Details

sample271.0ms

Algorithm

intervals

Results

138.0ms	1330×	body	80	nan
52.0ms	426×	body	80	valid
4.0ms	9×	body	640	valid
3.0ms	4×	body	1280	valid
2.0ms	11×	body	160	valid
2.0ms	6×	body	320	valid

simplify39.0ms

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: 1.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
0.0b	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
0.2b	(* y (- (log z) t))
6.8b	(log (- 1.0 z))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 188

Calls

4 calls:

23.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
51.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
15.0ms	(* y (- (log z) t))
3.0ms	(log (- 1.0 z))

series465.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
158.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
74.0ms	(* y (- (log z) t))
43.0ms	(log (- 1.0 z))

simplify103.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	947	2029
1	3790	1591
2	5001	1590

prune668.0ms

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

rewrite862.0ms

Algorithm

rewrite-expression-head

Rules

150×	`add-sqr-sqrt`
122×	`*-un-lft-identity`
94×	`add-cube-cbrt`
85×	`associate-r`
84×	`prod-diff`
80×	`times-frac`
56×	`unpow-prod-down`
54×	`distribute-rgt-in` `distribute-lft-in`
46×	`associate--l+`
32×	`pow1` `add-exp-log`
24×	`unpow2` `sqr-pow`
20×	`log-pow` `unswap-sqr`
19×	`distribute-lft-out--`
15×	`add-cbrt-cube`
13×	`prod-exp`
12×	`log-prod` `associate-l`
9×	`div-exp`
8×	`difference-of-squares`
6×	`pow-to-exp` `sub-neg` `pow-exp`
5×	`associate-*r/` `cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `*-commutative` `log1p-expm1-u` `add-log-exp`
2×	`flip3--` `flip--`
1×	`cbrt-undiv` `exp-sum` `div-inv`

Counts

4 → 292

Calls

4 calls:

27.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
314.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
489.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
16.0ms	(* y (- (log z) t))

series473.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
235.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
107.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
74.0ms	(* y (- (log z) t))

simplify66.0ms

Algorithm

egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1240	4245
1	5001	3020

prune927.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 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))
0.2b	(* y (- (log z) t))

rewrite545.0ms

Algorithm

rewrite-expression-head

Rules

132×	`prod-diff`
128×	`*-un-lft-identity`
122×	`add-sqr-sqrt`
94×	`add-cube-cbrt`
88×	`distribute-rgt-in` `distribute-lft-in`
58×	`associate--l+`
46×	`pow1`
34×	`log-pow`
25×	`associate-r`
24×	`log-prod`
23×	`distribute-lft-out--`
12×	`add-exp-log` `associate-l` `add-cbrt-cube`
10×	`sub-neg` `difference-of-squares`
8×	`associate-*r/`
4×	`expm1-log1p-u` `flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

4 → 277

Calls

4 calls:

483.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
18.0ms	(* y (- (log z) t))
15.0ms	(* y (- (log z) t))
15.0ms	(* y (- (log z) t))

series326.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
68.0ms	(* y (- (log z) t))
73.0ms	(* y (- (log z) t))
75.0ms	(* y (- (log z) t))

simplify88.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	623	4256
1	2409	2819
2	5001	2614

prune871.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite937.0ms

Algorithm

rewrite-expression-head

Rules

193×	`add-sqr-sqrt`
173×	`*-un-lft-identity`
158×	`associate-r`
144×	`prod-diff`
127×	`add-cube-cbrt`
91×	`distribute-rgt-in` `distribute-lft-in`
86×	`associate--l+`
80×	`times-frac`
74×	`exp-sum`
56×	`unpow-prod-down`
47×	`pow1`
33×	`add-exp-log`
32×	`log-pow`
31×	`distribute-lft-out--`
24×	`unpow2` `sqr-pow`
19×	`unswap-sqr`
18×	`log-prod` `add-cbrt-cube`
15×	`prod-exp`
14×	`difference-of-squares`
10×	`sub-neg` `associate-l`
9×	`div-exp`
7×	`cbrt-unprod`
6×	`pow-to-exp` `pow-prod-down` `pow-exp`
5×	`associate-*r/`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
2×	`flip3--` `flip--`
1×	`cbrt-undiv` `div-inv`

Counts

4 → 365

Calls

4 calls:

28.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
480.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
15.0ms	(* y (- (log z) t))
390.0ms	(* (* x (exp (* y (- (log z) t)))) (exp (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))

series540.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
108.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
74.0ms	(* y (- (log z) t))
301.0ms	(* (* x (exp (* y (- (log z) t)))) (exp (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))

simplify88.0ms

Algorithm

egg-herbie

Counts

377 → 377

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1621	6087
1	5001	4412

prune1.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes144.0ms

Accuracy

0% (0.0b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	51
1	36	51

end0.0ms

sample8.3s

Algorithm

intervals

Results

4.4s	42043×	body	80	nan
1.6s	12673×	body	80	valid
176.0ms	379×	body	640	valid
126.0ms	401×	body	320	valid
52.0ms	62×	body	1280	valid
48.0ms	225×	body	160	valid