Details

sample197.0ms

Algorithm

intervals

Results

102.0ms	1742×	body	80	nan
17.0ms	256×	body	80	valid

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	61	8
2	161	8
3	393	8
4	984	8
5	2256	8
6	4095	8
7	5001	8

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (log (+ x y)) (log z)) t)
0.1b	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
0.1b	(* (- a 0.5) (log t))
0.6b	(+ (log (+ x y)) (log z))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

91×	`*-un-lft-identity`
48×	`pow1`
43×	`add-sqr-sqrt`
42×	`prod-diff` `log-pow`
41×	`distribute-lft-out`
35×	`add-cube-cbrt`
28×	`associate-+l+`
19×	`log-prod`
14×	`add-log-exp`
13×	`fma-def`
11×	`distribute-lft-out--`
9×	`associate-+r+`
7×	`fma-neg`
6×	`add-exp-log` `distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-*l/` `sum-log` `add-cbrt-cube` `flip--`
5×	`associate-+l-` `associate-l`
4×	`expm1-log1p-u` `log-div` `flip3-+` `diff-log` `associate-r` `frac-add` `flip-+` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`+-commutative` `associate--l-` `sub-neg` `associate--l+`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 172

Calls

4 calls:

36.0ms	(- (+ (log (+ x y)) (log z)) t)
119.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
13.0ms	(* (- a 0.5) (log t))
12.0ms	(+ (log (+ x y)) (log z))

series494.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(- (+ (log (+ x y)) (log z)) t)
197.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
57.0ms	(* (- a 0.5) (log t))
76.0ms	(+ (log (+ x y)) (log z))

simplify79.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	706	1592
1	2722	1253
2	5001	1237

prune492.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.1b	(+ (+ (log (+ x y)) (- (log z) t)) (* (- a 0.5) (log t)))
0.1b	(* (- a 0.5) (log t))
0.2b	(+ (log (+ x y)) (- (log z) t))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
36×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
26×	`pow1`
24×	`prod-diff`
23×	`associate-+r+`
22×	`log-prod`
20×	`log-pow`
13×	`fma-def` `distribute-lft-out` `add-log-exp`
11×	`distribute-lft-out--`
7×	`associate-+l-` `sum-log`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `associate-*l/` `associate--l+` `add-cbrt-cube` `flip-+`
5×	`associate-+l+` `associate-l`
4×	`expm1-log1p-u` `log-div` `flip3--` `fma-neg` `associate-r` `frac-add` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`+-commutative` `associate-+r-` `sub-neg` `difference-of-squares`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 153

Calls

4 calls:

5.0ms	(- (log z) t)
75.0ms	(+ (+ (log (+ x y)) (- (log z) t)) (* (- a 0.5) (log t)))
11.0ms	(* (- a 0.5) (log t))
14.0ms	(+ (log (+ x y)) (- (log z) t))

series490.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (log z) t)
196.0ms	(+ (+ (log (+ x y)) (- (log z) t)) (* (- a 0.5) (log t)))
56.0ms	(* (- a 0.5) (log t))
174.0ms	(+ (log (+ x y)) (- (log z) t))

simplify77.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	736	1290
1	2722	1080
2	5002	1060

prune547.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (- (log z) t))) (* (- a 0.5) (log t)))
0.1b	(* (- a 0.5) (log t))
0.2b	(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (- (log z) t)))
0.2b	(+ (log (sqrt (+ x y))) (- (log z) t))

rewrite352.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
60×	`distribute-lft-out`
53×	`pow1`
49×	`log-pow`
29×	`add-sqr-sqrt` `log-prod` `fma-def`
25×	`add-cube-cbrt`
24×	`associate-+r+`
21×	`distribute-lft-out--`
17×	`add-log-exp`
16×	`sum-log`
15×	`associate-+l-` `associate-+l+`
12×	`prod-diff`
10×	`log-div` `flip3-+` `sqrt-div` `flip-+`
9×	`associate-+r-`
8×	`sqrt-prod`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `associate-*l/` `add-cbrt-cube`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `frac-add` `log1p-expm1-u`
3×	`+-commutative` `flip3--` `diff-log` `associate--l+` `flip--`
2×	`sqrt-pow1` `pow1/2`
1×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`

Counts

4 → 181

Calls

4 calls:

274.0ms	(+ (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (- (log z) t))) (* (- a 0.5) (log t)))
11.0ms	(* (- a 0.5) (log t))
40.0ms	(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (- (log z) t)))
19.0ms	(+ (log (sqrt (+ x y))) (- (log z) t))

series646.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(+ (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (- (log z) t))) (* (- a 0.5) (log t)))
53.0ms	(* (- a 0.5) (log t))
163.0ms	(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (- (log z) t)))
142.0ms	(+ (log (sqrt (+ x y))) (- (log z) t))

simplify93.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	859	1845
1	3084	1592
2	5002	1514

prune609.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt t) (cbrt t))
0.6b	(cbrt t)
0.6b	(cbrt t)
0.6b	(cbrt t)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt t) (cbrt t))
0.0ms	(cbrt t)
0.0ms	(cbrt t)
1.0ms	(cbrt t)

series749.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(* (cbrt t) (cbrt t))
183.0ms	(cbrt t)
186.0ms	(cbrt t)
185.0ms	(cbrt t)

simplify86.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	119	308
1	477	281
2	2972	258
3	5001	255

prune459.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes578.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	14
1	22	14

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.7s	56057×	body	80	nan
462.0ms	8029×	body	80	valid