Details

sample166.0ms

Algorithm

intervals

Results

68.0ms	1153×	body	80	nan
24.0ms	376×	body	80	valid
5.0ms	12×	body	640	valid
3.0ms	13×	body	320	valid
2.0ms	2×	body	1280	valid
1.0ms	9×	body	160	valid

simplify39.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.2b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
7.5b	(log (- 1.0 z))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

84×	`prod-diff`
76×	`add-sqr-sqrt` `*-un-lft-identity`
64×	`add-cube-cbrt`
53×	`distribute-rgt-in` `distribute-lft-in`
38×	`associate-+r+`
34×	`associate-+l+`
31×	`pow1`
30×	`log-prod`
25×	`associate--l+` `log-pow`
10×	`associate-*r/`
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×	`expm1-log1p-u` `fma-neg` `frac-add` `log1p-expm1-u`
3×	`associate-l`
2×	`log-div`
1×	`+-commutative` `fma-def` `flip3-+` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 203

Calls

4 calls:

4.0ms	(- (log z) t)
16.0ms	(* y (- (log z) t))
23.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series357.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (log z) t)
71.0ms	(* y (- (log z) t))
182.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
47.0ms	(log (- 1.0 z))

simplify97.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	856	1981
1	3296	1486
2	5002	1485

prune664.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite315.0ms

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:

107.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
4.0ms	(- (log z) t)
15.0ms	(* y (- (log z) t))
171.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series537.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
62.0ms	(- (log z) t)
71.0ms	(* y (- (log z) t))
236.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify112.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (81.0ms)

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

prune988.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`log-prod`
11×	`pow1` `associate-l`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-r`
6×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--`
3×	`exp-prod` `log-pow`
2×	`pow-prod-down` `associate-l/` `prod-exp` `sum-log` `-commutative` `cbrt-unprod` `rem-exp-log` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `flip3--` `fma-def` `flip3-+` `exp-sum` `flip--` `flip-+` `fma-udef` `difference-of-squares`

Counts

4 → 90

Calls

4 calls:

32.0ms	(* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)
9.0ms	(exp (+ (* y (log z)) (fma (- t) y (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))))
4.0ms	(+ (* y (log z)) (fma (- t) y (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))
4.0ms	(* y (log z))

series551.0ms

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)
192.0ms	(exp (+ (* y (log z)) (fma (- t) y (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))))
243.0ms	(+ (* y (log z)) (fma (- t) y (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))
38.0ms	(* y (log z))

simplify54.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	405	1143
1	1464	1023
2	5001	1014

prune477.0ms

Pruning

3 alts after pruning (2 fresh and 1 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	(+ (* y (log z)) (fma (- t) y (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))
0.0b	(pow E (+ (* y (log z)) (fma (- t) y (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))))
0.3b	(* y (log z))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`pow1` `log-prod`
11×	`associate-l`
9×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`associate-r`
6×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--`
3×	`unpow-prod-down` `pow-unpow` `log-pow`
2×	`pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
1×	`unpow-prod-up` `+-commutative` `pow-to-exp` `e-exp-1` `associate-+r+` `flip3--` `pow-pow` `fma-def` `flip3-+` `sum-log` `flip--` `flip-+` `fma-udef` `difference-of-squares` `sqr-pow`

Counts

4 → 96

Calls

4 calls:

32.0ms	(* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)
4.0ms	(+ (* y (log z)) (fma (- t) y (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))
3.0ms	(pow E (+ (* y (log z)) (fma (- t) y (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))))
8.0ms	(* y (log z))

series561.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)
240.0ms	(+ (* y (log z)) (fma (- t) y (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))
201.0ms	(pow E (+ (* y (log z)) (fma (- t) y (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))))
36.0ms	(* y (log z))

simplify56.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	460	1295
1	1750	1190
2	5001	1178

prune496.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes180.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	16
1	31	16

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.3s	40944×	body	80	nan
812.0ms	12492×	body	80	valid
143.0ms	390×	body	640	valid
93.0ms	411×	body	320	valid
50.0ms	68×	body	1280	valid
40.0ms	287×	body	160	valid