Details

sample162.0ms

Algorithm

intervals

Results

67.0ms	1178×	body	80	nan
24.0ms	386×	body	80	valid
5.0ms	13×	body	640	valid
2.0ms	2×	body	1280	valid
1.0ms	10×	body	160	valid
1.0ms	4×	body	320	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 1.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (log (- 1.0 z)) b))
0.0b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.2b	(* y (- (log z) t))
7.0b	(log (- 1.0 z))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
48×	`prod-diff`
42×	`add-cube-cbrt`
36×	`distribute-rgt-in` `distribute-lft-in`
23×	`pow1`
21×	`log-prod`
16×	`associate--l+`
15×	`log-pow`
12×	`associate-r`
9×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`distribute-lft-out--` `add-log-exp`
6×	`associate-l`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `sub-neg` `associate-*r/` `log1p-expm1-u`
3×	`exp-prod` `flip3--` `flip--`
2×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`rem-log-exp` `exp-sum` `sum-log`

Counts

4 → 155

Calls

4 calls:

19.0ms	(* a (- (log (- 1.0 z)) b))
18.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
17.0ms	(* y (- (log z) t))
4.0ms	(log (- 1.0 z))

series319.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* a (- (log (- 1.0 z)) b))
134.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
68.0ms	(* y (- (log z) t))
44.0ms	(log (- 1.0 z))

simplify72.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	698	1526
1	2648	1102
2	5002	1091

prune416.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite644.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
96×	`prod-diff`
90×	`add-sqr-sqrt`
68×	`add-cube-cbrt`
54×	`distribute-rgt-in` `distribute-lft-in`
49×	`associate--l+`
33×	`pow1`
25×	`log-pow`
21×	`distribute-lft-out--`
15×	`log-prod`
13×	`associate-r`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`sub-neg`
6×	`associate-l`
4×	`expm1-log1p-u` `fma-neg` `associate-*r/` `log1p-expm1-u`
3×	`exp-prod` `flip3--` `flip--`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`diff-log` `exp-sum` `sum-log`

Counts

4 → 210

Calls

4 calls:

5.0ms	(- (log z) t)
501.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
112.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
16.0ms	(* y (- (log z) t))

series398.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (log z) t)
99.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
166.0ms	(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))

simplify95.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	741	3682
1	2875	2500
2	5001	2306

prune594.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

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

rewrite803.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
55×	`add-cube-cbrt`
48×	`prod-diff`
37×	`pow1`
34×	`distribute-rgt-in` `distribute-lft-in`
26×	`sqrt-pow1`
22×	`sqrt-prod`
21×	`exp-prod`
19×	`associate-r`
14×	`log-pow`
13×	`associate-l`
12×	`log-prod` `associate--l+`
10×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr`
8×	`pow1/2` `pow-prod-down` `pow-prod-up`
7×	`add-log-exp`
6×	`pow-sqr` `unswap-sqr`
5×	`exp-sum`
4×	`expm1-log1p-u` `sub-neg` `associate-*r/` `log1p-expm1-u` `distribute-lft-out--`
3×	`prod-exp` `*-commutative` `cbrt-unprod`
2×	`flip3--` `flip--` `rem-exp-log` `difference-of-squares`
1×	`pow2` `pow-plus` `sqrt-unprod` `sum-log` `rem-square-sqrt`

Counts

4 → 196

Calls

4 calls:

111.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
653.0ms	(* (sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))) (sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))
15.0ms	(* y (- (log z) t))
16.0ms	(* y (- (log z) t))

series472.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
169.0ms	(* (sqrt (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))) (sqrt (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))
71.0ms	(* y (- (log z) t))

simplify85.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	501	2834
1	2157	2212
2	5003	2083

prune769.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
12×	`associate-r`
11×	`associate-l`
10×	`add-exp-log`
9×	`add-cube-cbrt`
8×	`pow1` `add-cbrt-cube`
6×	`unpow-prod-down` `add-log-exp`
5×	`fma-udef`
4×	`expm1-log1p-u` `exp-sum` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `log-pow` `-commutative` `cbrt-unprod` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `exp-prod` `flip3--` `exp-to-pow` `pow-prod-down` `pow-exp` `flip--` `rem-exp-log` `difference-of-squares`

Counts

4 → 80

Calls

4 calls:

10.0ms	(* x (pow (exp (* 2 (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))) 1/2))
36.0ms	(* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)
1.0ms	(exp (* 2 (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))

series884.0ms

Counts

4 → 12

Calls

4 calls:

376.0ms	(* x (pow (exp (* 2 (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))) 1/2))
77.0ms	(* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)
206.0ms	(exp (* 2 (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))))
225.0ms	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

simplify51.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	413	1392
1	1466	1224
2	5002	1215

prune446.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

regimes276.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	18
1	33	18

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.3s	40856×	body	80	nan
792.0ms	12476×	body	80	valid
131.0ms	369×	body	640	valid
94.0ms	432×	body	320	valid
47.0ms	66×	body	1280	valid
37.0ms	281×	body	160	valid