.0ms	384×	body	320	valid
49.0ms	262×	body	160	valid
41.0ms	53×	body	1280	valid